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Literal.String.Double */ <br \>.highlight .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */ <br \>.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */ <br \>.highlight .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */ <br \>.highlight .sx { color: #008000 } /* Literal.String.Other */ <br \>.highlight .sr { color: #BB6688 } /* Literal.String.Regex */ <br \>.highlight .s1 { color: #BA2121 } /* Literal.String.Single */ <br \>.highlight .ss { color: #19177C } /* Literal.String.Symbol */ <br \>.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */ <br \>.highlight .vc { color: #19177C } /* Name.Variable.Class */ <br \>.highlight .vg { color: #19177C } /* Name.Variable.Global */ <br \>.highlight .vi { color: #19177C } /* Name.Variable.Instance */ <br \>.highlight .il { color: #666666 } /* Literal.Number.Integer.Long */ <br \> </style> <br \> <br \> <br \><style type="text/css"> <br \>/* Overrides of notebook CSS for static HTML export */ <br \>body { <br \> overflow: visible; <br \> padding: 8px; <br \>} <br \> <br \>div#notebook { <br \> overflow: visible; <br \> border-top: none; <br \>} <br \> <br \>@media print { <br \> div.cell { <br \> display: block; <br \> page-break-inside: avoid; <br \> } <br \> div.output_wrapper { <br \> display: block; <br \> page-break-inside: avoid; <br \> } <br \> div.output { <br \> display: block; <br \> page-break-inside: avoid; <br \> } <br \>} <br \></style> <br \> <br \><p>Polar codes are easily the most significant recent development in the areas of coding and information theory research. A wide variety of applications have been proposed for polar codes mainly due to their capacity achieving property for many different communication channels.</p> <br \><p>In this post, we explore the trends in research publications on the topic of polar codes in their brief but exciting history.</p> <br \><p>This post also serves as a tutorial in exploratory data analysis using Python and Pandas along with Matplotlib for plotting.</p> <br \> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="o">%</span><span class="k">matplotlib</span> inline <br \> <br \><span class="kn">import</span> <span class="nn">matplotlib</span> <br \><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span> <br \><span class="n">matplotlib</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s">&#39;ggplot&#39;</span><span class="p">)</span> <br \> <br \><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span> <br \><span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span> <br \><span class="kn">import</span> <span class="nn">re</span> <br \> <br \><span class="c"># Make the graphs a bit prettier, and bigger</span> <br \><span class="n">pd</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s">&#39;display.mpl_style&#39;</span><span class="p">,</span> <span class="s">&#39;default&#39;</span><span class="p">)</span> <br \> <br \><span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">&#39;font.size&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="mf">14.0</span> <br \><span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">&#39;font.sans-serif&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s">&#39;Avant Garde&#39;</span> <br \><span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">&#39;xtick.labelsize&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s">&#39;large&#39;</span> <br \><span class="n">matplotlib</span><span class="o">.</span><span class="n">rcParams</span><span class="p">[</span><span class="s">&#39;ytick.labelsize&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="s">&#39;large&#39;</span> <br \> <br \><span class="c"># Other Pandas options</span> <br \><span class="n">pd</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s">&#39;display.width&#39;</span><span class="p">,</span> <span class="mi">5000</span><span class="p">)</span> <br \><span class="n">pd</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s">&#39;display.max_columns&#39;</span><span class="p">,</span> <span class="mi">60</span><span class="p">)</span> <br \><span class="n">pd</span><span class="o">.</span><span class="n">options</span><span class="o">.</span><span class="n">mode</span><span class="o">.</span><span class="n">chained_assignment</span> <span class="o">=</span> <span class="bp">None</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \></div> <br \> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><h2 id="Data-Collection-and-Cleaning">Data Collection and Cleaning<a class="anchor-link" href="#Data-Collection-and-Cleaning">&#182;</a></h2> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>For our analysis, it is sufficient to work with research publication citation data which is available from IEEE Xplore. We download the data using two search strings "polar codes" and "channel polarization".</p> <br \> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="c"># Read raw data from IEEE Xplore using search strings </span> <br \><span class="c"># &#39;polar codes&#39; and &#39;channel polarization&#39;</span> <br \><span class="n">pcdf1</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s">&#39;ieee_data/polar_codes_export2015.08.29-15.43.27.csv&#39;</span><span class="p">,</span> <span class="p">skiprows</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <br \><span class="n">pcdf2</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s">&#39;ieee_data/channel_polarization_export2015.08.29-15.55.28.csv&#39;</span><span class="p">,</span><span class="p">skiprows</span> <span class="o">=</span> <span class="mi">1</span><span class="p">)</span> <br \> <br \><span class="c"># Merge the two data frames</span> <br \><span class="n">pcdf</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span><span class="n">pcdf1</span><span class="p">,</span> <span class="n">pcdf2</span><span class="p">],</span> <span class="n">ignore_index</span> <span class="o">=</span> <span class="bp">True</span><span class="p">)</span> <br \> <br \><span class="c"># Rename columns to remove spaces in column names</span> <br \><span class="n">pcdf</span><span class="o">.</span><span class="n">rename</span><span class="p">(</span><span class="n">columns</span><span class="o">=</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s">&#39; &#39;</span><span class="p">,</span> <span class="s">&#39;_&#39;</span><span class="p">),</span> <span class="n">inplace</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span> <br \> <br \><span class="c"># Remove duplicate rows from the merged data frame</span> <br \><span class="n">pcdf</span> <span class="o">=</span> <span class="n">pcdf</span><span class="o">.</span><span class="n">drop_duplicates</span><span class="p">()</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \></div> <br \> <br \> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>However, the set of publications obtained is not entirely clean and there are some papers with the word "polarization" in their titles or abstracts that show up in our dataset but are not related to polar codes. We can clean them up using regular expression based filtering as follows. We also know that polar codes were invented in the year 2008 and hence can safely eliminate any papers with a publication date earlier than 2008.</p> <br \> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="c"># Construct a regex string to filter entries in the data frame</span> <br \><span class="c"># not related to polar codes</span> <br \><span class="n">polar_codes_regex_str</span> <span class="o">=</span> <span class="p">(</span><span class="s">&#39;([pP]olar [cC]odes)|([cC]hannel [pP]olarization)|&#39;</span><span class="s">&#39;[rR]ate.*[pP]olarization|[pP]olarized.*[cC]hannels|&#39;</span><span class="s">&#39;[cC]hannels.*[pP]olarized&#39;</span><span class="p">)</span> <br \><span class="n">relevant_titles</span> <span class="o">=</span> <span class="n">pcdf</span><span class="o">.</span><span class="n">Document_Title</span><span class="o">.</span><span class="n">str</span><span class="o">.</span><span class="n">contains</span><span class="p">(</span><span class="n">polar_codes_regex_str</span><span class="p">,</span> <span class="n">flags</span><span class="o">=</span><span class="n">re</span><span class="o">.</span><span class="n">IGNORECASE</span><span class="p">,</span> <span class="n">regex</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">na</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span> <br \><span class="n">pcdf</span> <span class="o">=</span> <span class="n">pcdf</span><span class="p">[</span><span class="n">relevant_titles</span><span class="p">]</span> <br \> <br \><span class="c"># Remove entries from earlier than 2008 as we know </span> <br \><span class="c"># polar codes were invented in 2008.</span> <br \><span class="n">pcdf</span> <span class="o">=</span> <span class="n">pcdf</span><span class="p">[</span><span class="n">pcdf</span><span class="p">[</span><span class="s">&#39;Year&#39;</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="mi">2008</span><span class="p">]</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \></div> <br \> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><h2 id="Exploratory-Data-Analysis">Exploratory Data Analysis<a class="anchor-link" href="#Exploratory-Data-Analysis">&#182;</a></h2> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>As a first step, we can simply look at the total number of papers published on polar codes in every year as follows.</p> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="c"># Study the total number of &#39;polar code&#39; publications with years </span> <br \><span class="n">pub_counts_per_year</span> <span class="o">=</span> <span class="n">pcdf</span><span class="p">[</span><span class="s">&#39;Year&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">(</span><span class="n">sort</span> <span class="o">=</span> <span class="bp">False</span><span class="p">)</span> <br \> <br \><span class="n">fig_1</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">[</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <br \><span class="n">pub_counts_per_year</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kind</span><span class="o">=</span><span class="s">&#39;bar&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">&#39;Year&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">&#39;Number of Publications&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">&quot;Total Publications on Polar Codes&quot;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> <br \></pre></div> <br \> 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\>OzLY1NSkffv26ciRIzp58qRGjRqlwsJCZWVlha07cOCANm/erA0bNui5557TkSNH5Ha7tXjxYt10 <br \>000R+d4BAPbAc/4AAPi3YDCoH/zgB8rOzlZcXJxqamq0ceNGuVyu0P5HH31Ubrdb+fn5cjqd2rFj <br \>h3p7e1VWVhb2tXbu3KmYmBiNHz9evb29eumll9Tc3Kxnn31WsbGxoXUHDhzQpk2bNHr0aOXm5io7 <br \>O1vNzc3Kzc0NvS4AAJcCR/4AAPi3qKgoFRQU6Nlnn5XT6dS8efPCBrCGhgb5fD797Gc/k9N59r/Q <br \>ZcuWadGiRWpsbFRmZmZo7ezZs8O+9n333aeioiK99957GjNmTNi+3t5eTZs2TdOnT5ckjR49+nJ9 <br \>iwAAG2P4AwDgI6ZMmaLdu3fr9OnT+tKXvhS27x//+Ie6u7v1zW9+M2x7f3+/fD5f2PB3zuDgoE6d <br \>OqWenh5J0qlTp85b43K5QoMfAACXC8MfAAAfk5aWpkAgoKio8PuidXV1KSMjQ9///vfP+5yPX/PX <br \>1tamnTt3qqGhQS6XS9dee62ks8PgxzkcjkuYHgCAoTH8AQDwMYODg0MOaYmJiTpx4oSSkpIuOrD1 <br \>9PTo8ccfV1ZWlp555hkNHz5cklRQUHDZMgMA8El41AMAAEMYari75ZZbdOrUKf3xj3+86Oe2tLTo <br \>X//6l+bOnRsa/I4dO3ZZcgIA8N/iyB8AAEMY6sjfuHHj9PnPf16bNm3SmTNnlJWVpUAgoKNHjyo/ <br \>Pz+0LikpSS6XS6+++qqmTZumf/7zn9q7d69cLpf6+voi+W0AABDC8AcAwMc4HI4LntZZXFysl19+ <br \>WXv27FFVVZXi4+N14403qqenJ/QIB7fbreLiYlVVVammpkZZWVl68MEH9eSTT+rDDz8c8vUAALjc <br \>eM4fAAAAANgA1/wBAAAAgA0w/AEAAACADTD8AQAAAIANMPwBAAAAgA0w/AEAAACADTD8AQAAAIAN <br \>MPwBAAAAgA0w/AEAAACADTD8AQAAAIAN/A+nWdtCzJi2fQAAAABJRU5ErkJggg== <br \>" <br \>> <br \></div> <br \> <br \></div> <br \> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>From the plot above, it very exciting to see that polar code research has been growing steadily since 2012 with the last year of 2014 recording well over 70 publications. <br \>The number of publications in 2015 seems a bit low however, the publications from recent conferences in 2015 such as ISIT and ICC are yet to appear on IEEE Xplore.</p> <br \><p>Next we look at the type of publications in our dataset.</p> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="c"># Study the publication counts grouped by IEEE Conference or IEEE Journal </span> <br \><span class="n">unique_document_ids</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">pcdf</span><span class="o">.</span><span class="n">Document_Identifier</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <br \><span class="k">print</span> <span class="n">unique_document_ids</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="output_wrapper"> <br \><div class="output"> <br \> <br \> <br \><div class="output_area"> <br \><div class="output_subarea output_stream output_stdout output_text"> <br \><pre>[&apos;IEEE Conference Publications&apos; &apos;IEEE Journals &amp; Magazines&apos; <br \> &apos;IEEE Early Access Articles&apos; &apos;VDE Conference Publications&apos; <br \> &apos;IET Journals &amp; Magazines&apos;] <br \></pre> <br \></div> <br \></div> <br \> <br \></div> <br \></div> <br \> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>In our analysis, we want to focus on IEEE Conference or Journal publications. We look at the total number of IEEE Conference and IEEE Journal publications in every year as follows.</p> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="n">pcdf_grouped</span> <span class="o">=</span> <span class="n">pcdf</span><span class="o">.</span><span class="n">groupby</span><span class="p">(</span><span class="s">&#39;Document_Identifier&#39;</span><span class="p">)</span> <br \><span class="n">pub_counts_per_year_2</span> <span class="o">=</span> <span class="n">pcdf_grouped</span><span class="p">[</span><span class="s">&#39;Year&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">(</span><span class="n">sort</span> <span class="o">=</span> <span class="bp">False</span><span class="p">)</span> <br \><span class="n">pub_counts_per_year_conf</span> <span class="o">=</span> <span class="n">pub_counts_per_year_2</span><span class="p">[</span><span class="s">&#39;IEEE Conference Publications&#39;</span><span class="p">]</span> <br \><span class="n">pub_counts_per_year_journal</span> <span class="o">=</span> <span class="n">pub_counts_per_year_2</span><span class="p">[</span><span class="s">&#39;IEEE Journals &amp; Magazines&#39;</span><span class="p">]</span> <br \> <br \><span class="n">fig_2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">[</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <br \> <br \><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span> <br \><span class="n">pub_counts_per_year_conf</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kind</span><span class="o">=</span><span class="s">&#39;bar&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">])</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">&#39;Year&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">&#39;Number of Publications&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">&#39;IEEE Conferences&#39;</span><span class="p">)</span> <br \> <br \><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span> <br \><span class="n">pub_counts_per_year_journal</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">kind</span><span class="o">=</span><span class="s">&#39;bar&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">])</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">&#39;Year&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">&#39;IEEE Journals&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="output_wrapper"> <br \><div class="output"> <br \> <br \> <br \><div class="output_area"> <br \> <br \> <br \><div class="output_png output_subarea "> <br \><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA38AAAF4CAYAAADkLUAeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz <br \>AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlclOX+//H3jAQjm7iQgBBobmhauKZ20urkltrJTCvL <br \>EqNyyToezaxjSuaemqUtJ08mlv7MU1qaxxZL+2a5ZmqZmRpu4B6yhQjcvz/6Ot8IRm9hbmZGXs/H <br \>w0fOPddc93sG8sOH+7rv22YYhiEAAAAAwGXN7ukAAAAAAADr0fwBAAAAQCVA8wcAAAAAlQDNHwAA <br \>AABUAjR/AAAAAFAJ0PwBAAAAQCVA8we3SU1Nld1uL/XPwYMHS4x/6623XI5v3bp1ifFr1651OT48 <br \>PPyS8tjtduXm5rrlfW/atEm9e/dW7dq1FRAQoDp16uiOO+7QsmXL3DJ/WW3YsEFt27ZVSEiIatWq <br \>pa5du6qgoMCjmQAA5VNZa+0fjR8/Xna7XWlpaW6f2xd9//33JT53Phu44ufpALh8hIeHa968eZKk <br 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\>3tLw4cMVHR2txx9/XKmpqYqJiXGOOXLkiObPn6927dp5MGnp7r33Xk2ePFlxcXGKiIhwOW7fvn0V <br \>mMo8h8NR4ge482655RZFR0dr5syZ6tChQwUnuzg/P79i2cPDw9WxY0fVqVOnxFhv/KFI+v3/3alT <br \>p2rt2rX617/+pTp16mjAgAE+8dvM//73vwoODpZhGLLb7UpLSyuROzc3Vw6HwzMB4Ta+XCN9uT5K <br \>1EhP8uX6KPl+jfTl+ih5b42k+ftfAwYM0KxZs/Tss89Kknr16qW+fftqwoQJGjZsmKKjo3Xw4EFJ <br \>8sr19A899JCmTZumwYMHKzQ0VDk5OapatapGjx5dbNyRI0e8ak239PtnP2fOHP3jH/9QVFRUqSez <br \>p6WlqU2bNrr//vs9nLak5s2b629/+5v2799/wcJWtWpVNWnSpAKTmVOvXj3t3LnT5cnejRo10oQJ <br \>E/p9nJ0AAAy3SURBVJzLi7xJ06ZNtW/fPjVs2NC5bciQISXG/fjjj6pbt25FRrskdrtdN998s9q3 <br \>b6/ly5fr2WefVZs2bTwd64JuvPFG5ebmOq9a1rJly1L/bfn+++//f3v3G1Nl/f9x/HmEziE4MGtt <br \>DTsgcCMMWw4xprU1h221bohuTZZt1MqtG66gWtLWX6utPzfCMK2tiXQjS3PLsrl5Q2O1eQeQNSuN <br \>ZjvCwXJFyTmAR4Jzfjfid76/o4Sc7w/5XO/O63EPzgU82WeH9z5c51yX5/7mSOYsz0jL8xE0I12y <br \>PB/h3zEjLc5H8PaM1AVfLvH777+Tm5vLwoULgb9fRvHVV18RDoe5/vrrqaur47rrrnNcOb1kMsm3 <br \>335LJBIhGAyyfPlyU1f9CofDdHd3E4lEGBkZwefzUVBQQCgUoqamxrN/mKyLRqMEAgECgcCMx42O <br \>jtLV1cXq1avnJ2wODQ4OMjExweLFi12nzMrQ0BAff/wx33zzDW+99ZaZ7n8yNjam2z78S1idkdbn <br \>I2hGupAN8xFszch/23yE+Z+R2vyJiIiIiIhkgQVXPkRERERERESs03v+/o9kMkl3dzc9PT1EIhFi <br \>sRg+n4/CwkJKSkpYsWJF2qWivcZ6/5WMjIzQ09PjuRt5zpb63bHcDrb7LbdLOsszxnL7bFl/rlnu <br \>t9wOtvstt4Obfp35mxKNRnnuuedoa2tjaGiIiooKVq1axcqVKykvL+e3336jtbWV559/nmg06jr3 <br \>Mtb7Z+PcuXPs3LnTdcZ/Tf3uWG4H2/2W2+U/LM8Yy+2ZsP5cs9xvuR1s91tuBzf9OvM3pb29nby8 <br \>PN577z2CwSCJRIJwOEwoFMLv9wMQi8VobW2lvb3dc1czs94/G5bu5zId9btjuR1s91tul/+wPGMs <br \>t2fC+nPNcr/ldrDdb7kd3PRr8zelt7eXF154IXUj2O3bt3Ps2DEqKipSl/AtLCzkgQce4LXXXnOZ <br \>Oi3L/Q0NDa4T/l/U747ldrDdb7ldMmd5xlhuB/vPNcv9ltvBdr/ldvB2vzZ/U3JychgfH099PDk5 <br \>CUAikUg7bmJiwpM3wrTcX15ejs/no76+fsbjzp07x549e+apavbU747ldrDdb7ldMmd5xlhuB/vP <br \>Ncv9ltvBdr/ldvB2vzZ/U1auXElHRwdPPPEEoVCIpqYmwuEwJSUlqWMGBwfZvXs3q1atclg6Pcv9 <br \>Gzdu5PXXX6esrGzGG8CePn16HqtmT/3uWG4H2/2W2yVzlmeM5Xaw/1yz3G+5HWz3W24Hb/fnvPzy <br \>yy/P+0/1oKVLl/L999+ze/dujh07xokTJzhz5gw9PT10dnayf/9+9u/fT2VlJZs2bSI311v7Zsv9 <br \>N954I5OTkyQSibRhfKl4PM7AwIDnbqKqfncst4PtfsvtkjnLM8ZyO9h/rlnut9wOtvstt4O3+3WT <br \>90uEw2G6u7uJRCKMjIzg8/koKCggFApRU1NDeXm568QZWe8XERHvsjxjLLeLiMwVbf5ERERERESy <br \>gO7zJyIiIiIikgW89cJ2x5LJJN3d3fT09BCJRIjFYvh8PgoLCykpKWHFihUsX77cdeY/stxvuR3U <br \>75LldrDdb7ldMmd5vS23g/pdstwOtvstt4N3+/WyzynRaJQ33niDgYEBlixZQnFxMfn5+QCMjY3x <br \>yy+/cOrUKRYvXsyWLVsoKipyXJzOcr/ldlC/S5bbwXa/5XbJnOX1ttwO6nfJcjvY7rfcDt7u1+Zv <br \>yrZt24hGozz11FMEg0ESiQThcJhQKITf7wcgFovR2tpKUVERzc3NjovTWe633A7qd8lyO9jut9wu <br \>mbO83pbbQf0uWW4H2/2W28Hj/UlJJpPJZGNjY/Knn35Kfbxt27bkhg0bks8++2zacX19fcnGxsb5 <br \>zrsiy/2W25NJ9btkuT2ZtN1vuV0yZ3m9Lbcnk+p3yXJ7Mmm733J7Muntfl3wZUpOTg7j4+Opjycn <br \>JwFIJBJpx01MTJCTkzOvbbNhud9yO6jfJcvtYLvfcrtkzvJ6W24H9btkuR1s91tuB2/36ybvU86d <br \>O8fRo0e55ZZbKCoqora2lpqaGtatW5dalMHBQd5//32WLVtGTU2N4+J0lvstt4P6XbLcDrb7LbdL <br \>5iyvt+V2UL9LltvBdr/ldvB2v97zNyUej/Puu+/S1dXFokWLpn1j5tmzZ6mtrWXz5s3k5eU5Lk5n <br \>ud9yO6jfJcvtYLvfcrtkzvJ6W24H9btkuR1s91tuB2/3a/N3iXA4THd3N5FIhJGREXw+HwUFBYRC <br \>IWpqaigvL3edOCPL/ZbbQf0uWW4H2/2W2yVzltfbcjuo3yXL7WC733I7eLNfmz8REREREZEsoAu+ <br \>iIiIiIiIZIFc1wFe0tfXx9GjRzl//jyLFi3irrvuoqysLO2YX3/9laamJvbu3esmcgaW+y23g/pd <br \>stwOtvstt0vmLK+35XZQv0uW28F2v+V28G6/zvxNOX78OC+++CL9/f0EAgG+++47WlpaaGtrY3R0 <br \>1HXeFVnut9wO6nfJcjvY7rfcLpmzvN6W20H9LlluB9v9ltvB2/068zfl008/5d577+Xhhx9OfW5g <br \>YIA9e/bQ0tLCli1bKC0tdRd4BZb7LbeD+l2y3A62+y23S+Ysr7fldlC/S5bbwXa/5Xbwdr/O/E2J <br \>RCKsXr067XMlJSW0tLSwfv16tm7dyvHjx93EzYLlfsvtoH6XLLeD7X7L7ZI5y+ttuR3U75LldrDd <br \>b7kdvN2vM39T8vLyuHjx4rSPrVmzhlAoxNtvv82dd945z2WzY7nfcjuo3yXL7WC733K7ZM7yeltu <br \>B/W7ZLkdbPdbbgdv9+vM35SKigpOnDjxj49XVlby6quv0tvbO49Vs2e533I7qN8ly+1gu99yu2TO <br \>8npbbgf1u2S5HWz3W24Hb/frPn9TotEogUCAQCAw43Gjo6N0dXVddirXNcv9lttB/S5Zbgfb/Zbb <br \>JXOW19tyO6jfJcvtYLvfcjt4u1+bPxERERERkSygl32KiIiIiIhkAW3+REREREREsoA2fyIiIiIi <br \>IllAmz8RBy5cuMCjjz7KRx99dNljX3zxBY2NjUSjUQdlIiIibmlGilw92vyJOHDttdeyfv16Dh8+ <br \>nDbA4vE4n3/+Offddx9FRUUOC0VERNzQjBS5erT5E3HknnvuoaCggAMHDqQ+d+jQIQDWrl3rKktE <br \>RMQ5zUiRqyPXdYBItrrmmmu4//776ejoYO3atfj9fg4ePMi6devIz89PHTc6OsqHH35IV1cXiUSC <br \>6upqHnnkkcv+63n69GkOHz7MyZMnOX/+PDfddBONjY1UVVWlHdfZ2Ul7ezttbW3s3LmTkydPEgwG <br \>2bx5M7feeuu8/O4iIiIz0YwUuTp0nz8RhxKJBE8++STV1dXk5+dz5MgRtm/fjt/vTz3+0ksvEQwG <br \>qa+vJzc3l7179zI+Ps7WrVvTvte+ffsIBALcdtttjI+P88knn9Df38+OHTvIy8tLHdfZ2cmuXbso <br \>LS2ltraW6upq+vv7qa2tTf1cERER1zQjReaezvyJOLRgwQIaGhrYsWMHubm5PPjgg2nDpbe3l0gk <br \>wgcffEBu7t9P16effppNmzZx6tQplixZkjp2w4YNad/7scceo6mpiTNnzlBZWZn22Pj4OHV1daxZ <br \>swaA0tLSq/UrioiI/Fc0I0XmnjZ/Io7dcccdHDhwgAsXLnD33XenPfbDDz8wNjbGQw89lPb5iYkJ <br \>IpFI2mD7X8lkkuHhYeLxOADDw8OXHeP3+1NDTURExKs0I0XmljZ/Ih5QVlZGLBZjwYL0azCNjo5S <br \>UVHB448/ftnXXPp+hrNnz7Jv3z56e3vx+/3ccMMNwN+D7lI+n28O60VERK4ezUiRuaPNn4gHJJPJ <br \>aQdQUVERQ0NDFBcXzziM4vE4r7zyClVVVbzzzjssXLgQgIaGhqvWLCIiMh80I0Xmjm71IOIR0w2u <br \>ZcuWMTw8zNdffz3j1w4MDPDnn3+ycePG1FD7+eefr0qniIjIfNOMFJkbOvMn4hHT/Vdz6dKl3H77 <br \>7ezatYuLFy9SVVVFLBajr6+P+vr61HHFxcX4/X6+/PJL6urq+PHHHzl06BB+v5+//vprPn8NERGR <br \>OacZKTI3tPkT8QCfz/ePL1lpbm7ms88+4+DBg3R0dFBQUMDNN99MPB5PXZ46GAzS3NxMR0cHR44c <br \>oaqqimeeeYY333yTP/74Y9qfJyIiYoFmpMjc0X3+REREREREsoDe8yciIiIiIpIFtPkTERERERHJ <br \>Atr8iYiIiIiIZAFt/kRERERERLKANn8iIiIiIiJZQJs/ERERERGRLKDNn4iIiIiISBbQ5k9ERERE <br \>RCQLaPMnIiIiIiKSBf4H5Hax0JJ/ZxgAAAAASUVORK5CYII= <br \>" <br \>> <br \></div> <br \> <br \></div> <br \> <br \></div> <br \></div> <br \> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>Clearly, the conference papers outnumber the journal publications by a significant margin and this is expected. The year 2013 seems to represent a peak in journal publications but it is difficult to conclude much as one must keep in mind the large turnaround times for journal publication reviews.</p> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>As IEEE conference publications make up most of the polar code publications in the dataset, one would be interested in knowing which conferences are popular venues for presenting polar code research. For this we can create a scatter plot as follows using knowledge of 8 popular IEEE conferences in information theory and coding theory research which are ISIT, ITW, Allerton, ICC, ICNC, WCNC, GLOBECOM, and Asilomar conferences.</p> <br \> <br \></div> <br \></div> <br \></div> <br \><div class="cell border-box-sizing code_cell rendered"> <br \><div class="input"> <br \><div class="inner_cell"> <br \> <div class="input_area"> <br \><div class=" highlight hl-ipython2"><pre><span class="c"># Study the publication counts grouped by major IEEE conferences in every year</span> <br \><span class="n">pcdf_confs</span> <span class="o">=</span> <span class="n">pcdf</span><span class="p">[</span><span class="n">pcdf</span><span class="p">[</span><span class="s">&#39;Document_Identifier&#39;</span><span class="p">]</span> <span class="o">==</span> <span class="s">&#39;IEEE Conference Publications&#39;</span><span class="p">]</span> <br \><span class="n">unique_confs</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">pcdf_confs</span><span class="o">.</span><span class="n">Publication_Title</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <br \> <br \><span class="n">conf_names</span> <span class="o">=</span> <span class="p">[</span><span class="s">&#39;ISIT&#39;</span><span class="p">,</span> <span class="s">&#39;ITW&#39;</span><span class="p">,</span> <span class="s">&#39;Allerton&#39;</span><span class="p">,</span> <span class="s">&#39;ICC&#39;</span><span class="p">,</span> <span class="s">&#39;ICNC&#39;</span><span class="p">,</span> \ <br \> <span class="s">&#39;WCNC&#39;</span><span class="p">,</span> <span class="s">&#39;GLOBECOM&#39;</span><span class="p">,</span> <span class="s">&#39;Asilomar&#39;</span><span class="p">]</span> <br \> <br \><span class="k">def</span> <span class="nf">get_conf_name</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">conf_names</span><span class="p">):</span> <br \> <span class="n">is_conf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">y</span> <span class="ow">in</span> <span class="n">x</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">conf_names</span><span class="p">])</span> <br \> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">is_conf</span><span class="p">):</span> <br \> <span class="k">return</span> <span class="n">conf_names</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">conf_names</span><span class="p">))[</span><span class="n">is_conf</span><span class="p">]]</span> <br \> <span class="k">else</span><span class="p">:</span> <br \> <span class="k">return</span> <span class="s">&#39;&#39;</span> <br \> <br \><span class="n">pcdf_confs</span><span class="p">[</span><span class="s">&#39;IEEE_Conference&#39;</span><span class="p">]</span> <span class="o">=</span> \ <br \> <span class="n">pcdf_confs</span><span class="p">[</span><span class="s">&#39;Publication_Title&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">get_conf_name</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">conf_names</span><span class="p">))</span> <br \> <br \><span class="n">pcdf_confs_grouped</span> <span class="o">=</span> <span class="n">pcdf_confs</span><span class="o">.</span><span class="n">groupby</span><span class="p">(</span><span class="s">&#39;IEEE_Conference&#39;</span><span class="p">)</span> <br \><span class="n">pcdf_confs_grouped_counts</span> <span class="o">=</span> <span class="n">pcdf_confs_grouped</span><span class="p">[</span><span class="s">&#39;Year&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">value_counts</span><span class="p">(</span><span class="n">sort</span> <span class="o">=</span> <span class="bp">False</span><span class="p">)</span> <br \><span class="n">pcdf_confs_grouped_counts</span> <span class="o">=</span> <span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">unstack</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <br \><span class="n">pcdf_confs_grouped_counts</span> <span class="o">=</span> <span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">fillna</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <br \><span class="n">pcdf_confs_grouped_counts</span> <span class="o">=</span> <span class="n">pcdf_confs_grouped_counts</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <br \> <br \><span class="n">fig_3</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">[</span><span class="mi">15</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span> <br \><span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span> <br \><span class="n">ylabel_list</span> <span class="o">=</span> <span class="p">[]</span> <br \><span class="n">ylabel_ticks</span> <span class="o">=</span> <span class="p">[]</span> <br \><span class="n">xlabel_list</span> <span class="o">=</span> <span class="p">[</span><span class="nb">str</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">columns</span><span class="p">]</span> <br \><span class="n">xlabel_ticks</span> <span class="o">=</span> <span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">columns</span><span class="p">]</span> <br \><span class="n">plot_colors</span> <span class="o">=</span> <span class="p">[</span><span class="s">&quot;#9b59b6&quot;</span><span class="p">,</span> <span class="s">&quot;#3498db&quot;</span><span class="p">,</span> <span class="s">&quot;#95a5a6&quot;</span><span class="p">,</span> <span class="s">&quot;#e74c3c&quot;</span><span class="p">,</span> \ <br \> <span class="s">&quot;#34495e&quot;</span><span class="p">,</span> <span class="s">&quot;#2ecc71&quot;</span><span class="p">,</span> <span class="s">&quot;#b05b6f&quot;</span><span class="p">,</span> <span class="s">&quot;#008080&quot;</span><span class="p">]</span> <br \><span class="n">yoffset</span> <span class="o">=</span> <span class="mi">0</span> <br \><span class="n">i</span> <span class="o">=</span> <span class="mi">0</span> <br \><span class="k">for</span> <span class="n">conf</span> <span class="ow">in</span> <span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">index</span><span class="p">:</span> <br \> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">columns</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">]</span><span class="o">*</span><span class="nb">len</span><span class="p">(</span><span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">columns</span><span class="p">))</span> <span class="o">+</span> <span class="n">yoffset</span><span class="p">,</span><span class="n">s</span><span class="o">=</span><span class="n">pcdf_confs_grouped_counts</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">conf</span><span class="p">,</span> <span class="p">:]</span><span class="o">*</span><span class="mi">70</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">plot_colors</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <br \> <span class="n">ylabel_ticks</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">yoffset</span><span class="p">)</span> <br \> <span class="n">ylabel_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">conf</span><span class="p">)</span> <br \> <span class="n">yoffset</span> <span class="o">+=</span> <span class="mi">5</span> <br \> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span> <br \> <br \><span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">ylabel_ticks</span><span class="p">)</span> <br \><span class="n">ax</span><span class="o">.</span><span class="n">set_yticklabels</span><span class="p">(</span><span class="n">ylabel_list</span><span class="p">)</span> <br \><span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">xlabel_ticks</span><span class="p">)</span> <br \><span class="n">ax</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">(</span><span class="n">xlabel_list</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">&#39;Year&#39;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">&quot;Publication Count for Conferences&quot;</span><span class="p">)</span> <br \><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> <br \></pre></div> <br \> <br \></div> <br \></div> <br \></div> <br \> <br \><div class="output_wrapper"> <br \><div class="output"> <br \> <br \> <br \><div class="output_area"> <br 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\>ZNhse+7cuXjqqadQUlKCuLg4m3Wtra2YMGECJk6cCACIiopy1RCJiMiNsTglIiLqR8aNG4cPPvgA <br \>zc3NmDRpks26wsJCGI1GzJ4922Z5e3s7ysrKbIrT60RRRH19PUwmEwCgvr7ero1arbYWpkRERK7C <br \>4pSIiKifiYmJQWNjIxQK2/saGgwGxMbGYsGCBXbvufGa0/LycuzYsQPHjx+HWq1GUFAQgGvF6o0E <br \>QXBi9ERERB1jcUpERNTPiKLYYRGp0+lQU1ODsLCwTgtKk8mEpUuXIiEhAWvXroW/vz8AYObMmS6L <br \>mYiIqCt8lAwREVE/1FHxOWrUKNTX1+PgwYOdvvfSpUuoq6vDrFmzrIVpUVGRS+IkIiJyFM+cEhER <br \>9UMdnTlNTExEeno6Nm3ahJaWFiQkJKCxsRHfffcdpk+fbm0XFhYGtVqNPXv2YMKECTh37hw+/vhj <br \>qNVqtLW1STkMIiIiKxanRERE/YwgCDedtrtw4ULs3LkTu3fvxubNm+Hj44Phw4fDZDJZHxGj1Wqx <br \>cOFCbN68Gfv27UNCQgKeeeYZrFq1CrW1tR32R0RE5Gp8zikRERERERHJjtecEhERERERkexYnBIR <br \>EREREZHsWJwSERERERGR7FicEhERERERkexYnBIREREREZHsWJwSERERERGR7FicEhERERERkexY <br \>nBIREREREZHsWJwSERERERGR7P4/6PQoSUaeQVgAAAAASUVORK5CYII= <br \>" <br \>> <br \></div> <br \> <br \></div> <br \> <br \></div> <br \></div> <br \> <br \></div> <br \><div class="cell border-box-sizing text_cell rendered"> <br \><div class="inner_cell"> <br \><div class="text_cell_render border-box-sizing rendered_html"> <br \><p>Clearly, the IEEE International Symposium on Information Theory (ISIT) seems to be the most popular conference for publishing polar code papers followed by the IEEE Information Theory Workshop (ITW) and the IEEE International Conference on Communications (ICC). We also see that the data for 2015 is incomplete as the ISIT-2015 and ICC-2015 conference proceedings are yet to appear on IEEE Xplore and the Allerton conference and GLOBECOM-2015 are yet to happen in October and December 2015 respectively. <br \>So far, the results of our preliminary analysis seem very interesting even on such a small dataset. We will continue our data analysis in further posts. Stay tuned!</p> <br \></div> <br \></div> <br \></div> http://veeresht.info/blog/quatrains-i Some poems written by me.<br/> <br/> <br \> <br \>A time to talk; A time to walk<br/> <br \>A time to sit and watch and balk<br/> <br \>Time is, but all I have<br/> <br \>To sketch my life with a chalk<br/> <br \> <br \><hr> <br \> <br \>It is now old; what once was new<br/> <br \>Every passing moment melts like dew<br/> <br \>A lifetime in each, I would live<br/> <br \>If only the secret, I knew<br/> <br \> <br \><hr> <br \> <br \>Life is but a set of strings to be pulled,<br/> <br \>To make a song as best as we could,<br/> <br \>Touch the hearts of one and all, it should,<br/> <br \>Then gift a memory to life, we would.<br/> <br \> http://veeresht.info/blog/getting-matplotlib-working-virtualenv <p> After installing matplotlib (in a virtualenv) in various different ways using pip/easy_install/manual install from github repo, and even though the matplotlib plotting code worked fine without errors, I was still not able to generate a plot (window).</p> <br \> <br \><p> One of the issues seems to be of setting the appropriate backend in the <b>matplotlibrc</b> file which is generally found in <b>/site-packages/matplotlib/mpl-data/</b>. However, setting the backend to <b>Qt4Agg</b> and backend.qt4 to <b>PyQt4</b> led to a new problem of installing PyQt4 in the virtualenv. </p> <br \> <br \><p> I tried and failed to install PyQt4 using pip/easy_install and the simplest way to fix this problem seems to be to copy my global installation of PyQt4 into the virtualenv's site-packages folder. Also need to copy the global <b>sip.so</b> file similarly. </p> http://veeresht.info/blog/multipath-fading-channels-and-3gpp-lte-design <p> This article attempts to explain the rationale behind choosing particular parameter values in the design of the 3GPP-LTE standard using the concepts related to the effects of multipath fading channels in wireless communications. </p> <br \> <br \> <p> Multipath fading channels are often defined by four key parameters in the theory of wireless communications. These are the Delay Spread (\(T_d\)) and the Coherence Bandwidth (\(W_c\)) defining the multipath characteristics of the wireless channel; the Doppler Spread (\(D_s\)) and the Coherence Time (\(T_c\)) defining the fading characteristics of the wireless channel. [1] presents an excellent treatment of these concepts.</p> <br \> <br \> <p> The 3GPP-LTE standard specification [2] defines the system parameters for the OFDMA based physical layer downlink signal. Considering a system of bandwidth 10 MHz, other parameters defined are as follows: <br \> <ul> <br \> <li> Sampling Rate: 15.36 MHz </li> <br \> <li> FFT Size: 1024 </li> <br \> <li> Sub-carrier Spacing: 15 KHz </li> <br \> <li> Normal mode CP Length: 72 (4.6875 \(\mu s\)) </li> <br \> <li> Duration of one OFDM symbol: \(\approx\) 71.3541 \(\mu s\) </li> <br \> <li> Frequency domain spacing between reference symbol sub-carriers: 6 (\(\Delta\)W = 0.09 MHz) </li> <br \> <li> Time domain spacing between reference OFDM symbols: 3 or 4; for this analysis, choose 4 (\(\Delta T \approx\) 285.42 \(\mu s\)) </li> <br \> </ul> <br \> <br \> <p> The 3GPP-LTE standard specification [3] defines multipath fading channel models to be used in the design and evaluation of an LTE system. <br \>For our analysis, let us choose the Extended Typical Urban model (ETU) which has the highest worst case delay spread of 5000 ns among the models defined. The maximum doppler frequency for the ETU300Hz model is 300 Hz. </p> <br \> <br \> <p> \(T_d\) = 5000 ns </p> <br \> <br \> <p> Therefore, the coherence bandwidth \(W_c\) is given by [1] <br/> <br \> $$ W_c = \frac{1}{2T_d} = 0.1 MHz $$ <br \> Comparing this with \(\Delta\)W as defined above, we have <br \> \( \Delta W \) < \( W_c \), that is the spacing of the reference sub-carriers in the frequency domain is less than the coherence bandwidth of the channel and hence we can assume a flat fading channel characteristic for all the sub-carriers between the reference sub-carriers. <br \>This implies that the channel estimates obtained using the known reference sub-carriers can also be used for equalization of the other sub-carriers. </p> <br \> <br \><p> The ISI due to the multipath components of the channel is compensated by the CP and we see that the the CP Length in the normal mode (4.6875 \(\mu s\)) is slightly less than the worst case delay spread (5 \(\mu s\)). However LTE also supports an extended mode of CP where the length of the CP is 16.67 \(\mu s\) and this is sufficient to handle the worst case delay spread. </p> <br \> <br \> <p> \(D_s\) = 300 Hz- (-300 Hz) = 600 Hz </p> <br \> <br \> <p> Therefore, the coherence time \(T_c\) is given by [1] <br/> <br \> $$ T_c = \frac{1}{4D_s} \approx 416.67 \mu s $$ <br \> Comparing this with \(\Delta\)T as defined above, we have \(\Delta T\) < \(T_c\), that is the spacing of the reference symbols in <br \>time domain is less than the coherence time of the channel and hence we can assume that the channel does not change during the time interval corresponding to \(\Delta\)T. This implies that the channel estimates obtained using the known reference symbols can also be used for equalization of the other non-reference OFDM symbols. <br \> <br \><p> <strong> References </strong> </p> <br \><p> [1]. Tse, D and Viswanath, P. The wireless channel, In: Fundamentals of Wireless Communication. Cambridge University Press, 2005, 10 - 48. </p> <br \><p> [2]. 3GPP TS 36.211. Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation. </p> <br \><p> [3]. 3GPP TS 36.101. Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception. </p> <br \><script type="text/javascript" <br \> src="https://d3eoax9i5htok0.cloudfront.net/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> <br \> </script> http://veeresht.info/blog/cfo <p> Carrier Frequency Offset (CFO) is one of the most common impairments found in a communication system. As the name suggests, it is due to the mismatch between the carrier frequencies used by the transmitter and the receiver. The effects produced by CFO on single carrier and OFDM systems is very different. To illustrate this, a simple simulation of a 64-QAM based single carrier and OFDM system using CommPy is shown below.</p> <br \> <div> <br \> <script src="https://gist.github.com/2280592.js"></script> <br \> </div> <br \> <p> We have to look at the received IQ symbols to study the effect of frequency offset. Shown below are the IQ-constellations generated during the simulation. </p> <br \> <br \> <figure> <br \> <center> <br \> <img src = "http://dl.dropbox.com/u/21829015/ideal.png" width = 600px height = 440px /> <br \> </center> <br \> <figcaption style="text-align:center"> Figure 1: Ideal 64-QAM constellation </figcaption> <br \> </figure> <br \> <br \> <figure> <br \> <center> <br \> <img src = "http://dl.dropbox.com/u/21829015/SC_with_offset.png" width = 600px height = 440px/> <br \> </center> <br \> <figcaption style="text-align:center"> Figure 2: Received 64-QAM constellation in single carrier system with CFO </figcaption> <br \> </figure> <br \> <br \> <figure> <br \> <center> <br \> <img src = "http://dl.dropbox.com/u/21829015/OFDM_with_offset.png" width = 600px height = 440px/> <br \> </center> <br \> <figcaption style="text-align:center"> Figure 3: Received 64-QAM constellation in OFDM system with CFO </figcaption> <br \> </figure> <br \> <br \> <p> As seen from the figures above, the constellation points are rotated by varying amounts in the case of a single carrier system whereas, in the case of an OFDM system the constellation points appear noisy. To answer the question of why this difference in the received constellation, we can do a mathematical analysis of the both the systems as follows. </p> <br \> <br \> <h3> Assumptions and Parameters</h3> <br \> <ul> <br \> <li> Ideal System with frequency offset as the only impairment </li> <br \> <li> Modulation Scheme : 64-QAM </li> <br \> <li> Sampling Frequency \( (F_s) \) : 15.36 MHz </li> <br \> <li> FFT Size in OFDM : 1024 subcarriers </li> <br \> <li> Number of Bits : 6144 (equivalent to 1024 64-QAM symbols) </li> <br \> </ul> <br \> <br \> <h3> Single Carrier System </h3> <br \> <p> Let us denote, <br/> <br \> the 64-QAM modulated IQ symbols at the transmitter by \( x(n) \), <br/> <br \> the 64-QAM modulated IQ symbols at the receiver by \( r(n) \), <br/> <br \> the frequency offset (in Hz) introduced by \( \Delta f \), <br/> <br \> the sampling frequency (in Hz) of the system by \( F_s \).</p> <br \> <br \> <p> The relationship between \( r(n) \) and \( x(n) \) is expressed as <br \> <div style="font-size:1.2em"> $$ r(n) = x(n)e^{\frac{j2\pi\Delta f n}{F_s}} $$ </div> </p> <br \> <p> This can be further modified as <br \> <div style="font-size:1.2em"> <br \> $$ r(n) = A(n)e^{j\theta(n)}e^{\frac{j2\pi\Delta f n}{F_s}} = A(n)e^{j\left(\theta(n) + \frac{2\pi\Delta f n}{F_s} \right)} $$ </div> <br/> where \( A(n) \) and \( \theta(n) \) are the magnitude and the phase of the symbol \( x(n) \) respectively. </p> <br \> <p> From these equations, it is clear that the frequency offset introduces varying amounts of phase offset depending on the time instant \( n \) of the modulated symbol \( x(n) \). This explains the varying rotation of the received constellation points observed in Figure 2.</p> <br \> <br \> <h3> OFDM System </h3> <br \> <p> Let us denote, <br/> <br \> the 64-QAM modulated IQ symbols at the transmitter by \( X(k) \), <br/> <br \> the OFDM signal at the transmitter by \( x(n) \), <br/> <br \> the OFDM signal at the receiver by \( r(n) \), <br/> <br \> the 64-QAM modulated IQ symbols at the receiver by \( R(k) \), <br/> <br \> the frequency offset (in Hz) introduced by \( \Delta f \), <br/> <br \> the sampling frequency (in Hz) of the system by \( F_s \), <br/> <br \> the sub-carrier spacing (in Hz) of the system by \( \Delta f_{sc} \), <br/> <br \> the number of subcarriers (size of the DFT/IDFT) by \( N \). <br \> </p> <br \> <p> The OFDM signal is generated from the modulated symbols using a inverse Discrete Fourier Transform (IDFT) and is given by <br \> <div style="font-size:1.2em"> $$ x(n) = \sum_{k=0}^{N-1}~X(k)e^{\frac{j2\pi kn}{N}} $$ </div> </p> <br \> <p> The relationship between \( r(n) \) and \( x(n) \) is expressed as <br \> <div style="font-size:1.2em"> $$ r(n) = x(n)e^{\frac{j2\pi\Delta f n}{F_s}} $$ </div> </p> <br \> <p> From the modulation property of the DFT and noting that \( \Delta f_{sc} = F_s/N \), we can express the received 64-QAM modulated symbols as <br \> <div style="font-size:1.2em"> $$ R(k) = X\left(k-\frac{\Delta f}{\Delta f_{sc}} \right) $$ </div> <br \> Thus the effect of the frequency offset is a change in the sampling instants of the modulated symbols. To express \( R(k) \) in terms of \( X(k) \), we invoke the Sampling theorem as follows. The continuous time representation \( x(t) \) is given by, <br \> <div style="font-size:1em"> $$ x(t) = \sum_{k=-\infty}^{\infty}~X(k) \frac{sin[\pi (2Wt - k)]}{\pi(2Wt - k)} $$ </div> <br \> where \( W \) represents the baseband bandwidth of the signal. Therefore, \( R(m) \) is given by <br \> <div style="font-size:1em"> $$ R(m) = X\left(m-\frac{\Delta f}{\Delta f_{sc}} \right) = \sum_{k=-\infty}^{\infty}~X(k) \frac{ sin \left[ \pi \left( \frac{2W}{F_s} \left( m - \frac{\Delta f}{\Delta f_{sc}} \right) - k \right) \right]}{ \pi \left( \frac{2W}{F_s} \left( m - \frac{\Delta f}{\Delta f_{sc}} \right) - k \right)} $$ </div> <br \> Assuming \( F_s = 2W \) to simplify the equation we have, <br \> <div style="font-size:1em"> $$ R(m) = X\left(m-\frac{\Delta f}{\Delta f_{sc}} \right) = \sum_{k=-\infty}^{\infty}~X(k) \frac{ sin \left[ \pi \left( m - \frac{\Delta f}{\Delta f_{sc}} - k \right) \right]}{ \pi \left( m - \frac{\Delta f}{\Delta f_{sc}} - k \right)} $$ </div></p> <br \> <p> This equation shows us that every received IQ symbol is the sum of scaled versions of all the transmitted IQ symbols, the scaling factor depends on \( m, k \) and the ratio \( \Delta f / \Delta f_{sc} \). The key point to note is that every IQ symbol (subcarrier) \( X(k) \) is a random variable (assuming the data is random ) and hence the received IQ symbol \( R(m) \) is a sum of random variables which tends to a Gaussian random variable (by the Central Limit Theorem). This explains the observation in Figure 3, where the IQ constellation points appear to be affected by random noise. Since all the subcarriers interfere with the current subcarrier due to the CFO (loss of orthogonality), the effect of CFO on OFDM systems is commonly known by the term Inter-Carrier Interference (ICI). <br \> <script type="text/javascript" <br \> src="https://d3eoax9i5htok0.cloudfront.net/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> <br \> </script> http://veeresht.info/blog/viterbi-algorithm-illustrated <p> It is often helpful to visualize the operation of the Viterbi Algorithm used in the decoding of convolutional codes. <br \>Here is an attempt to do the same using Python, Matplotlib, NumPy, SciPy and CommPy.</p> <br \> <br \><p> Below is a video which shows one such illustration of the Viterbi Algorithm in action using the following parameters. </p> <br \> <br \><p> Convolutional code represented by the encoder matrix, <br/> <br \><center> G(D) = [1+D², 1+D+D²] </center> </p> <br \> <br \><p> Let us assume the transmitted message is [1, 0, 0, 0] and hence the corresponding codeword is [11, 01, 11, 00]. Also assume that there was a single bit error during the transmission and therefore, let the received codeword be [11, 11, 11, 00]. The Viterbi algorithm operates on this received codeword and recovers the correct codeword [11, 01, 11, 00] as shown below. </p> <br \> <br \><video width="640" height="480" controls> <br \><source src="http://dl.dropbox.com/u/21829015/viterbi-4.webm" type='video/webm; codecs="vp8.0, vorbis"'> <br \></video> <br \> <br \><p> This animation was generated using Python code. The code along with this example can be found <a href="https://github.com/veeresht/viterbi-algorithm-animation"> here </a>. </p> http://veeresht.info/blog/plotting-trellis-diagrams-commpy <p>A trellis diagram is a representation of a convolutional code. During the study <br \>of convolutional and turbo codes, one often encounters situations where we <br \>would like to visualize the trellis diagram representation of a simple 4-state or an 8-state <br \>convolutional code.</p> <br \> <br \><p> CommPy is an open source toolkit implementing digital communication algorithms in Python using NumPy, SciPy, Matplotlib and Cython. The visualize function in CommPy's Trellis class is an attempt to make plotting <br \>trellis diagrams easy and simple. Here's how to use it.</p> <br \> <br \><p> <br \><div style="font-size:0.8em"> <br \><script src="https://gist.github.com/2142975.js"> </script> <br \></div> <br \></p> <br \> <br \><figure> <br \><center><img name="4 State Trellis" title="A 4-state Trellis diagram" src="http://veeresht.info/site_media/jquery/images/4_trellis.png"/></center> <br \><figcaption style="text-align:center"> A 4-state Trellis diagram </figcaption> <br \></figure> <br \> <br \><p> <br \>The snippet of code above and the trellis diagram correspond to the <br \>convolutional code generated using the encoder matrix <br/> <br \><center> G(D) = [1+D², 1+D+D²] </center> <br/> <br \>the polynomial entries correspond to the octal <br \>representations 101 (05) and 111 (07). </p> <br \> <br \><p>The input/output labels are shown along with the states first stage of the trellis and the edge colors <br \>depict the output. </p> <br \> <br \><p> <br \>Show below is another trellis diagram representation of the encoder matrix <br/> <br \><center> G(D) = [1+D²+D³, 1+D+D²+D³] </center> </p> <br \> <br \><figure> <br \><center><img name="8 State Trellis" title="An 8-state Trellis diagram" src="http://veeresht.info/site_media/jquery/images/8_trellis.png"/></center> <br \><figcaption style="text-align:center"> An 8-state Trellis diagram </figcaption> <br \></figure> <br \> <br \><p> <br \>Note: Since <a href="https://github.com/veeresht/CommPy"> CommPy </a> doesn't have an installer yet, you need to download/clone it from GitHub to try it out. Details can be found in the .readme file of the repository. <br \></p> <br/> http://veeresht.info/blog/symphony-engineer-nitk <p style="text-align: justify;">With <a href="http://engineer.org.in/">Engineer 2010</a> coming up in a few days time, I had this sudden urge to post something related to one of my favourite events at Engineer, <a href="http://engineer.org.in/events/design/symphony">Symphony</a>.</p> <br \> <br \><p style="text-align: justify;">Symphony is a competition to build a real time musical fountain controller circuit using electronic components such as resistors, capacitors, OpAmps etc.</p> <br \> <br \><p style="text-align: justify;"></p> <br \> <br \><p>And guess what, I had this small presentation on Symphony done by me and my friends during our final year to help the participants. When I found that the problem statement hasn't changed much, I thought what better than to post this presentation which may be of help for future participants.</p> <br \> <br \><script src="http://speakerdeck.com/embed/4f531ddd038e6f001f00f967.js"></script> <br \> http://veeresht.info/blog/technological-singularity <p>"A <strong>technological singularity</strong> is a hypothetical event occurring when technological progress becomes very rapid due to positive feedback, making the future after the Singularity qualitatively different and hard to predict." as defined in <a href="http://en.wikipedia.org/wiki/Technological_singularity" target="_blank">Wikipedia</a>.</p> <br \> <br \><p></p> <br \> <br \><p>Here's a small presentation by me explaining the technological singularity.</p> <br \> <br \><p> <br \><script src="http://speakerdeck.com/embed/4f53180e038e6f002201004f.js"></script> <br \> <br \></p> <br \> <br \><p>For those of you wondering as to why I chose to put this on my blog, this presentation was my technical seminar at NITK (my undergraduate school).</p> <br \>