From fd6d695275f88e83ebba6fa39afc044e329a690f Mon Sep 17 00:00:00 2001
From: "Matthias P. Braendli" <matthias.braendli@mpb.li>
Date: Sun, 25 Dec 2016 23:53:51 +0100
Subject: Add first version of EDI input

---
 lib/fec/decode_rs.h | 298 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 298 insertions(+)
 create mode 100644 lib/fec/decode_rs.h

(limited to 'lib/fec/decode_rs.h')

diff --git a/lib/fec/decode_rs.h b/lib/fec/decode_rs.h
new file mode 100644
index 0000000..647b885
--- /dev/null
+++ b/lib/fec/decode_rs.h
@@ -0,0 +1,298 @@
+/* The guts of the Reed-Solomon decoder, meant to be #included
+ * into a function body with the following typedefs, macros and variables supplied
+ * according to the code parameters:
+
+ * data_t - a typedef for the data symbol
+ * data_t data[] - array of NN data and parity symbols to be corrected in place
+ * retval - an integer lvalue into which the decoder's return code is written
+ * NROOTS - the number of roots in the RS code generator polynomial,
+ *          which is the same as the number of parity symbols in a block.
+            Integer variable or literal.
+ * NN - the total number of symbols in a RS block. Integer variable or literal.
+ * PAD - the number of pad symbols in a block. Integer variable or literal.
+ * ALPHA_TO - The address of an array of NN elements to convert Galois field
+ *            elements in index (log) form to polynomial form. Read only.
+ * INDEX_OF - The address of an array of NN elements to convert Galois field
+ *            elements in polynomial form to index (log) form. Read only.
+ * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
+ * FCR - An integer literal or variable specifying the first consecutive root of the
+ *       Reed-Solomon generator polynomial. Integer variable or literal.
+ * PRIM - The primitive root of the generator poly. Integer variable or literal.
+ * DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
+ *         undefined for production code
+
+ * The memset(), memmove(), and memcpy() functions are used. The appropriate header
+ * file declaring these functions (usually <string.h>) must be included by the calling
+ * program.
+ */
+
+
+#if !defined(NROOTS)
+#error "NROOTS not defined"
+#endif
+
+#if !defined(NN)
+#error "NN not defined"
+#endif
+
+#if !defined(PAD)
+#error "PAD not defined"
+#endif
+
+#if !defined(ALPHA_TO)
+#error "ALPHA_TO not defined"
+#endif
+
+#if !defined(INDEX_OF)
+#error "INDEX_OF not defined"
+#endif
+
+#if !defined(MODNN)
+#error "MODNN not defined"
+#endif
+
+#if !defined(FCR)
+#error "FCR not defined"
+#endif
+
+#if !defined(PRIM)
+#error "PRIM not defined"
+#endif
+
+#if !defined(NULL)
+#define NULL ((void *)0)
+#endif
+
+#undef MIN
+#define	MIN(a,b)	((a) < (b) ? (a) : (b))
+#undef A0
+#define A0 (NN)
+
+{
+  int deg_lambda, el, deg_omega;
+  int i, j, r,k;
+  data_t u,q,tmp,num1,num2,den,discr_r;
+  data_t lambda[NROOTS+1], s[NROOTS];	/* Err+Eras Locator poly
+					 * and syndrome poly */
+  data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
+  data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
+  int syn_error, count;
+
+  /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
+  for(i=0;i<NROOTS;i++)
+    s[i] = data[0];
+
+  for(j=1;j<NN-PAD;j++){
+    for(i=0;i<NROOTS;i++){
+      if(s[i] == 0){
+	s[i] = data[j];
+      } else {
+	s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
+      }
+    }
+  }
+
+  /* Convert syndromes to index form, checking for nonzero condition */
+  syn_error = 0;
+  for(i=0;i<NROOTS;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;
+  }
+  memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
+  lambda[0] = 1;
+
+  if (no_eras > 0) {
+    /* Init lambda to be the erasure locator polynomial */
+    lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
+    for (i = 1; i < no_eras; i++) {
+      u = MODNN(PRIM*(NN-1-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=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
+      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) {
+      fprintf(stderr, "count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
+      count = -1;
+      goto finish;
+    }
+#if DEBUG >= 2
+    fprintf(stderr, "\n Erasure positions as determined by roots of Eras Loc Poly:\n");
+    for (i = 0; i < count; i++)
+      fprintf(stderr, "%d ", loc[i]);
+    fprintf(stderr, "\n");
+#endif
+#endif
+  }
+  for(i=0;i<NROOTS+1;i++)
+    b[i] = INDEX_OF[lambda[i]];
+  
+  /*
+   * Begin Berlekamp-Massey algorithm to determine error+erasure
+   * locator polynomial
+   */
+  r = no_eras;
+  el = no_eras;
+  while (++r <= NROOTS) {	/* 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-1] != A0)) {
+	discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
+      }
+    }
+    discr_r = INDEX_OF[discr_r];	/* Index form */
+    if (discr_r == A0) {
+      /* 2 lines below: B(x) <-- x*B(x) */
+      memmove(&b[1],b,NROOTS*sizeof(b[0]));
+      b[0] = A0;
+    } else {
+      /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
+      t[0] = lambda[0];
+      for (i = 0 ; i < NROOTS; 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 <= NROOTS; i++)
+	  b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
+      } else {
+	/* 2 lines below: B(x) <-- x*B(x) */
+	memmove(&b[1],b,NROOTS*sizeof(b[0]));
+	b[0] = A0;
+      }
+      memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
+    }
+  }
+
+  /* Convert lambda to index form and compute deg(lambda(x)) */
+  deg_lambda = 0;
+  for(i=0;i<NROOTS+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 */
+  memcpy(&reg[1],&lambda[1],NROOTS*sizeof(reg[0]));
+  count = 0;		/* Number of roots of lambda(x) */
+  for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
+    q = 1; /* lambda[0] is always 0 */
+    for (j = deg_lambda; j > 0; j--){
+      if (reg[j] != A0) {
+	reg[j] = MODNN(reg[j] + j);
+	q ^= ALPHA_TO[reg[j]];
+      }
+    }
+    if (q != 0)
+      continue; /* Not a root */
+    /* store root (index-form) and error location number */
+#if DEBUG>=2
+    fprintf(stderr, "count %d root %d loc %d\n",count,i,k);
+#endif
+    root[count] = i;
+    loc[count] = k;
+    /* 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**NROOTS). in index form. Also find deg(omega).
+   */
+  deg_omega = deg_lambda-1;
+  for (i = 0; i <= deg_omega;i++){
+    tmp = 0;
+    for(j=i;j >= 0; j--){
+      if ((s[i - j] != A0) && (lambda[j] != A0))
+	tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
+    }
+    omega[i] = INDEX_OF[tmp];
+  }
+
+  /*
+   * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
+   * inv(X(l))**(FCR-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] * (FCR - 1) + NN)];
+    den = 0;
+    
+    /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
+    for (i = MIN(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
+      if(lambda[i+1] != A0)
+	den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
+    }
+#if DEBUG >= 1
+    if (den == 0) {
+      fprintf(stderr, "\n ERROR: denominator = 0\n");
+      count = -1;
+      goto finish;
+    }
+#endif
+    /* Apply error to data */
+    if (num1 != 0 && loc[j] >= PAD) {
+      data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
+    }
+  }
+ finish:
+  if(eras_pos != NULL){
+    for(i=0;i<count;i++)
+      eras_pos[i] = loc[i];
+  }
+  retval = count;
+}
-- 
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