1 | /* |
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2 | * ECC algorithm for M-systems disk on chip. We use the excellent Reed |
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3 | * Solmon code of Phil Karn (karn@ka9q.ampr.org) available under the |
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4 | * GNU GPL License. The rest is simply to convert the disk on chip |
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5 | * syndrom into a standard syndom. |
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6 | * |
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7 | * Author: Fabrice Bellard (fabrice.bellard@netgem.com) |
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8 | * Copyright (C) 2000 Netgem S.A. |
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9 | * |
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10 | * $Id: docecc.c,v 1.4 2001/10/02 15:05:13 dwmw2 Exp $ |
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11 | * |
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12 | * This program is free software; you can redistribute it and/or modify |
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13 | * it under the terms of the GNU General Public License as published by |
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14 | * the Free Software Foundation; either version 2 of the License, or |
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15 | * (at your option) any later version. |
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16 | * |
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17 | * This program is distributed in the hope that it will be useful, |
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18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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20 | * GNU General Public License for more details. |
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21 | * |
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22 | * You should have received a copy of the GNU General Public License |
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23 | * along with this program; if not, write to the Free Software |
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24 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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25 | */ |
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26 | |
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27 | #include <config.h> |
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28 | #include <common.h> |
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29 | #include <malloc.h> |
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30 | |
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31 | #undef ECC_DEBUG |
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32 | #undef PSYCHO_DEBUG |
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33 | |
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34 | #include <linux/mtd/doc2000.h> |
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35 | |
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36 | /* need to undef it (from asm/termbits.h) */ |
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37 | #undef B0 |
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38 | |
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39 | #define MM 10 /* Symbol size in bits */ |
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40 | #define KK (1023-4) /* Number of data symbols per block */ |
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41 | #define B0 510 /* First root of generator polynomial, alpha form */ |
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42 | #define PRIM 1 /* power of alpha used to generate roots of generator poly */ |
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43 | #define NN ((1 << MM) - 1) |
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44 | |
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45 | typedef unsigned short dtype; |
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46 | |
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47 | /* 1+x^3+x^10 */ |
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48 | static const int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 }; |
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49 | |
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50 | /* This defines the type used to store an element of the Galois Field |
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51 | * used by the code. Make sure this is something larger than a char if |
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52 | * if anything larger than GF(256) is used. |
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53 | * |
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54 | * Note: unsigned char will work up to GF(256) but int seems to run |
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55 | * faster on the Pentium. |
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56 | */ |
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57 | typedef int gf; |
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58 | |
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59 | /* No legal value in index form represents zero, so |
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60 | * we need a special value for this purpose |
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61 | */ |
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62 | #define A0 (NN) |
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63 | |
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64 | /* Compute x % NN, where NN is 2**MM - 1, |
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65 | * without a slow divide |
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66 | */ |
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67 | static inline gf |
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68 | modnn(int x) |
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69 | { |
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70 | while (x >= NN) { |
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71 | x -= NN; |
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72 | x = (x >> MM) + (x & NN); |
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73 | } |
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74 | return x; |
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75 | } |
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76 | |
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77 | #define CLEAR(a,n) {\ |
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78 | int ci;\ |
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79 | for(ci=(n)-1;ci >=0;ci--)\ |
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80 | (a)[ci] = 0;\ |
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81 | } |
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82 | |
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83 | #define COPY(a,b,n) {\ |
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84 | int ci;\ |
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85 | for(ci=(n)-1;ci >=0;ci--)\ |
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86 | (a)[ci] = (b)[ci];\ |
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87 | } |
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88 | |
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89 | #define COPYDOWN(a,b,n) {\ |
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90 | int ci;\ |
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91 | for(ci=(n)-1;ci >=0;ci--)\ |
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92 | (a)[ci] = (b)[ci];\ |
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93 | } |
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94 | |
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95 | #define Ldec 1 |
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96 | |
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97 | /* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m] |
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98 | lookup tables: index->polynomial form alpha_to[] contains j=alpha**i; |
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99 | polynomial form -> index form index_of[j=alpha**i] = i |
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100 | alpha=2 is the primitive element of GF(2**m) |
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101 | HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows: |
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102 | Let @ represent the primitive element commonly called "alpha" that |
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103 | is the root of the primitive polynomial p(x). Then in GF(2^m), for any |
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104 | 0 <= i <= 2^m-2, |
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105 | @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) |
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106 | where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation |
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107 | of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for |
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108 | example the polynomial representation of @^5 would be given by the binary |
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109 | representation of the integer "alpha_to[5]". |
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110 | Similarily, index_of[] can be used as follows: |
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111 | As above, let @ represent the primitive element of GF(2^m) that is |
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112 | the root of the primitive polynomial p(x). In order to find the power |
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113 | of @ (alpha) that has the polynomial representation |
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114 | a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) |
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115 | we consider the integer "i" whose binary representation with a(0) being LSB |
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116 | and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry |
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117 | "index_of[i]". Now, @^index_of[i] is that element whose polynomial |
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118 | representation is (a(0),a(1),a(2),...,a(m-1)). |
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119 | NOTE: |
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120 | The element alpha_to[2^m-1] = 0 always signifying that the |
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121 | representation of "@^infinity" = 0 is (0,0,0,...,0). |
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122 | Similarily, the element index_of[0] = A0 always signifying |
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123 | that the power of alpha which has the polynomial representation |
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124 | (0,0,...,0) is "infinity". |
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125 | |
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126 | */ |
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127 | |
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128 | static void |
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129 | generate_gf(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1]) |
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130 | { |
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131 | register int i, mask; |
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132 | |
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133 | mask = 1; |
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134 | Alpha_to[MM] = 0; |
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135 | for (i = 0; i < MM; i++) { |
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136 | Alpha_to[i] = mask; |
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137 | Index_of[Alpha_to[i]] = i; |
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138 | /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */ |
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139 | if (Pp[i] != 0) |
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140 | Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */ |
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141 | mask <<= 1; /* single left-shift */ |
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142 | } |
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143 | Index_of[Alpha_to[MM]] = MM; |
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144 | /* |
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145 | * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by |
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146 | * poly-repr of @^i shifted left one-bit and accounting for any @^MM |
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147 | * term that may occur when poly-repr of @^i is shifted. |
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148 | */ |
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149 | mask >>= 1; |
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150 | for (i = MM + 1; i < NN; i++) { |
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151 | if (Alpha_to[i - 1] >= mask) |
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152 | Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1); |
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153 | else |
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154 | Alpha_to[i] = Alpha_to[i - 1] << 1; |
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155 | Index_of[Alpha_to[i]] = i; |
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156 | } |
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157 | Index_of[0] = A0; |
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158 | Alpha_to[NN] = 0; |
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159 | } |
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160 | |
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161 | /* |
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162 | * Performs ERRORS+ERASURES decoding of RS codes. bb[] is the content |
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163 | * of the feedback shift register after having processed the data and |
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164 | * the ECC. |
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165 | * |
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166 | * Return number of symbols corrected, or -1 if codeword is illegal |
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167 | * or uncorrectable. If eras_pos is non-null, the detected error locations |
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168 | * are written back. NOTE! This array must be at least NN-KK elements long. |
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169 | * The corrected data are written in eras_val[]. They must be xor with the data |
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170 | * to retrieve the correct data : data[erase_pos[i]] ^= erase_val[i] . |
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171 | * |
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172 | * First "no_eras" erasures are declared by the calling program. Then, the |
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173 | * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2). |
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174 | * If the number of channel errors is not greater than "t_after_eras" the |
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175 | * transmitted codeword will be recovered. Details of algorithm can be found |
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176 | * in R. Blahut's "Theory ... of Error-Correcting Codes". |
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177 | |
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178 | * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure |
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179 | * will result. The decoder *could* check for this condition, but it would involve |
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180 | * extra time on every decoding operation. |
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181 | * */ |
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182 | static int |
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183 | eras_dec_rs(dtype Alpha_to[NN + 1], dtype Index_of[NN + 1], |
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184 | gf bb[NN - KK + 1], gf eras_val[NN-KK], int eras_pos[NN-KK], |
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185 | int no_eras) |
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186 | { |
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187 | int deg_lambda, el, deg_omega; |
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188 | int i, j, r,k; |
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189 | gf u,q,tmp,num1,num2,den,discr_r; |
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190 | gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly |
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191 | * and syndrome poly */ |
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192 | gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1]; |
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193 | gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK]; |
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194 | int syn_error, count; |
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195 | |
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196 | syn_error = 0; |
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197 | for(i=0;i<NN-KK;i++) |
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198 | syn_error |= bb[i]; |
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199 | |
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200 | if (!syn_error) { |
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201 | /* if remainder is zero, data[] is a codeword and there are no |
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202 | * errors to correct. So return data[] unmodified |
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203 | */ |
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204 | count = 0; |
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205 | goto finish; |
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206 | } |
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207 | |
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208 | for(i=1;i<=NN-KK;i++){ |
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209 | s[i] = bb[0]; |
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210 | } |
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211 | for(j=1;j<NN-KK;j++){ |
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212 | if(bb[j] == 0) |
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213 | continue; |
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214 | tmp = Index_of[bb[j]]; |
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215 | |
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216 | for(i=1;i<=NN-KK;i++) |
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217 | s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)]; |
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218 | } |
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219 | |
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220 | /* undo the feedback register implicit multiplication and convert |
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221 | syndromes to index form */ |
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222 | |
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223 | for(i=1;i<=NN-KK;i++) { |
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224 | tmp = Index_of[s[i]]; |
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225 | if (tmp != A0) |
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226 | tmp = modnn(tmp + 2 * KK * (B0+i-1)*PRIM); |
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227 | s[i] = tmp; |
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228 | } |
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229 | |
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230 | CLEAR(&lambda[1],NN-KK); |
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231 | lambda[0] = 1; |
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232 | |
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233 | if (no_eras > 0) { |
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234 | /* Init lambda to be the erasure locator polynomial */ |
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235 | lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])]; |
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236 | for (i = 1; i < no_eras; i++) { |
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237 | u = modnn(PRIM*eras_pos[i]); |
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238 | for (j = i+1; j > 0; j--) { |
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239 | tmp = Index_of[lambda[j - 1]]; |
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240 | if(tmp != A0) |
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241 | lambda[j] ^= Alpha_to[modnn(u + tmp)]; |
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242 | } |
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243 | } |
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244 | #ifdef ECC_DEBUG |
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245 | /* Test code that verifies the erasure locator polynomial just constructed |
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246 | Needed only for decoder debugging. */ |
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247 | |
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248 | /* find roots of the erasure location polynomial */ |
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249 | for(i=1;i<=no_eras;i++) |
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250 | reg[i] = Index_of[lambda[i]]; |
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251 | count = 0; |
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252 | for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) { |
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253 | q = 1; |
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254 | for (j = 1; j <= no_eras; j++) |
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255 | if (reg[j] != A0) { |
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256 | reg[j] = modnn(reg[j] + j); |
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257 | q ^= Alpha_to[reg[j]]; |
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258 | } |
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259 | if (q != 0) |
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260 | continue; |
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261 | /* store root and error location number indices */ |
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262 | root[count] = i; |
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263 | loc[count] = k; |
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264 | count++; |
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265 | } |
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266 | if (count != no_eras) { |
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267 | printf("\n lambda(x) is WRONG\n"); |
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268 | count = -1; |
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269 | goto finish; |
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270 | } |
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271 | #ifdef PSYCHO_DEBUG |
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272 | printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n"); |
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273 | for (i = 0; i < count; i++) |
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274 | printf("%d ", loc[i]); |
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275 | printf("\n"); |
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276 | #endif |
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277 | #endif |
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278 | } |
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279 | for(i=0;i<NN-KK+1;i++) |
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280 | b[i] = Index_of[lambda[i]]; |
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281 | |
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282 | /* |
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283 | * Begin Berlekamp-Massey algorithm to determine error+erasure |
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284 | * locator polynomial |
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285 | */ |
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286 | r = no_eras; |
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287 | el = no_eras; |
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288 | while (++r <= NN-KK) { /* r is the step number */ |
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289 | /* Compute discrepancy at the r-th step in poly-form */ |
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290 | discr_r = 0; |
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291 | for (i = 0; i < r; i++){ |
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292 | if ((lambda[i] != 0) && (s[r - i] != A0)) { |
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293 | discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])]; |
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294 | } |
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295 | } |
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296 | discr_r = Index_of[discr_r]; /* Index form */ |
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297 | if (discr_r == A0) { |
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298 | /* 2 lines below: B(x) <-- x*B(x) */ |
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299 | COPYDOWN(&b[1],b,NN-KK); |
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300 | b[0] = A0; |
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301 | } else { |
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302 | /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */ |
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303 | t[0] = lambda[0]; |
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304 | for (i = 0 ; i < NN-KK; i++) { |
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305 | if(b[i] != A0) |
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306 | t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])]; |
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307 | else |
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308 | t[i+1] = lambda[i+1]; |
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309 | } |
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310 | if (2 * el <= r + no_eras - 1) { |
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311 | el = r + no_eras - el; |
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312 | /* |
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313 | * 2 lines below: B(x) <-- inv(discr_r) * |
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314 | * lambda(x) |
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315 | */ |
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316 | for (i = 0; i <= NN-KK; i++) |
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317 | b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN); |
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318 | } else { |
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319 | /* 2 lines below: B(x) <-- x*B(x) */ |
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320 | COPYDOWN(&b[1],b,NN-KK); |
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321 | b[0] = A0; |
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322 | } |
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323 | COPY(lambda,t,NN-KK+1); |
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324 | } |
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325 | } |
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326 | |
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327 | /* Convert lambda to index form and compute deg(lambda(x)) */ |
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328 | deg_lambda = 0; |
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329 | for(i=0;i<NN-KK+1;i++){ |
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330 | lambda[i] = Index_of[lambda[i]]; |
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331 | if(lambda[i] != A0) |
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332 | deg_lambda = i; |
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333 | } |
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334 | /* |
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335 | * Find roots of the error+erasure locator polynomial by Chien |
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336 | * Search |
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337 | */ |
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338 | COPY(®[1],&lambda[1],NN-KK); |
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339 | count = 0; /* Number of roots of lambda(x) */ |
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340 | for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) { |
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341 | q = 1; |
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342 | for (j = deg_lambda; j > 0; j--){ |
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343 | if (reg[j] != A0) { |
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344 | reg[j] = modnn(reg[j] + j); |
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345 | q ^= Alpha_to[reg[j]]; |
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346 | } |
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347 | } |
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348 | if (q != 0) |
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349 | continue; |
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350 | /* store root (index-form) and error location number */ |
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351 | root[count] = i; |
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352 | loc[count] = k; |
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353 | /* If we've already found max possible roots, |
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354 | * abort the search to save time |
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355 | */ |
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356 | if(++count == deg_lambda) |
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357 | break; |
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358 | } |
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359 | if (deg_lambda != count) { |
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360 | /* |
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361 | * deg(lambda) unequal to number of roots => uncorrectable |
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362 | * error detected |
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363 | */ |
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364 | count = -1; |
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365 | goto finish; |
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366 | } |
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367 | /* |
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368 | * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo |
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369 | * x**(NN-KK)). in index form. Also find deg(omega). |
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370 | */ |
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371 | deg_omega = 0; |
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372 | for (i = 0; i < NN-KK;i++){ |
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373 | tmp = 0; |
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374 | j = (deg_lambda < i) ? deg_lambda : i; |
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375 | for(;j >= 0; j--){ |
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376 | if ((s[i + 1 - j] != A0) && (lambda[j] != A0)) |
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377 | tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])]; |
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378 | } |
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379 | if(tmp != 0) |
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380 | deg_omega = i; |
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381 | omega[i] = Index_of[tmp]; |
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382 | } |
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383 | omega[NN-KK] = A0; |
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384 | |
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385 | /* |
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386 | * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = |
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387 | * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form |
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388 | */ |
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389 | for (j = count-1; j >=0; j--) { |
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390 | num1 = 0; |
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391 | for (i = deg_omega; i >= 0; i--) { |
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392 | if (omega[i] != A0) |
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393 | num1 ^= Alpha_to[modnn(omega[i] + i * root[j])]; |
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394 | } |
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395 | num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)]; |
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396 | den = 0; |
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397 | |
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398 | /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */ |
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399 | for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) { |
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400 | if(lambda[i+1] != A0) |
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401 | den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])]; |
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402 | } |
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403 | if (den == 0) { |
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404 | #ifdef ECC_DEBUG |
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405 | printf("\n ERROR: denominator = 0\n"); |
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406 | #endif |
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407 | /* Convert to dual- basis */ |
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408 | count = -1; |
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409 | goto finish; |
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410 | } |
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411 | /* Apply error to data */ |
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412 | if (num1 != 0) { |
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413 | eras_val[j] = Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])]; |
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414 | } else { |
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415 | eras_val[j] = 0; |
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416 | } |
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417 | } |
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418 | finish: |
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419 | for(i=0;i<count;i++) |
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420 | eras_pos[i] = loc[i]; |
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421 | return count; |
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422 | } |
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423 | |
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424 | /***************************************************************************/ |
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425 | /* The DOC specific code begins here */ |
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426 | |
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427 | #define SECTOR_SIZE 512 |
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428 | /* The sector bytes are packed into NB_DATA MM bits words */ |
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429 | #define NB_DATA (((SECTOR_SIZE + 1) * 8 + 6) / MM) |
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430 | |
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431 | /* |
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432 | * Correct the errors in 'sector[]' by using 'ecc1[]' which is the |
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433 | * content of the feedback shift register applyied to the sector and |
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434 | * the ECC. Return the number of errors corrected (and correct them in |
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435 | * sector), or -1 if error |
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436 | */ |
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437 | int doc_decode_ecc(unsigned char sector[SECTOR_SIZE], unsigned char ecc1[6]) |
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438 | { |
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439 | int parity, i, nb_errors; |
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440 | gf bb[NN - KK + 1]; |
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441 | gf error_val[NN-KK]; |
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442 | int error_pos[NN-KK], pos, bitpos, index, val; |
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443 | dtype *Alpha_to, *Index_of; |
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444 | |
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445 | /* init log and exp tables here to save memory. However, it is slower */ |
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446 | Alpha_to = malloc((NN + 1) * sizeof(dtype)); |
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447 | if (!Alpha_to) |
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448 | return -1; |
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449 | |
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450 | Index_of = malloc((NN + 1) * sizeof(dtype)); |
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451 | if (!Index_of) { |
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452 | free(Alpha_to); |
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453 | return -1; |
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454 | } |
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455 | |
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456 | generate_gf(Alpha_to, Index_of); |
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457 | |
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458 | parity = ecc1[1]; |
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459 | |
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460 | bb[0] = (ecc1[4] & 0xff) | ((ecc1[5] & 0x03) << 8); |
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461 | bb[1] = ((ecc1[5] & 0xfc) >> 2) | ((ecc1[2] & 0x0f) << 6); |
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462 | bb[2] = ((ecc1[2] & 0xf0) >> 4) | ((ecc1[3] & 0x3f) << 4); |
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463 | bb[3] = ((ecc1[3] & 0xc0) >> 6) | ((ecc1[0] & 0xff) << 2); |
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464 | |
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465 | nb_errors = eras_dec_rs(Alpha_to, Index_of, bb, |
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466 | error_val, error_pos, 0); |
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467 | if (nb_errors <= 0) |
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468 | goto the_end; |
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469 | |
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470 | /* correct the errors */ |
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471 | for(i=0;i<nb_errors;i++) { |
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472 | pos = error_pos[i]; |
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473 | if (pos >= NB_DATA && pos < KK) { |
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474 | nb_errors = -1; |
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475 | goto the_end; |
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476 | } |
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477 | if (pos < NB_DATA) { |
---|
478 | /* extract bit position (MSB first) */ |
---|
479 | pos = 10 * (NB_DATA - 1 - pos) - 6; |
---|
480 | /* now correct the following 10 bits. At most two bytes |
---|
481 | can be modified since pos is even */ |
---|
482 | index = (pos >> 3) ^ 1; |
---|
483 | bitpos = pos & 7; |
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484 | if ((index >= 0 && index < SECTOR_SIZE) || |
---|
485 | index == (SECTOR_SIZE + 1)) { |
---|
486 | val = error_val[i] >> (2 + bitpos); |
---|
487 | parity ^= val; |
---|
488 | if (index < SECTOR_SIZE) |
---|
489 | sector[index] ^= val; |
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490 | } |
---|
491 | index = ((pos >> 3) + 1) ^ 1; |
---|
492 | bitpos = (bitpos + 10) & 7; |
---|
493 | if (bitpos == 0) |
---|
494 | bitpos = 8; |
---|
495 | if ((index >= 0 && index < SECTOR_SIZE) || |
---|
496 | index == (SECTOR_SIZE + 1)) { |
---|
497 | val = error_val[i] << (8 - bitpos); |
---|
498 | parity ^= val; |
---|
499 | if (index < SECTOR_SIZE) |
---|
500 | sector[index] ^= val; |
---|
501 | } |
---|
502 | } |
---|
503 | } |
---|
504 | |
---|
505 | /* use parity to test extra errors */ |
---|
506 | if ((parity & 0xff) != 0) |
---|
507 | nb_errors = -1; |
---|
508 | |
---|
509 | the_end: |
---|
510 | free(Alpha_to); |
---|
511 | free(Index_of); |
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512 | return nb_errors; |
---|
513 | } |
---|