notebooks/9.1_error_correction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9-1. 古典エラー\n",
    "データ蓄積の方法は時間ともに初期化されてしまう揮発性のものと、原則としてほぼ劣化しない不揮発性のものに分類される。ここでは揮発性のメモリの一種であるDRAMのメモリセルを考える。\n",
    "現代の計算機は0,1のバイナリ情報を、コンデンサに蓄えらえれた電子の量が多いか少ないかというアナログな連続量で表現する。（通信ならある周波数帯や時間区間に含まれる光子の数で表現する。）\n",
    "ここではエネルギーが蓄えられた状態を1、エネルギーが完全に放出された状態を0とする。\n",
    "\n",
    "こうしたアナログな量は、外部との相互作用により常に一定値にいることはない。電子は時間とともにトランジスタのリーク電流などによってあるレートで放出される。\n",
    "従って、1の状態はしばらくたつと0の状態に変化してしまう。この変化は現代のデバイスではおよそ秒未満の無視できないスケールで起きる。\n",
    "これは「操作の有無に寄らず時間の変化によって一定レートで起きるエラー」である。\n",
    "こうしたエラーは古典デバイスでは「0,1が判定不能になるより十分前に、一定時間おきに残電子量を読み出し、その数に応じて充電しなおす」ことで訂正されている。\n",
    "この操作はリフレッシュと呼ばれ、ユーザが意図せずとも定期的に行われる。当然、電源が落ちるとリフレッシュは行われなくなる。このことを指しDRAMを揮発メモリと呼ぶ。\n",
    "\n",
    "リフレッシュが行われリークによる影響が無視できるとき、次に重要となるエラーの要因は中性子線によるトランジスタの誤動作である。\n",
    "中性子線は宇宙線の一種であり、金属などを貫通するために防護が困難である。この中性子線がトランジスタを通過するとき、生じた電荷がトランジスタを誤動作させることがある。\n",
    "従って、中性子線エラーは「何らかの操作がトリガーとなり、単発的に起きるエラー」である。\n",
    "読み出しタイミングでないときトランジスタが動作しゲートが解放されると、コンデンサの状態はbit lineの状態に合わせて変化し意図しないものになってしまう。\n",
    "このエラーによってビットが反転される確率は一般のユーザには無視できるほど小さいが、規模が非常に大きな計算では無視できなくなる。\n",
    "仮に単位ビット当たりに単位時間で中性子線が衝突し誤動作する確率を$p$とすると、$n$ビットのメモリが$t$秒間の間１ビットも変化しない確率は\n",
    "$q = (1-p)^{nt}$である。$n=10^{12}, t=10^{3}$とし、$q=0.99$を実現するためには、$p\\sim 10^{-18}$でなければならない。\n",
    "\n",
    "中性子線エラーとリークとの大きな違いは、リークはすぐさま確認すれば復元が可能であるものの、中性子線は生じた後にはもとはどの状態であったか知ることができない点にある。\n",
    "このため、中性子線エラーが問題となる領域での応用では、誤り訂正機能の付いたECC (Error-correcting code) メモリが利用される。ECCメモリでは後述の誤り訂正を行い、1bitまでのエラーを小さなオーバーヘッドで訂正する。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 古典エラー訂正: 多数決\n",
    "最も単純な符号は多数決である。多数決では個々のビットを$d$倍にコピーする。この時、$k$ビットの情報を$n:=dk$ビットで表現することになる。多数決の引き分けを防ぐため、$d$は奇数とする。\n",
    "現実に存在する$n$ビットのことを物理ビット、実態として表現している$k$ビットのことを論理ビットと呼ぶ。\n",
    "\n",
    "多数決では以下のように誤りの検知と訂正を行う。個々の論理ビットについて複製した$d$ビットの情報を読み出し、0,1のどちらが多いかを数える。そして、頻度が高かった値がその論理ビットの値であったと判定する。初期の値がどうあれ、符号化された状態は全ての値が同じであるから、$d$ビットの値が一つでも一致していない場合、何らかのエラーが生じていることが確信できる。従って$n$ビットが丸ごと反転しない限り必ず誤りを検知することができる。\n",
    "\n",
    "誤りを訂正したい場合は半数以上のビットが正しい値を保持していれば正しい結果を得ることができる。それぞれのビットに1より十分小さい確率$p$でエラーが生じるとすると、半数以上のビットがエラーを起こす確率はおよそ$p^{\\lfloor d/2 \\rfloor+1}$である。\n",
    "従って、$d$を2増やすごとに、多数決が失敗する確率はオーダーで$p$倍小さくなることがわかる。\n",
    "最も単純な$k=1$の場合をシミュレートするコードを書くと以下のようになる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original bit: 1\n",
      "decoded bit: 1\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "data = 1\n",
    "d = 31\n",
    "p = 0.01\n",
    "\n",
    "print(\"original bit: {}\".format(data))\n",
    "state = np.repeat(data, d)\n",
    "is_flipped = (np.random.rand(d)<p).astype(np.int)\n",
    "state = (state + is_flipped)%2\n",
    "if np.sum(state==0) < np.sum(state==1):\n",
    "    majority = 1\n",
    "else:\n",
    "    majority = 0\n",
    "        \n",
    "print(\"decoded bit: {}\".format(majority))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上記はランダムに成功不成功が変わるが、成功する確率は確率$p$に関する二項分布の累積として知ることができる。\n",
    "横軸を各ビットのエラー確率、縦軸を復号の成功確率として、様々な奇数の$d$についてプロットすると以下のようになる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "d = 31\n",
    "fail_prob_list = []\n",
    "p_list = np.linspace(0,1,21)\n",
    "for p in p_list:\n",
    "    fail_prob = []\n",
    "    binomial = [1]\n",
    "    for m in np.arange(2,d+2):\n",
    "        nbin = np.zeros(m)\n",
    "        for i in range(m):\n",
    "            if i!=0:\n",
    "                nbin[i] += binomial[i-1]*p\n",
    "            if i+1<m:\n",
    "                nbin[i] += binomial[i]*(1-p)\n",
    "        binomial = nbin\n",
    "        if m%2==0:\n",
    "            fail = np.sum(binomial[m//2:])\n",
    "            fail_prob.append(fail)\n",
    "    fail_prob_list.append(fail_prob)\n",
    "fail_prob_list = np.array(fail_prob_list).T\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.subplot(1,2,1)\n",
    "for index,line in enumerate(fail_prob_list[:6]):\n",
    "    plt.plot(p_list, line, label = \"n={}\".format(2*index+1))\n",
    "plt.ylim(0,1)\n",
    "plt.xlim(0,1)\n",
    "plt.xlabel(\"Error probability per each bit\")\n",
    "plt.ylabel(\"Failure probability\")\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "for index,line in enumerate(fail_prob_list.T[:7]):\n",
    "    if index==0:\n",
    "        continue\n",
    "    distance_list = np.arange((d+1)//2)*2+1\n",
    "    plt.plot(distance_list,line, label = \"p={:.3}\".format(p_list[index]))\n",
    "plt.ylim(1e-5,0.5)\n",
    "plt.yscale(\"log\")\n",
    "plt.xlabel(\"distance\")\n",
    "plt.ylabel(\"Failure probability\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "左のグラフから$p$がある一定値(今回は0.5)以下であれば、$d$を大きくすればするほど性能が良くなることがわかる。\n",
    "一方、$p$がある値以上の場合、$d$を増やすとよくなるどころかむしろ性能が悪化してしまう。\n",
    "このことから、多数決で誤り訂正を行うには、少なくとも各デバイスがある誤り率以下であることが必要条件となることがわかる。\n",
    "\n",
    "このふるまいは量子符号を含むスケールする符号にたびたび見られる性質であり、このしきいとなるエラー確率のことをエラーしきい値(error threshold)と呼ぶ。一般の古典誤り訂正はエラーしきい値よりはるかに小さい値で行われるが、量子誤り訂正では現状のエラーがこのしきい値付近であるため、たびたび言及される。\n",
    "\n",
    "右のグラフは$p$をしきい値以下の一定値に固定し、$d$を大きくしたときにどの程度復号の失敗確率が減少するかを指数プロットしたものである。$p$がしきい値より十分小さい場合、$d$を大きくすることで概ね指数的に復号の失敗確率が減少していくことがわかる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 線形符号\n",
    "上記の多数決の枠組みは線形符号という符号の一種である。下記では線形符号の枠組みで多数決を解説する。\n",
    "ある$k$ビットの情報$v$を$n=dk$ビットの情報$v'$に冗長化する操作は、$k \\times n$の行列$G$を以下のように構成し、$v' = vG$という計算を行うと言い換えることができる。\n",
    "(Nielsen-Chuangの `10.4.1 Classical linear codes` も参照)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original vector: v\n",
      "[0 1 0 1]\n",
      "generator matrix: G\n",
      "[[1 1 1 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 1 1 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 1 1 1]]\n",
      "encoded vector: v' = vG\n",
      "[0 0 0 1 1 1 0 0 0 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "k = 4\n",
    "m = 3\n",
    "n = k*m\n",
    "v = np.random.randint(2,size=k)\n",
    "print(\"original vector: v\\n{}\".format(v))\n",
    "\n",
    "G = np.zeros((k,n),dtype=np.int)\n",
    "for y in range(k):\n",
    "    G[y,y*m:(y+1)*m]=1\n",
    "print(\"generator matrix: G\\n{}\".format(G))\n",
    "\n",
    "vd = (v@G)%2\n",
    "print(\"encoded vector: v' = vG\\n{}\".format(vd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この行列$G$は生成行列という。\n",
    "\n",
    "生成される$2^n$パターンの$n$ビット列のうち、$vG$の形で作られる高々$2^k$個の$n$ビット列を符号語と呼ぶ。符号語の集合を$W$としたとき、$w \\neq w'$となる二つの符号語のハミング距離の最小値を符号の距離(distance)と呼ぶ。今の多数決の構成では、符号の距離は個々の論理ビットを複製する数$d$である。距離$d$以上の数のビットが一斉に反転してしまうとある符号語から別の符号語に変化してしまうため、現在の符号が正しく生成されたのか、他の符号にエラーが載ったものなのか区別がつかなくなる。このことから、エラーが生じるビット数が距離$d$未満であることがエラーが検知できる条件であることが分かる。\n",
    "\n",
    "次に、mod 2のもとで$GH_c = 0$となり、かつ各行ベクトルが独立になるような$n \\times (n-k)$行列$H_c$を考える。今回の場合、3ビットごとに二つの隣接したパリティを見る以下のような$H_c$が条件を満たす。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "check matrix: H\n",
      "[[1 0 0 0 0 0 0 0]\n",
      " [1 1 0 0 0 0 0 0]\n",
      " [0 1 0 0 0 0 0 0]\n",
      " [0 0 1 0 0 0 0 0]\n",
      " [0 0 1 1 0 0 0 0]\n",
      " [0 0 0 1 0 0 0 0]\n",
      " [0 0 0 0 1 0 0 0]\n",
      " [0 0 0 0 1 1 0 0]\n",
      " [0 0 0 0 0 1 0 0]\n",
      " [0 0 0 0 0 0 1 0]\n",
      " [0 0 0 0 0 0 1 1]\n",
      " [0 0 0 0 0 0 0 1]]\n",
      "G Hc = \n",
      "[[0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "Hc = np.zeros((n,n-k),dtype=np.int)\n",
    "for x in range(n-k):\n",
    "    Hc[x//2*m+x%2:x//2*m+x%2+2,x]=1\n",
    "print(\"check matrix: H\\n{}\".format(Hc))\n",
    "\n",
    "print(\"G Hc = \\n{}\".format( (G@Hc)%2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_c$の列ベクトルは独立であるため、$2^n$パターンの$n$ビット列$w$のうち、$w H_c = 0$を満たすパターンは$2^n / 2^{n-k} = 2^k$個である。また、符号語の集合$W$に属する符号語$w$は、$w H_c = v G H_c = 0$である。したがって、符号語の集合$W$とは、$w H_c = 0$を満たすビット列の集合と言い換えることもできる。同時に$n$ビット列$w$が符号語ではない$(w \\neq W)$ことは、$w H_c \\neq 0$であることに等しい。この符号語に属している($w \\in W$)ときかつその時に限り$0$になるベクトル$s = w H_c$のことを$w$の **シンドローム** と呼ぶ。\n",
    "\n",
    "まとめると、符号語の集合$W$は二つの行列$G,H_c$のいずれでも特徴づけることができ、\n",
    "\n",
    "\\begin{align}\n",
    "W &= \\left\\{w \\in \\{0,1\\}^n \\mathrel{}\\middle|\\mathrel{} \\exists v \\in \\{0,1\\}^k , w = vG \\right\\} \\\\\n",
    "W &= \\left\\{w \\in \\{0,1\\}^n \\mathrel{}\\middle|\\mathrel{} w H_c = 0 \\right\\}\n",
    "\\end{align}\n",
    "\n",
    "である。\n",
    "\n",
    "符号化した後にエラー$e$が生じた場合、エラーが起きた後の符号の状態は$v'+e$となった状態である。\n",
    "この時、$v'+e$のシンドローム値$s = (v'+e)H_c$がすべて0であるかどうかを調べることで、エラーの検出を行える。\n",
    "シンドローム値が一つでも0でない場合、何らかのエラーが生じている。シンドローム値がすべて0の場合、エラーは生じていないか、検知不可能な$d$ビット以上のエラーが生じていることがわかる。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "encoded vector: v'\n",
      "[0 0 0 1 1 1 0 0 0 1 1 1]\n",
      "error vector: e\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "encoded vector with noise: v'+e\n",
      "[0 0 0 1 1 1 0 0 0 1 1 1]\n",
      "syndrome values: s = (v'+e)Hc\n",
      "[0 0 0 0 0 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "p = 0.05\n",
    "print(\"encoded vector: v'\\n{}\".format(vd))\n",
    "e = np.random.choice([0,1],size=len(vd),p = [1-p,p])\n",
    "print(\"error vector: e\\n{}\".format(e))\n",
    "vde = (vd+e)%2\n",
    "print(\"encoded vector with noise: v'+e\\n{}\".format(vde))\n",
    "s = (vde@Hc)%2\n",
    "print(\"syndrome values: s = (v'+e)Hc\\n{}\".format(s))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$GH_c=0$という性質から、$s =(v'+e)H_c = vGH_c + eH_c = eH_c$となる。つまり、シンドローム値は初期状態のベクトル$v$と独立であることが分かる。\n",
    "\n",
    "$n$ビットの多数決は$v'+e$を左から$m$個ずつ見て多数決を行えばよい。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "encoded vector: v'\n",
      "[0 0 0 1 1 1 0 0 0 1 1 1]\n",
      "error vector: e\n",
      "[0 0 0 0 0 0 0 0 0 0 0 1]\n",
      "encoded vector with noise: v'+e\n",
      "[0 0 0 1 1 1 0 0 0 1 1 0]\n",
      "syndrome values: s = (v'+e)Hc\n",
      "[0 0 0 0 0 0 0 1]\n",
      "recovered vector: \n",
      "[0 0 0 1 1 1 0 0 0 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "p = 0.1\n",
    "print(\"encoded vector: v'\\n{}\".format(vd))\n",
    "e = np.random.choice([0,1],size=len(vd),p = [1-p,p])\n",
    "print(\"error vector: e\\n{}\".format(e))\n",
    "vde = (vd+e)%2\n",
    "print(\"encoded vector with noise: v'+e\\n{}\".format(vde))\n",
    "s = (vde@Hc)%2\n",
    "print(\"syndrome values: s = (v'+e)Hc\\n{}\".format(s))\n",
    "def decode(vde,k,m):\n",
    "    for x in range(k):\n",
    "        subset = vde[x*m:(x+1)*m]\n",
    "        val = np.argmax(np.bincount(subset))\n",
    "        vde[x*m:(x+1)*m] = val\n",
    "    return vde\n",
    "vde_recovery = decode(vde,k,m)\n",
    "print(\"recovered vector: \\n{}\".format(vde_recovery))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上記の復号はエラーを大きくしていくと、$m$の半数以上が間違えて訂正に失敗することがあることが分かる。\n",
    "\n",
    "$e H_c=0$となる$0$でないベクトル$e$が生じた場合、そのようなエラーは訂正することができない。すなわち、符号の距離$d$は検査行列$H_c$に対して\n",
    "\n",
    "$$\n",
    "d := \\min w(e) \\, \\text{s.t.} \\, H_e e = 0\n",
    "$$\n",
    "\n",
    "という値だと考えることもできる。（ここで $w(x)$ はビット列 $x$ のウェイト、つまり $0\\cdots0$ とのハミング距離である）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 水平垂直パリティ検査符号\n",
    "現実の誤り訂正では多数決の手法はあまり性能が良くないためそれほど使われない。ここでは現実の誤り訂正でよく使われるパリティ検査符号の一例として、水平垂直パリティ検査符号の枠組みを学ぶ。\n",
    "\n",
    "パリティとは、与えられた複数のビットの和を2で割った余り、すなわち1の数の偶奇を意味する。(1,1,1)のパリティは1、(0,1,1)のパリティは0である。\n",
    "パリティ検査符号は、元の情報のデータについてのいくつかのパリティを保持することで誤りの検知や訂正を可能にする。\n",
    "元の情報やパリティにエラーが生じた場合、パリティの値と元の情報に整合性が保たれなくなるためエラーを検出することができる。\n",
    "\n",
    "最もシンプルなパリティ検査符号はチェックサムである。チェックサムは小さなブロック$(x_1,\\ldots, x_b)$ごとに、ブロックに含まれるビット列のパリティ$p= \\sum_i x_i \\bmod 2$をチェックサムとして記入しておく。\n",
    "もし、伝送の途中でブロック中のビットやチェックサムのビットの記入を高々1bit誤った場合、ブロックに含まれるビット列のパリティを再計算すると保持するパリティ$p$と整合性が取れなくなる。\n",
    "従って、ブロックかパリティのどこかにビットエラーが生じたことがわかる。ただし、この方法はどこでエラーが生じたかを知ることはできないし、2ビットエラーが生じた場合はエラーを検知することもできない。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original bitarray: [0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0]\n",
      "checksum: 1\n",
      "error:             [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]\n",
      "noisy bitarray:    [0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1]\n",
      "checksum: 0\n",
      "Error detected!\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "length = 16\n",
    "p = 0.05\n",
    "\n",
    "# set random bitarray\n",
    "bitstring = np.random.randint(2,size = length)\n",
    "checksum = np.sum(bitstring)%2\n",
    "print(\"original bitarray: {}\". format(bitstring))\n",
    "print(\"checksum: {}\".format(checksum))\n",
    "\n",
    "# error occurs\n",
    "error = np.random.choice([0,1], size = length, p = [1-p, p])\n",
    "print(\"error:             {}\". format(error))\n",
    "\n",
    "bitstring = (bitstring + error)%2\n",
    "print(\"noisy bitarray:    {}\". format(bitstring))\n",
    "new_checksum = np.sum(bitstring)%2\n",
    "print(\"checksum: {}\".format(new_checksum))\n",
    "\n",
    "# verify checksum\n",
    "if checksum == new_checksum:\n",
    "    print(\"No error detected\")\n",
    "else:\n",
    "    print(\"Error detected!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1ビットのビットエラーの検知だけでなく訂正を行うには、どこでエラーが生じたかを分かるようにしなければいけない。\n",
    "これを実現するナイーブな手法は、水平垂直パリティ検査という手法である。\n",
    "保護する対象を$k=16$ビットをベクトルとし、これを$4*4$の行列に配置する。\n",
    "ここで、各行のベクトルのパリティと各列のベクトルのパリティを$8$ビット保存しておく。\n",
    "この場合、もし$k$ビットの中でエラーが生じると、一つの列と行のパリティと整合が取れなくなる。この場合、整合が取れない列と行に一致するデータビットが反転したと判定する。\n",
    "もし、行のパリティビットにエラーが生じた場合、列のパリティは全て整合が取れているはずである。このように一方のパリティだけにエラーがある場合、パリティが反転したと結論付ける。列のエラーも同様である。\n",
    "こうすることで、どの場所でビットエラーが生じてもそれが1ビットであれば原因を特定できる。このコードの距離は3ビットであり$[n,k,d] = [24,16,3]$である。一般には$[w^2+2w,w^2,3]$である。（ここで、$[n,k,d]$は符号の特徴を示す3つ組の数字であり、$n$は使用するビット数、$k$は符号化できるビット数、$d$は符号の距離である）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original bitarray: [1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0]\n",
      "stored as : \n",
      "[1 0 0 1] | 0\n",
      "[0 0 0 1] | 1\n",
      "[0 0 1 1] | 0\n",
      "[1 0 0 0] | 1\n",
      "--------\n",
      "[0 0 1 1]\n",
      "\n",
      "result is : \n",
      "[1 1 0 1] | 0\n",
      "[0 0 0 1] | 1\n",
      "[0 1 1 1] | 0\n",
      "[1 0 0 0] | 1\n",
      "--------\n",
      "[0 0 1 1]\n",
      "\n",
      "Too many error occurs\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "width = 4\n",
    "height = 4\n",
    "size = width*height\n",
    "p = 0.03\n",
    "\n",
    "def show(bitmatrix, vertical_parity, horizontal_parity):\n",
    "    for y in range(height):\n",
    "        print(\"{} | {}\".format(bitmatrix[y,:], horizontal_parity[y] ))\n",
    "    print(\"-\"*width*2)\n",
    "    print(\"{}\".format(vertical_parity ))\n",
    "    print()\n",
    "\n",
    "# set random bitarray\n",
    "bitstring = np.random.randint(2,size=size)\n",
    "print(\"original bitarray: {}\". format(bitstring))\n",
    "\n",
    "# check horizontal and vertical parity\n",
    "bitmatrix = bitstring.reshape( (height,width) )\n",
    "vertical_parity = np.sum(bitmatrix, axis = 0)%2\n",
    "horizontal_parity = np.sum(bitmatrix, axis = 1)%2\n",
    "print(\"stored as : \")\n",
    "show(bitmatrix,vertical_parity, horizontal_parity)\n",
    "\n",
    "# error occurs\n",
    "encoded_size = size + width + height\n",
    "error = np.random.choice([0,1], size = encoded_size, p = [1-p, p])\n",
    "bitmatrix = (bitmatrix + error[:size].reshape((height,width)))%2\n",
    "vertical_parity = (vertical_parity + error[size:size+width])%2\n",
    "horziontal_parity = (vertical_parity + error[size+width:])%2\n",
    "\n",
    "# result\n",
    "print(\"result is : \")\n",
    "show(bitmatrix,vertical_parity, horizontal_parity)\n",
    "\n",
    "# verify checksum\n",
    "result_vertical_parity = np.sum(bitmatrix, axis = 0)%2\n",
    "result_horizontal_parity = np.sum(bitmatrix, axis = 1)%2\n",
    "vertical_flip_count = np.sum((result_vertical_parity + vertical_parity)%2)\n",
    "horizontal_flip_count = np.sum((result_horizontal_parity + horizontal_parity)%2)\n",
    "\n",
    "if vertical_flip_count == 0 and horizontal_flip_count == 0:\n",
    "    print(\"No error detected\")\n",
    "    print(\"decoded bitarray: \")\n",
    "    show(bitmatrix, result_vertical_parity, result_horizontal_parity)\n",
    "elif vertical_flip_count == 1 and horizontal_flip_count == 0:\n",
    "    print(\"Error occurs on vertical parity\")\n",
    "    print(\"decoded bitarray: \")\n",
    "    show(bitmatrix, result_vertical_parity, result_horizontal_parity)\n",
    "elif vertical_flip_count == 0 and horizontal_flip_count == 1:\n",
    "    print(\"Error occurs on horizontal parity\")\n",
    "    print(\"decoded bitarray: \")\n",
    "    show(bitmatrix, result_vertical_parity, result_horizontal_parity)\n",
    "elif vertical_flip_count == 1 and horizontal_flip_count == 1:\n",
    "    print(\"Error occurs on data bit\")\n",
    "    print(\"decoded bitarray: \")\n",
    "    x = np.argmax((result_vertical_parity + vertical_parity)%2)\n",
    "    y = np.argmax((result_horizontal_parity + horizontal_parity)%2)\n",
    "    bitmatrix[y,x] = (bitmatrix[y,x]+1)%2\n",
    "    show(bitmatrix, vertical_parity, horizontal_parity)\n",
    "else:\n",
    "    print(\"Too many error occurs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "水平垂直パリティ検査符号も多数決と同様に生成行列と検査行列を考えることができる。\n",
    "簡単のために、$2 \\times 3$の6ビットに対する水平垂直パリティ検査の場合を例に考える。\n",
    "水平垂直パリティ検査で符号化するビットの横ベクトルを$v$とする。この時、$(1,2,3)$番目のパリティを観測する計算は、$1,2,3$番目のみが1で他が0となっているベクトル$w = (1,1,1,0,0,0)$を用意し、ベクトル間の内積$v w^{\\rm T} \\bmod 2$を計算することに等しい。従って、元のデータに追加されるパリティビットは以下のような行列$A$をmod 2のもとで作用することで生成できる。なお、以降のバイナリビット間の演算では特に断りが無い限りはmod 2を省略する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 1 0 0]\n",
      " [1 0 0 1 0]\n",
      " [1 0 0 0 1]\n",
      " [0 1 1 0 0]\n",
      " [0 1 0 1 0]\n",
      " [0 1 0 0 1]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "    [1 , 0 , 1 , 0 , 0],\n",
    "    [1 , 0 , 0 , 1 , 0],\n",
    "    [1 , 0 , 0 , 0 , 1],\n",
    "    [0 , 1 , 1 , 0 , 0],\n",
    "    [0 , 1 , 0 , 1 , 0],\n",
    "    [0 , 1 , 0 , 0 , 1]\n",
    "])\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "この時、パリティの値を並べたベクトル$p$は$p = vA$であり、符号化後のバイナリベクトルは$v' = (v,p)$である。従って生成行列として$k \\times n$行列$G$を$G = (I, A)$と置けば、$v' = v G$という形にできる。\n",
    "\n",
    "符号化したバイナリベクトルにはエラー$e$が生じる。この時、$e$のうちデータ部に生じたエラーを$e_v$、パリティ部に生じたエラーを$e_p$とする。エラーが生じた後のバイナリベクトルは$v'+e = (v+e_v, p+e_p)$となる。水平垂直パリティ検査では、エラーが生じた後にパリティ値が一致しているかどうかをもとにエラーが生じたかを判断する。このことを式で書くと、\n",
    "\n",
    "$$\n",
    "(v + e_v)A = p + e_p\n",
    "$$\n",
    "\n",
    "が成り立つか否かが、エラーを検知するかどうかの判定に等しい。$p=vA$を用いて上記の等式を整理すると、エラーが検知されない条件は\n",
    "\n",
    "$$\n",
    "e_v A + e_p = (e_v, e_p) \\left(\\begin{matrix} A \\\\ I \\end{matrix}\\right) = 0\n",
    "$$\n",
    "\n",
    "である。行列$H_c$を$H_c = \\left( \\begin{matrix} A \\\\ I \\end{matrix} \\right)$と置くと、\n",
    "\n",
    "$$\n",
    "G H_c = (I, A) \\left(\\begin{matrix} A \\\\ I \\end{matrix}\\right) = A + A = 0\n",
    "$$\n",
    "\n",
    "である。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generator matrix: G\n",
      "[[1. 0. 0. 0. 0. 0. 1. 0. 1. 0. 0.]\n",
      " [0. 1. 0. 0. 0. 0. 1. 0. 0. 1. 0.]\n",
      " [0. 0. 1. 0. 0. 0. 1. 0. 0. 0. 1.]\n",
      " [0. 0. 0. 1. 0. 0. 0. 1. 1. 0. 0.]\n",
      " [0. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 0. 1. 0. 1. 0. 0. 1.]]\n",
      "\n",
      "check matrix: Hc \n",
      "[[1. 0. 1. 0. 0.]\n",
      " [1. 0. 0. 1. 0.]\n",
      " [1. 0. 0. 0. 1.]\n",
      " [0. 1. 1. 0. 0.]\n",
      " [0. 1. 0. 1. 0.]\n",
      " [0. 1. 0. 0. 1.]\n",
      " [1. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0.]\n",
      " [0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 1.]]\n",
      "\n",
      "GHc = \n",
      "[[0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "G = np.hstack( (np.eye(A.shape[0]), A) )\n",
    "Hc = np.vstack( (A, np.eye(A.shape[1])) )\n",
    "print(\"generator matrix: G\\n{}\\n\".format(G))\n",
    "print(\"check matrix: Hc \\n{}\\n\".format(Hc))\n",
    "print(\"GHc = \\n{}\\n\".format( (G@Hc)%2 ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数値的にも確かに$GH_c = 0$となることが分かる。$H_c$は$n \\times (n-k)$行列で、かつ列ベクトルは単位行列の部分行列を持つことから明らかに列ごとに独立であり、確かに検査行列の性質を満たしている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "このとき、シンドローム値$s$は$s = e H_c$となる。シンドローム値が全て0の時、符号はエラーが生じていないと判定する。もちろん、大きなエラーが生じている場合、エラーが生じているにもかかわらず$s=0$となりエラーが無いと判定されることもある。\n",
    "\n",
    "$s \\neq 0$である場合、何らかのエラーが起きていることはわかる。この状態でエラーを訂正するには、$(v'+e)$の値から符号化前の$v$を推測しなければならない。今回の場合、冒頭のコードで示したような方法でエラーが一つまでならデータビットとパリティビットのどこにエラーがあるのかを$O(1)$で特定することができる。\n",
    "\n",
    "パリティ検査符号の枠組みをまとめると以下のようになる。\n",
    "\n",
    "- 符号：生成行列$G$と検査行列$H_c$で特徴づけられる。これらは$GH_c = 0$を満たす。\n",
    "- 符号化前：$k$-bitの横ベクトルデータ $v$ がある。\n",
    "- 符号化: $k \\times n$の生成行列$G$を用いて、符号化した状態$v'$は$v'=vG$となる。\n",
    "- エラー: 符号化後の$v'$にランダムに$n$-bit列 $e$ が足される。\n",
    "- エラー検査: $n \\times (n-k)$の検査行列$H_c$を用いてシンドローム$s = e H_c$が得られる。$s \\neq 0$ならばエラーがあると検知できる。$s=0$ならば、エラーが生じていないか、検査できる限界以上のエラーが生じている。\n",
    "- エラー訂正: $(v'+e)$の値に従って、$k$-bitの横ベクトルデータ $v$ を推測する。$v'+e$から$v$を求めるアルゴリズムを復号アルゴリズムと呼ぶ。\n",
    "- 距離: $e H_c = 0$となる$e$の最小weightが符号の距離$d$である。\n",
    "\n",
    "パリティ検査符号は非常に広い枠組みであり、例えばECCメモリではハミング符号と呼ばれるパリティ検査行列の一種が用いられている。\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一般の線形符号のケース\n",
    "\n",
    "上記では多数決、チェックサム、水平垂直検査という特定の例を挙げたが、実際に使用する際には目的に対し最も性能の良い符号がほしい。しかし、一般に与えられた$(n,k,d)$に対して最適な線形符号$G,H_c$を求めることは組み合わせ論の問題となり、一般に困難である。\n",
    "\n",
    "また、仮に最適な$(G,H_c)$という符号を与えられても復号に関して問題がある。ナイーブな復号アルゴリズムの例は、シンドローム$s$を観測した時、$s = e'H_c$を満たすような$e'$のうち、最も少ないビットにエラーを起こすものを起きたエラーとみなし、$(v' + e + e')$が正しい符号語になると期待して復元を試みる最小距離復号である。上記の最適化は\n",
    "\n",
    "$$\n",
    "\\min_{e \\in \\{0,1\\}^n} w(e') \\, \\text{s.t.} \\, s = e' H_c \n",
    "$$\n",
    "\n",
    "という$n$-bitの0,1計画問題となるため、最小距離復号は一般には符号のサイズに対してNP困難である。しかも、この復号は実際には最適な復号とと一致するとは限らない。一方、符号や起きるエラーの種類を限定すると効率的に最小距離復号が実施でき、かつ多くの場合この復号方法は最適に近い復号である。例えば多数決は常に最小距離復号が可能であり、水平垂直パリティ検査符号では生じるエラーを $w(e)=1$ に限定すれば$O(1)$で最小距離復号が可能である。\n",
    "\n",
    "### 線形符号上での演算\n",
    "ノイジーな通信路に情報を通す場合はパリティ検査符号で符号化された情報を転送するだけである場合でよい。しかし、計算機自体がノイジーな場合、パリティ検査符号で符号化した状態で計算を行わなければならない。例えば、CPU自体がノイジーであり、符号化した状態のままで計算を行いたい場合は、計算のたびに復号してしまっては符号化の意味がない。\n",
    "\n",
    "上記の水平垂直パリティ検査を用いる場合、行列の$(i,j)$要素に対するビット反転操作を行うとすると、この操作がエラーとして検知されないようにするには関連するパリティの値も更新しなくてはいけない。つまり、$1$ビットを更新するためには、符号化されたビット列に対して$3$ビットの操作が必要となる。\n",
    "\n",
    "操作のコストを考えると、ある論理ビットを操作するときに実際に操作せねばならないビットの数は少なければ少ないほど良い。\n",
    "論理ビットの反転のために実際に反転しなければいけないビットの数は高々$\\max_i w(G_i)$である。ただし、$G_i$は$G$の$i$行ベクトルである。水平垂直パリティ検査では$G$の行のweightはすべて3になっている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 低密度パリティ検査符号\n",
    "宇宙との通信など通信できる時間が限られていたり通信路が劣悪にならざるを得ない場合、できるだけ限界に近いレートで大量のデータを送りたい。このことが、符号化や復号にかかる計算コストは大きくとも良いので、符号化するビット数あたりの論理誤り率が最も小さくなる符号を作るモチベーションとなる。\n",
    "\n",
    "通信路のノイズが既知である場合、ノイズのある通信路で送信可能な情報量のレートの限界はシャノン限界として計算できる。このレートは構成することができる符号の性能の限界を意味する。低密度パリティ検査符号はこのシャノン限界に近い性能を実現する符号である。\n",
    "\n",
    "低密度パリティ検査符号では、検査行列$H_c$が疎行列となるパリティ検査符号の総称である。ここでいう疎行列とは、各列に含まれる$1$の数が高々$O(k)$程度であることを意味する。すなわち、個々のシンドローム値は$O(k)$個のビットのエラーのパリティで表現できるということである。\n",
    "\n",
    "低密度パリティ検査符号の利点はその性能がシャノン限界に近い点である。一方、低密度パリティ検査符号の欠点は、復号の計算量的な困難さである。この困難を回避するため、信頼伝播法といった近似アルゴリズムが復号のためにしばしば用いられる。\n",
    "\n",
    "信頼伝播法では、次のようなグラフを考える。符号化後のビットをノードとみなす。あるパリティ値があるデータビットのエラーをパリティの一部に含むとき、対応するパリティビットのノードからデータビットのノードへ無向エッジを張る。こうして、$n$頂点が$nO(k)$個の辺で繋がれたの無向グラフ$G(V,E)$が完成する。信頼伝播法はこのグラフ上での逐次的な最適化を状態が符号後となるまで繰り返す。\n",
    "信頼伝播法の性能はグラフ$G$における最小のループが大きければ大きいほど良いことが知られている。したがって、そのようなグラフを構築するべく、様々な低密度パリティ検査符号の構築方法が提案されている。\n",
    "\n"
   ]
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