BERT.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BERT\n",
    "\n",
    "### Bit Error Rate Testing for M17\n",
    "\n",
    "This document outlines the BERT (bit error rate testing) standard for M17.\n",
    "The purpose of this standard is to provide test equipment and device equipment\n",
    "manufacturers with a standard means of testing the performance of M17 devices.\n",
    "\n",
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-sa/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-sa/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-sa/4.0/\">Creative Commons Attribution-ShareAlike 4.0 International License</a>.\n",
    "\n",
    "Please attribute the work to *Rob Riggs, WX9O, Mobilinkd LLC*.\n",
    "\n",
    "## PRBS9\n",
    "\n",
    "The standard for testing M17 is using the PRBS9 generator.  This uses a LFSR\n",
    "with the polynomial\n",
    "\n",
    "  $ x^{9}+x^{5}+1 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "\n",
    "import numpy as np\n",
    "from pylfsr import LFSR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1400x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state = [1,0,0,0,0,0,0,0,0]\n",
    "fpoly = [9,5]\n",
    "L = LFSR(initstate=state,fpoly=fpoly,counter_start_zero=False)\n",
    "L.Viz(show=False, show_labels=False,title='PRBS9')\n",
    "plt.savefig(\"PRBS9.svg\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0,\n",
       "       1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1,\n",
       "       0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1,\n",
       "       0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1,\n",
       "       0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1,\n",
       "       0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0,\n",
       "       0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0,\n",
       "       1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,\n",
       "       0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,\n",
       "       0, 0, 0, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.runKCycle(197+9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1. Periodicity\n",
      "------------------\n",
      " - Expected period = 2^M-1 = 511\n",
      " - Pass?:  True\n",
      "\n",
      "2. Balance Property\n",
      "-------------------\n",
      " - Number of 1s = Number of 0s+1 (in a period): (N1s,N0s) =  (256, 255)\n",
      " - Pass?:  True\n",
      "\n",
      "3. Runlength Property\n",
      "-------------------\n",
      " - Number of Runs in a period should be of specific order, e.g. [4,2,1,1]\n",
      " - Runs:  [128  64  32  16   8   4   2   1   1]\n",
      " - Pass?:  True\n",
      "\n",
      "4. Autocorrelation Property\n",
      "-------------------\n",
      " - Autocorrelation of a period should be noise-like, specifically, 1 at k=0, -1/m everywhere else\n",
      " - Rxx(k):  [ 1.         -0.00195695 -0.00195695 ... -0.00195695 -0.00195695\n",
      "  1.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " - Pass?:  True\n",
      "\n",
      "\n",
      "\n",
      "==================\n",
      "Passed all the tests\n",
      "==================\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.test_properties(verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8,3))\n",
    "for _ in range(1):\n",
    "  ax.clear()\n",
    "  L.Viz(ax=ax, title='R1')\n",
    "  plt.ylim([-0.1,None])\n",
    "  #plt.tight_layout()\n",
    "  L.next()\n",
    "  fig.canvas.draw()\n",
    "  plt.pause(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pygraphviz as pgv\n",
    "from IPython.display import Image,SVG\n",
    "\n",
    "def svg(dot):\n",
    "    return SVG(pgv.AGraph(dot).draw(format='svg', prog='dot'))\n",
    "def draw(dot):\n",
    "    return Image(pgv.AGraph(dot).draw(format='png', prog='dot'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"610pt\" height=\"141pt\" viewBox=\"0.00 0.00 610.00 141.00\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 137)\">\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-137 606,-137 606,4 -4,4\"/>\n",
       "<text text-anchor=\"middle\" x=\"301\" y=\"-7.8\" font-family=\"DejaVu Sans\" font-size=\"14.00\">Traditional LFSR</text>\n",
       "<!-- struct1 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>struct1</title>\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"89.5,-96.5 89.5,-132.5 512.5,-132.5 512.5,-96.5 89.5,-96.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"113\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 1 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"136.5,-96.5 136.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"160\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 2 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"183.5,-96.5 183.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"207\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 3 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"230.5,-96.5 230.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"254\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 4 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"277.5,-96.5 277.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"301\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 5 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"324.5,-96.5 324.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"348\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 6 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"371.5,-96.5 371.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"395\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 7 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"418.5,-96.5 418.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"442\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 8 </text>\n",
       "<polyline fill=\"none\" stroke=\"black\" points=\"465.5,-96.5 465.5,-132.5 \"/>\n",
       "<text text-anchor=\"middle\" x=\"489\" y=\"-108.3\" font-family=\"DejaVu Sans\" font-size=\"24.00\"> 9 </text>\n",
       "</g>\n",
       "<!-- out -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>out</title>\n",
       "<text text-anchor=\"middle\" x=\"575\" y=\"-110.8\" font-family=\"DejaVu Sans\" font-size=\"14.00\">out</text>\n",
       "</g>\n",
       "<!-- struct1&#45;&gt;out -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>struct1:e-&gt;out</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M513,-114C513,-114 537.99,-114 537.99,-114\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"537.99,-117.5 547.99,-114 537.99,-110.5 537.99,-117.5\"/>\n",
       "</g>\n",
       "<!-- plus2 -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>plus2</title>\n",
       "<text text-anchor=\"middle\" x=\"293\" y=\"-34.8\" font-family=\"DejaVu Sans\" font-size=\"24.00\">⨁</text>\n",
       "</g>\n",
       "<!-- struct1&#45;&gt;plus2 -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>struct1:b4s-&gt;plus2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M293,-96.33C293,-96.33 293,-69.21 293,-69.21\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"296.5,-69.21 293,-59.21 289.5,-69.21 296.5,-69.21\"/>\n",
       "</g>\n",
       "<!-- plus3 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>plus3</title>\n",
       "<text text-anchor=\"middle\" x=\"489\" y=\"-34.8\" font-family=\"DejaVu Sans\" font-size=\"24.00\">⨁</text>\n",
       "</g>\n",
       "<!-- struct1&#45;&gt;plus3 -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>struct1:s-&gt;plus3</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M487.25,-96.5C487.25,-96.5 487.25,-69.17 487.25,-69.17\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"490.75,-69.17 487.25,-59.17 483.75,-69.17 490.75,-69.17\"/>\n",
       "</g>\n",
       "<!-- alignment1 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>alignment1</title>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-108.3\" font-family=\"Times,serif\" font-size=\"24.00\"> </text>\n",
       "</g>\n",
       "<!-- alignment1&#45;&gt;struct1 -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>alignment1-&gt;struct1:b0</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-114C27,-114 79.04,-114 79.04,-114\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"79.04,-117.5 89.04,-114 79.04,-110.5 79.04,-117.5\"/>\n",
       "</g>\n",
       "<!-- alignment1&#45;&gt;plus2 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>alignment1-&gt;plus2</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-114.5C27,-114.5 27,-41 27,-41 27,-41 197.57,-41 265.54,-41\"/>\n",
       "</g>\n",
       "<!-- plus2&#45;&gt;plus3 -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>plus2-&gt;plus3</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M330.25,-41C330.25,-41 461.98,-41 461.98,-41\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"330.25,-37.5 320.25,-41 330.25,-44.5 330.25,-37.5\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g0 = \"\"\"digraph {\n",
    "    graph [splines=ortho;];\n",
    "    fontname=\"DejaVu Sans\";\n",
    "    label = \"Traditional LFSR\";\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontname=\"DejaVu Sans\", fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "        \n",
    "        \n",
    "        out [label=\"out\", fontname=\"DejaVu Sans\", shape=none];\n",
    "\n",
    "        plus2 [label=\"⨁\", fontname=\"DejaVu Sans\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontname=\"DejaVu Sans\", fontsize=24, shape=none];\n",
    "        alignment1 [label=\" \", fontsize=24, shape=none, peripheries=0];    }\n",
    "      \n",
    "    { rank = min; alignment1; struct1; out;};\n",
    "    { rank = same; plus3; plus2};\n",
    "\n",
    "    subgraph cluster1 {\n",
    "        struct1:b8:s -> plus3;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster2 {\n",
    "        struct1:b4s -> plus2;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster3 {\n",
    "        alignment1 -> struct1:b0 [tailclip=false];\n",
    "    }\n",
    "\n",
    "    subgraph cluster4 {\n",
    "        alignment1-> plus2 [dir=none, tailclip=false];\n",
    "        plus2 -> plus3 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"               \"];\n",
    "    }\n",
    "    \n",
    "    subgraph cluster5 {\n",
    "        struct1:b8:e -> out;\n",
    "    }\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "svg(g0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g1 = \"\"\"digraph {\n",
    "    graph [splines=ortho];\n",
    "    label = \"M17 PRBS Generator\";\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "        \n",
    "        \n",
    "        out [label=\"out\", shape=none];\n",
    "\n",
    "        plus2 [label=\"⨁\", fontname=\"DejaVu Sans\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontname=\"DejaVu Sans\", fontsize=24, shape=none];\n",
    "        alignment1 [label=\" \", fontsize=24, shape=none, peripheries=0];    }\n",
    "      \n",
    "    { rank = min; out;};\n",
    "    { rank = same; alignment1; struct1;};\n",
    "    { rank = same; plus3; plus2};\n",
    "\n",
    "    subgraph cluster1 {\n",
    "        struct1:b8:s -> plus3;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster2 {\n",
    "        struct1:b4s -> plus2;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster3 {\n",
    "        alignment1 -> struct1:b0 [tailclip=false];\n",
    "    }\n",
    "    \n",
    "    subgraph cluster4 {\n",
    "        alignment1-> plus2 [dir=none, tailclip=false];\n",
    "        plus2 -> plus3 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"              \"];\n",
    "    }\n",
    "    alignment1 -> out [tailclip=false];\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "draw(g1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g2 = \"\"\"digraph {\n",
    "    graph [splines=ortho];\n",
    "    label = \"Traditional Scrambler\"\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "        \n",
    "        out [label=\"out\", shape=none];\n",
    "        in [label=\"in\", shape=none];\n",
    "\n",
    "        plus1 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus2 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        alignment1 [style=invis, width=0.1];\n",
    "    }\n",
    "    \n",
    "    { rank = min; out;};\n",
    "    { rank = same; in; plus1; struct1; alignment1;};\n",
    "    { rank = same; plus3; plus2};\n",
    "\n",
    "    subgraph from_9 {\n",
    "        struct1:b8:s -> plus2;\n",
    "    }\n",
    "\n",
    "    subgraph from_4 {\n",
    "        struct1:b4:s -> plus3;\n",
    "    }\n",
    "\n",
    "    subgraph cluster {\n",
    "        in -> plus1 -> {struct1:b0,out};\n",
    "        plus1 -> plus3 [dir=back];\n",
    "        plus3 -> plus2 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"              \"];\n",
    "    }\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "draw(g2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g2 = \"\"\"digraph {\n",
    "    graph [splines=ortho];\n",
    "    label = \"M17 PRBS9 Generator (as a multiplicative scrambler)\"\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "        \n",
    "        out [label=\"out\", shape=none];\n",
    "\n",
    "        zero [label=\"0\", fontsize=24, shape=none];\n",
    "        plus1 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus2 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        alignment1 [style=invis, width=0.1];\n",
    "    }\n",
    "    \n",
    "    { rank = min; out;};\n",
    "    { rank = same; zero; plus1; struct1; alignment1;};\n",
    "    { rank = same; plus3; plus2};\n",
    "\n",
    "    subgraph {\n",
    "        struct1:b8:s -> plus2;\n",
    "    }\n",
    "\n",
    "    zero -> plus1 -> {struct1:b0,out};\n",
    "    struct1:b4:s -> plus3;\n",
    "    plus1 -> plus3 [dir=back];\n",
    "    plus3 -> plus2 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"              \"];\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "draw(g2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g3 = \"\"\"digraph {\n",
    "    graph [splines=ortho];\n",
    "    label = \"M17 PRBS Synchronization\";\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "        \n",
    "        out [label=\"compare\", shape=none];\n",
    "        in [label=\"input\", shape=none];\n",
    "\n",
    "        compare [label=\"⭙\", fontsize=24, shape=none];\n",
    "        plus2 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        alignment1 [style=invis, width=0.1];\n",
    "    }\n",
    "    \n",
    "\n",
    "    { rank = same; in; struct1; alignment1;};\n",
    "    { rank = same; out, compare; plus3; plus2};\n",
    "\n",
    "    in -> compare;\n",
    "    in -> {struct1:b0};\n",
    "    out -> compare [dir=back];\n",
    "    struct1:b4 -> plus3;\n",
    "    compare -> plus3 [dir=back];\n",
    "    struct1:b8 -> plus2 [align=right];\n",
    "    plus3 -> plus2 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"              \"];\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "draw(g3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g4 = \"\"\"digraph {\n",
    "    graph [splines=ortho, nodesep=0.0];\n",
    "    label = \"M17 PRBS Validation\";\n",
    "    /* Node customization. */\n",
    "    {\n",
    "        struct1 [shape=record;fontsize=24, label=\"{<b0>&nbsp;1&nbsp;}|\n",
    "            {<b1>&nbsp;2&nbsp;}|{<b2>&nbsp;3&nbsp;}|{<b3>&nbsp;4&nbsp;}|{<b4>&nbsp;5&nbsp;}|\n",
    "            {<b5>&nbsp;6&nbsp;}|{<b6>&nbsp;7&nbsp;}|{<b7>&nbsp;8&nbsp;}|{<b8>&nbsp;9&nbsp;}\"];\n",
    "\n",
    "        in [label=\"in\", shape=none];\n",
    "        out [label=\"out (1 = error)\", shape=none];\n",
    "\n",
    "        compare [label=\"⭙\", fontsize=24, shape=none];\n",
    "        plus2 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        plus3 [label=\"⨁\", fontsize=24, shape=none];\n",
    "        alignment1 [label=\" \", fontsize=24, shape=none, peripheries=0];\n",
    "    }\n",
    "\n",
    "    { rank = min; in; compare; out;};\n",
    "    { rank = same; alignment1; struct1;};\n",
    "    { rank = same; plus3; plus2};\n",
    "\n",
    "    subgraph cluster1 {\n",
    "        struct1:b8:s -> plus3;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster2 {\n",
    "        struct1:b4:s -> plus2;\n",
    "    }\n",
    "    \n",
    "    subgraph cluster3 {\n",
    "        alignment1 -> struct1:b0 [tailclip=false];\n",
    "    }\n",
    "\n",
    "    subgraph cluster4 {\n",
    "        alignment1-> plus2 [dir=none, tailclip=false];\n",
    "        plus2 -> plus3 [dir=back, fontname=\"DejaVu Sans Mono\", label=\"              \"];\n",
    "    }\n",
    "    \n",
    "    graph [nodesep=0.2]\n",
    "    alignment1 -> compare [tailclip=false];\n",
    "    in -> compare -> out;\n",
    "}\n",
    "\"\"\"\n",
    "\n",
    "draw(g4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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