maxicode.c

This is program with source code to convert ascii text files to the maxicode barcode standard.

	  /*	  data[len+j] = base_reg[j]; */
          tint = base_reg[EClen-1-j];
	  // put_back(tint);
          ecc_results[j] = tint;
	}

  }

  void coeff_init_32()
  {
   mods_10[0] = 1;
   mods_10[1] = 31;
   mods_10[2] = 28;
   mods_10[3] = 39;
   mods_10[4] = 42;
   mods_10[5] = 57;
   mods_10[6] = 2;
   mods_10[7] = 3;
   mods_10[8] = 49;
   mods_10[9] = 44;
   mods_10[10] = 46;

   mods_20[0] = 1;
   mods_20[1] = 23;
   mods_20[2] = 44;
   mods_20[3] = 11;
   mods_20[4] = 33;
   mods_20[5] = 27;
   mods_20[6] = 8;
   mods_20[7] = 22;
   mods_20[8] = 37;
   mods_20[9] = 57;
   mods_20[10] = 36;
   mods_20[11] = 15;
   mods_20[12] = 48;
   mods_20[13] = 22;
   mods_20[14] = 17;
   mods_20[15] = 38;
   mods_20[16] = 33;
   mods_20[17] = 31;
   mods_20[18] = 19;
   mods_20[19] = 23;
   mods_20[20] = 59;
  
   mods_28[0] = 1;
   mods_28[1] = 22;
   mods_28[2] = 45;
   mods_28[3] = 53;
   mods_28[4] = 10;
   mods_28[5] = 41;
   mods_28[6] = 55;
   mods_28[7] = 35;
   mods_28[8] = 10;
   mods_28[9] = 22;
   mods_28[10] = 29;
   mods_28[11] = 23;
   mods_28[12] = 13;
   mods_28[13] = 61;
   mods_28[14] = 45;
   mods_28[15] = 34;
   mods_28[16] = 55;
   mods_28[17] = 40;
   mods_28[18] = 37;
   mods_28[19] = 46;
   mods_28[20] = 49;
   mods_28[21] = 34;
   mods_28[22] = 41;
   mods_28[23] = 9;
   mods_28[24] = 43;
   mods_28[25] = 7;
   mods_28[26] = 20;
   mods_28[27] = 11;
   mods_28[28] = 28;

  } /* end */

int modbase(int x)
{
  return ( x % (GPRIME -1 ));

}

int modnn(int x)
{
  while (x >= NN) {
    x -= NN;
    x = (x >> MM) + (x & NN);
  }
  return x;
}

void generate_gf(void)
{
  register int i, mask;
  int debug;

  mask = 1;
  Alpha_to[MM] = 0;
  for (i = 0; i < MM; i++) {
    Alpha_to[i] = mask;
    Index_of[Alpha_to[i]] = i;
    /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
    if (Pp[i] != 0)
      Alpha_to[MM] ^= mask;	/* Bit-wise EXOR operation */
    mask <<= 1;	/* single left-shift */
  }
  Index_of[Alpha_to[MM]] = MM;
  /*
   * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
   * poly-repr of @^i shifted left one-bit and accounting for any @^MM
   * term that may occur when poly-repr of @^i is shifted.
   */
  mask >>= 1;
  for (i = MM + 1; i < NN; i++) {
    if (Alpha_to[i - 1] >= mask)
      Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
    else
      Alpha_to[i] = Alpha_to[i - 1] << 1;
    Index_of[Alpha_to[i]] = i;
  }
  Index_of[0] = A0;
  Alpha_to[NN] = 0;
  if (debug)
    {
    for(i = 0; i < 64; i += 1)
     {
      printf("Alpha_to[%d] = %d \n", i, Alpha_to[i]);
     }
    for(i = 0; i < 64; i += 1)
     {
      printf("Index_of[%d] = %d \n", i, Index_of[i]);
     }
    }
}

/*
 * Obtain the generator polynomial of the TT-error correcting, length
 * NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0,
 * ... ,(2*TT-1)
 *
 * Examples:
 *
 * If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2.
 * g(x) = (x+@) (x+@**2)
 *
 * If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4.
 * g(x) = (x+1) (x+@) (x+@**2) (x+@**3)
 */
static void
gen_poly(void)
{
  register int i, j;

  Gg[0] = 1;
  for (i = 0; i < NN - KK; i++) {
    Gg[i+1] = 1;
    /*
     * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
     * (@**(B0+i)*PRIM + x)
     */
    for (j = i; j > 0; j--)
      if (Gg[j] != 0)
	Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + (B0 + i) *PRIM)];
      else
	Gg[j] = Gg[j - 1];
    /* Gg[0] can never be zero */
    Gg[0] = Alpha_to[modnn(Index_of[Gg[0]] + (B0 + i) * PRIM)];
  }
  /* convert Gg[] to index form for quicker encoding */
  for (i = 0; i <= NN - KK; i++)
    Gg[i] = Index_of[Gg[i]];
}

void init_rs()
{
  generate_gf();
  gen_poly();

  RS_init = 1;
}

 
/*
 * take the string of symbols in data[i], i=0..(k-1) and encode
 * systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
 * is input and bb[] is output in polynomial form. Encoding is done by using
 * a feedback shift register with appropriate connections specified by the
 * elements of Gg[], which was generated above. Codeword is   c(X) =
 * data(X)*X**(NN-KK)+ b(X)
 */
int
encode_rs(int data[KK], int bb[NN-KK])
{
  register int i, j;
  int feedback;


  /* Check for illegal input values */
  for(i=0;i<KK;i++)
    if(data[i] > NN)
      return -1;

  //  if(!RS_init)
  //  init_rs();

  CLEAR(bb,NN-KK);


  for(i = KK - 1; i >= 0; i--) {
    feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
    if (feedback != A0) {	/* feedback term is non-zero */
      for (j = NN - KK - 1; j > 0; j--)
	if (Gg[j] != A0)
	  bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
	else
	  bb[j] = bb[j - 1];
      bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
    } else {	/* feedback term is zero. encoder becomes a
		 * single-byte shifter */
      for (j = NN - KK - 1; j > 0; j--)
	bb[j] = bb[j - 1];
      bb[0] = 0;
    }
  }

  return 0;
}
 

/*
 * Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
 * writes the codeword into data[] itself. Otherwise data[] is unaltered.
 *
 * Return number of symbols corrected, or -1 if codeword is illegal
 * or uncorrectable. If eras_pos is non-null, the detected error locations
 * are written back. NOTE! This array must be at least NN-KK elements long.
 * 
 * First "no_eras" erasures are declared by the calling program. Then, the
 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
 * If the number of channel errors is not greater than "t_after_eras" the
 * transmitted codeword will be recovered. Details of algorithm can be found
 * in R. Blahut's "Theory ... of Error-Correcting Codes".

 * Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
 * will result. The decoder *could* check for this condition, but it would involve
 * extra time on every decoding operation.
 */
int
eras_dec_rs(int data[NN], int eras_pos[NN-KK], int no_eras,
            int data_len, int synd_len)
{
  int deg_lambda, el, deg_omega;
  int i, j, r,k;
  int u,q,tmp,num1,num2,den,discr_r;
  int lambda[512 + 1], s[512 + 1];	/* Err+Eras Locator poly
					 * and syndrome poly */
  int b[512 + 1], t[512 + 1], omega[512 + 1];
  int root[512], reg[512 + 1], loc[512];
  int syn_error, count;
  int fix_loc;
  int error_val;
  int mismatch;
  int debug;
  int ci;
  int ato;

  if(!RS_init)
     init_rs();

  debug = 0;

  if (set_debug)
    {
      debug =1 ;
    }


  /* Check for illegal input values */
  for(i=0;i< data_len;i++)
    if(data[i] > GPRIME)
      return -1;
  /* form the syndromes; i.e., evaluate data(x) at roots of g(x)
   * namely @**(B0+i)*PRIM, i = 0, ... ,(NN-KK-1)
   */
  for(i=1;i<=synd_len;i++){
    s[i] = data[data_len-1];
    
  }
  if (debug) { printf("data[data_len-1] = %d I_of same = %d \n",
		      data[data_len-1] , Index_of[data[data_len-1]]); }

  for(j=1;j<data_len;j++){
    if(data[data_len-1-j] == 0)
              continue;
    tmp = Index_of[data[data_len-1-j]];
        
    if (debug)
      {
    printf("Data[%d] = %d tmp = %d \n", data_len-j-1, data[data_len-j-1],
                  tmp);
      }
    /*	s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*j)]; */
    for(i=1;i<=synd_len;i++)
      {
	ato = Alpha_to[modnn(tmp+(i*j))];
	if ( debug) { printf("pre s[%d] = %d \n", i, s[i]); }
       s[i] = (s[i] ^ Alpha_to[modnn(tmp + (i*j))]) ;
       if (debug) { printf("s[%d] = %d \n",i,s[i]); }
       if (debug) { printf("modnn = %d \n",modnn(tmp + (i*j))); }
       if (debug) { printf(" i = %d j = %d tmp = %d \n",i,j,tmp); }
       if (debug) { printf("ato = %d \n",ato); }
      }
  }

  mismatch = FALSE;
  for ( j= 0; j < synd_len ; j += 1)
    {
      if ( s[j + 1] != synd_array[j])
        {
          if (debug)
            {
	  printf("Syndrome mismatch j = %d s[j] = %d I_of s[j] = %d  synd_array[j] = %d \n",
		 j, s[j+1],Index_of[s[j+1]], synd_array[j]);
	  mismatch = TRUE;
            }
        }
    }

  if ( mismatch == FALSE)
    {
      if (debug)
	{
         printf("Correct syndromes \n"); 
        }
    }
   else
     {
       printf("Syndrome mismatch \n");
     }


  /* Convert syndromes to index form, checking for nonzero condition */
  syn_error = 0;
  for(i=1;i<=synd_len;i++){
    syn_error |= s[i];
    s[i] = Index_of[s[i]];
  }
  
  if (!syn_error) {
    /* if syndrome is zero, data[] is a codeword and there are no
     * errors to correct. So return data[] unmodified
     */
    count = 0;
    goto finish;
  }
  //  CLEAR(&lambda[1],NN-KK);

  for(ci=synd_len-1;ci >=0;ci--)
    lambda[ci+1] = 0;

  lambda[0] = 1;

  if (no_eras > 0) {
    /* Init lambda to be the erasure locator polynomial */
    lambda[1] = Alpha_to[modnn(PRIM * eras_pos[0])];
    for (i = 1; i < no_eras; i++) {
      u = modnn(PRIM*eras_pos[i]);
      for (j = i+1; j > 0; j--) {
	tmp = Index_of[lambda[j - 1]];
	if(tmp != A0)
	  lambda[j] ^= Alpha_to[modnn(u + tmp)];
      }
    }
#if DEBUG >= 1
    /* Test code that verifies the erasure locator polynomial just constructed
       Needed only for decoder debugging. */
    
    /* find roots of the erasure location polynomial */
    for(i=1;i<=no_eras;i++)
      reg[i] = Index_of[lambda[i]];
    count = 0;
    for (i = 1,k=data_len-Ldec; i <= data_len + synd_len
                            ; i++,k = modnn(data_len+k-Ldec)) {
      q = 1;
      for (j = 1; j <= no_eras; j++)
	if (reg[j] != A0) {
	  reg[j] = modnn(reg[j] + j);
	  q ^= Alpha_to[reg[j]];
	}
      if (q != 0)
	continue;
      /* store root and error location number indices */
      root[count] = i;
      loc[count] = k;
      count++;
    }
    if (count != no_eras) {
      printf("\n lambda(x) is WRONG\n");
      count = -1;
      goto finish;
    }
#if DEBUG >= 2
    printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
    for (i = 0; i < count; i++)
      printf("%d ", loc[i]);
    printf("\n");
#endif
#endif
  }
  for(i=0;i<synd_len+1;i++)
    b[i] = Index_of[lambda[i]];
  
  /*
   * Begin Berlekamp-Massey algorithm to determine error+erasure
   * locator polynomial
   */
  r = no_eras;
  el = no_eras;
  if (debug) { printf("no_eras = %d \n",no_eras); }

  while (++r <= synd_len) {	/* r is the step number */
    /* Compute discrepancy at the r-th step in poly-form */
    discr_r = 0;
    for (i = 0; i < r; i++){
      if ((lambda[i] != 0) && (s[r - i] != A0)) {
	discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
        if (debug) { printf("discr_r = %d i = %d r = %d lambda[i] = %d s[r-i] = %d \n", discr_r, i, r, lambda[i], s[r-i] ); }
      }
    }
    discr_r = Index_of[discr_r];	/* Index form */
    if (debug) { printf("I_of[discr_r] = %d \n", discr_r); }

    if (discr_r == A0) {
      /* 2 lines below: B(x) <-- x*B(x) */
      //      COPYDOWN(&b[1],b,NN-KK);
      for(ci=synd_len-1;ci >=0;ci--)
        {
         b[ci+1] = b[ci];
        }
      b[0] = A0;
    } else {
      /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
      t[0] = lambda[0];
      for (i = 0 ; i < synd_len; i++) {
	if(b[i] != A0)
	  t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
	else
	  t[i+1] = lambda[i+1];
      }
      if (2 * el <= r + no_eras - 1) {
	el = r + no_eras - el;
	/*
	 * 2 lines below: B(x) <-- inv(discr_r) *
	 * lambda(x)
	 */
	for (i = 0; i <= synd_len; i++)
	  b[i]=(lambda[i]==0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
      } else {
	/* 2 lines below: B(x) <-- x*B(x) */
	//	COPYDOWN(&b[1],b,NN-KK);
        for(ci=synd_len-1;ci >=0;ci--)
	  {
           b[ci+1] = b[ci];
          }
	b[0] = A0;
      }
      //  COPY(lambda,t,NN-KK+1);
      for(ci=synd_len;ci >=0;ci--)
	{
          lambda[ci] = t[ci];
          if (debug) { printf("ci = %d Lambda = %d i_of Lambda = %d \n", 
           ci, t[ci], Index_of[t[ci]]); }
        }
    }
  }

  /* Convert lambda to index form and compute deg(lambda(x)) */
  deg_lambda = 0;
  for(i=0;i<synd_len+1;i++){
    lambda[i] = Index_of[lambda[i]];
    if(lambda[i] != A0)
      deg_lambda = i;
  }
  /*
   * Find roots of the error+erasure locator polynomial by Chien
   * Search
   */
  //  COPY(&reg[1],&lambda[1],NN-KK);

   for(ci=synd_len-1;ci >=0;ci--)
     reg[ci+1] = lambda[ci+1];

  count = 0;		/* Number of roots of lambda(x) */
  for (i = 1; i <= NN+1; i++) {
    q = 1;
    
    for (j = deg_lambda; j > 0; j--){
      if (debug) {
	  printf(" Reg[j] = %d q = %d i = %d j=%d\n", reg[j], q, i, j ); }
      if (reg[j] != A0) {
	reg[j] = modnn(reg[j] + j);
	q ^= Alpha_to[reg[j]];
      }
    }
    if (debug) {
	  printf(" q after  = %d i = %d\n", q, i ); }
    if (q != 0)
      continue;
    /* store root (index-form) and error location number */
    root[count] = i;
    
    loc[count] = NN + 1 - i;

    /* If we've already found max possible roots,
     * abort the search to save time
     */
    if(++count == deg_lambda)
      break;
  }
  if (deg_lambda != count) {
    /*
     * deg(lambda) unequal to number of roots => uncorrectable
     * error detected
     */
    count = -1;
    goto finish;
  }
  /*
   * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
   * x**(NN-KK)). in index form. Also find deg(omega).
   */
  deg_omega = 0;
  for (i = 0; i < synd_len;i++){
    tmp = 0;
    j = (deg_lambda < i) ? deg_lambda : i;
    for(;j >= 0; j--){
      if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
	tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
    }
    if(tmp != 0)
      deg_omega = i;
    omega[i] = Index_of[tmp];
  }
  omega[synd_len] = A0;
  
  /*
   * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
   * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
   */
  for (j = count-1; j >=0; j--) {
    num1 = 0;
    for (i = deg_omega; i >= 0; i--) {
      if (omega[i] != A0)
	num1  ^= Alpha_to[modnn(omega[i] + i * root[j])];
    }
    // num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
    num2 = 1;
    den = 0;
    

    // denominator if product of all (1 - Bj Bk) for k != j
    // if count = 1, then den = 1
    //  alternate way to find denominator...

    //    den  = 1;
    // for ( k = 0; k < count ; k += 1)
    //  {
    //	if ( k != j)
    //          {
    //             tmp = modnn( 0xff ^ Alpha_to[modnn(root[k] + root[j])]);
    //            
    //            den = Alpha_to[ modnn( Index_of[den]  + Index_of[tmp])];
    //	      }
    //  }

    /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
    for (i = min(deg_lambda,synd_len-1) & ~1; i >= 0; i -=2) {
      if(lambda[i+1] != A0)
	den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];