Assignment - 6.ipynb

{
 "cells": [
  {
   "attachments": {
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     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "55511290",
   "metadata": {},
   "source": [
    "## Gagan Chordia\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6a218700",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import floor, log, pow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2f5c74e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = []\n",
    "for x in range (1,21):\n",
    "    if x % 2 == 0:\n",
    "        l.append(x)\n",
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "be90aa45",
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_binary(x):\n",
    "    bin = \"{0:b}\".format(int(x))\n",
    "    bin_without_msb = bin[1:]\n",
    "    return bin_without_msb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0eb0f11f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Elias Gamma\n",
    "\n",
    "def elias_gamma_encoding(x):\n",
    "    if(x == 0):\n",
    "        return '0'\n",
    "    n = 1 + floor(log(x, 2))\n",
    "    unary = (n - 1) * '0' + '1'\n",
    "    return (unary + to_binary(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7a68a75a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elias Gamma Encoding\n",
      "{2: '010', 4: '00100', 6: '00110', 8: '0001000', 10: '0001010', 12: '0001100', 14: '0001110', 16: '000010000', 18: '000010010', 20: '000010100'}\n"
     ]
    }
   ],
   "source": [
    "gamma_encode = dict()\n",
    "\n",
    "for x in l:\n",
    "    gamma_encode[x] = elias_gamma_encoding(x)\n",
    "\n",
    "print('Elias Gamma Encoding')\n",
    "print(gamma_encode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "34db0ce3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def elias_gamma_decoding(x):\n",
    "    x = list(x)\n",
    "    k = 0\n",
    "    while True:\n",
    "        if not x[k] == '0':\n",
    "            break\n",
    "        k = k + 1\n",
    "    \n",
    "    x = x[k : 2 * k + 1]\n",
    "    n = 0\n",
    "    x.reverse()\n",
    "    \n",
    "    for i in range(len(x)):\n",
    "        if x[i] == '1':\n",
    "            n += pow(2, i)\n",
    "    \n",
    "    return int(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "df35ce4f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elias Gamma Decoding\n",
      "{'010': 2, '00100': 4, '00110': 6, '0001000': 8, '0001010': 10, '0001100': 12, '0001110': 14, '000010000': 16, '000010010': 18, '000010100': 20}\n"
     ]
    }
   ],
   "source": [
    "gamma_decode = dict()\n",
    "temp = list(gamma_encode.values())\n",
    "\n",
    "for x in temp:\n",
    "    gamma_decode[x] = elias_gamma_decoding(x)\n",
    "    \n",
    "print('Elias Gamma Decoding')\n",
    "print(gamma_decode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d036b2e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Elias Delta\n",
    "\n",
    "def elias_delta_encoding(x):\n",
    "    gamma = elias_gamma_encoding(1 + log(x, 2))\n",
    "    binary = to_binary(x)\n",
    "    return (gamma + binary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7fa49331",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elias Delta Encoding\n",
      "{2: '0100', 4: '01100', 6: '01110', 8: '00100000', 10: '00100010', 12: '00100100', 14: '00100110', 16: '001010000', 18: '001010010', 20: '001010100'}\n"
     ]
    }
   ],
   "source": [
    "delta_encode = dict()\n",
    "\n",
    "for x in l:\n",
    "    delta_encode[x] = elias_delta_encoding(x)\n",
    "    \n",
    "print('Elias Delta Encoding')\n",
    "print(delta_encode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e02ed58b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def elias_delta_decoding(x):\n",
    "    x = list(x)\n",
    "    k = 0\n",
    "    while True:\n",
    "        if not x[k] == '0':\n",
    "            break\n",
    "        k = k + 1\n",
    "    \n",
    "    x = x[2*k+1:]\n",
    "    n = 0\n",
    "    x.insert(0, '1')\n",
    "    x.reverse()\n",
    "    \n",
    "    for i in range(len(x)):\n",
    "        if x[i] == '1':\n",
    "            n += pow(2, i)\n",
    "    \n",
    "    return int(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "898ae175",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elias Delta Decoding\n",
      "{'0100': 2, '01100': 4, '01110': 6, '00100000': 8, '00100010': 10, '00100100': 12, '00100110': 14, '001010000': 16, '001010010': 18, '001010100': 20}\n"
     ]
    }
   ],
   "source": [
    "delta_decode = dict()\n",
    "temp = list(delta_encode.values())\n",
    "\n",
    "for x in temp:\n",
    "    delta_decode[x] = elias_delta_decoding(x)\n",
    "    \n",
    "print('Elias Delta Decoding')\n",
    "print(delta_decode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7121f3e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Golumb\n",
    "\n",
    "def golomb_encoding(x, b):\n",
    "    q = x // b\n",
    "    r = x % b\n",
    "    qu = q * '0' + '1'\n",
    "    \n",
    "    z = floor(log(b, 2))\n",
    "    k = 2**(z + 1) - b\n",
    "    \n",
    "    if r < k:\n",
    "        rem = bin(r)[2:]\n",
    "        l = len(rem)\n",
    "        \n",
    "        if l < z:\n",
    "            rem = (z - l) * '0' + rem\n",
    "    else:\n",
    "        rem = bin(r + k)[2:]\n",
    "        l = len(rem)\n",
    "        \n",
    "        if l < z + 1:\n",
    "            rem = (b - l + 1) * '0' + rem\n",
    "    \n",
    "    return qu + rem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1c4abaf1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Golomb Encoding\n",
      "{2: '1010', 4: '1100', 6: '11100', 8: '11110', 10: '01000', 12: '01010', 14: '01100', 16: '011100', 18: '011110', 20: '001000'}\n"
     ]
    }
   ],
   "source": [
    "golomb_encode = dict()\n",
    "\n",
    "b = 10 # from the question\n",
    "\n",
    "for x in l:\n",
    "    golomb_encode[x] = golomb_encoding(x, b)\n",
    "\n",
    "print('Golomb Encoding')\n",
    "print(golomb_encode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "314d77fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bin_to_int(x):\n",
    "    num = 0\n",
    "    for i in range(len(x)):\n",
    "        num += (int(x[len(x) - i - 1]) * pow(2, i))\n",
    "    return num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fdb4ad30",
   "metadata": {},
   "outputs": [],
   "source": [
    "def golomb_decoding(x):\n",
    "    x = list(x)\n",
    "    b = 10 #from question\n",
    "    i = floor(log(b, 2))\n",
    "    d = pow(2, i + 1) - b\n",
    "    \n",
    "    temp = 0\n",
    "    l = 1\n",
    "    \n",
    "    while(temp < len(x)):\n",
    "        t = 0\n",
    "        flag = False\n",
    "        r = []\n",
    "        k = i\n",
    "        q = 0\n",
    "        \n",
    "        for j in range(temp, len(x)):\n",
    "            if(x[j] == '0' and not flag):\n",
    "                t += 1\n",
    "                continue\n",
    "            \n",
    "            if(x[j] == '1' and not flag):\n",
    "                q = t\n",
    "                flag = True\n",
    "                continue\n",
    "                \n",
    "            r.append(x[j])\n",
    "            \n",
    "            k -= 1\n",
    "            \n",
    "            if(k == 0):\n",
    "                rnum = bin_to_int(r)\n",
    "                if(rnum < d):\n",
    "                    temp = j + 1\n",
    "                    break\n",
    "                \n",
    "            if(k == -1):\n",
    "                rnum = bin_to_int(r)\n",
    "                rnum = rnum - d\n",
    "                temp = j + 1\n",
    "                break\n",
    "        res = q * b + rnum\n",
    "        l = 0\n",
    "    return int(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "afa48686",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Golomb Decoding\n",
      "{'1010': 2, '1100': 4, '11100': 6, '11110': 8, '01000': 10, '01010': 12, '01100': 14, '011100': 16, '011110': 18, '001000': 20}\n"
     ]
    }
   ],
   "source": [
    "golomb_decode = dict()\n",
    "temp = list(golomb_encode.values())\n",
    "\n",
    "for x in temp:\n",
    "    golomb_decode[x] = golomb_decoding(x)\n",
    "    \n",
    "print('Golomb Decoding')\n",
    "print(golomb_decode)"
   ]
  }
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