metrics.c

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/* Generate metric tables for a soft-decision convolutional decoder
 * assuming gaussian noise on a PSK channel.
 *
 * Works from "first principles" by evaluating the normal probability
 * function and then computing the log-likelihood function
 * for every possible received symbol value
 *
 * Copyright 1995 Phil Karn, KA9Q
 */

/* Symbols are offset-binary, with 128 corresponding to an erased (no
 * information) symbol
 */
#define	OFFSET	128

#include <stdlib.h>
#include <math.h>

/* Normal function integrated from -Inf to x. Range: 0-1 */
#define	normal(x)	(0.5 + 0.5*erf((x)/M_SQRT2))

/* Logarithm base 2 */
#define	log2(x)	(log(x)*M_LOG2E)

/* Generate log-likelihood metrics for 8-bit soft quantized channel
 * assuming AWGN and BPSK
 */
int
gen_met(
int mettab[2][256],	/* Metric table, [sent sym][rx symbol] */
int amp,		/* Signal amplitude, units */
double noise,		/* Relative noise voltage */
double bias,		/* Metric bias; 0 for viterbi, rate for sequential */
int scale		/* Scale factor */
){
  double n;
  int s,bit;
  double metrics[2][256];
  double p0,p1;

  /* Zero is a special value, since this sample includes all
   * lower samples that were clipped to this value, i.e., it
   * takes the whole lower tail of the curve 
   */
  p1 = normal(((0-OFFSET+0.5)/amp - 1)/noise);	/* P(s|1) */

  /* Prob of this value occurring for a 0-bit */	/* P(s|0) */
  p0 = normal(((0-OFFSET+0.5)/amp + 1)/noise);
  metrics[0][0] = log2(2*p0/(p1+p0)) - bias;
  metrics[1][0] = log2(2*p1/(p1+p0)) - bias;

  for(s=1;s<255;s++){
    /* P(s|1), prob of receiving s given 1 transmitted */
    p1 = normal(((s-OFFSET+0.5)/amp - 1)/noise) -
      normal(((s-OFFSET-0.5)/amp - 1)/noise);
    
    /* P(s|0), prob of receiving s given 0 transmitted */
    p0 = normal(((s-OFFSET+0.5)/amp + 1)/noise) -
      normal(((s-OFFSET-0.5)/amp + 1)/noise);
    
#ifdef notdef
    printf("P(%d|1) = %lg, P(%d|0) = %lg\n",s,p1,s,p0);
#endif
    metrics[0][s] = log2(2*p0/(p1+p0)) - bias;
    metrics[1][s] = log2(2*p1/(p1+p0)) - bias;
  }
  /* 255 is also a special value */
  /* P(s|1) */
  p1 = 1 - normal(((255-OFFSET-0.5)/amp - 1)/noise);
  /* P(s|0) */
  p0 = 1 - normal(((255-OFFSET-0.5)/amp + 1)/noise);
  
  metrics[0][255] = log2(2*p0/(p1+p0)) - bias;
  metrics[1][255] = log2(2*p1/(p1+p0)) - bias;
#ifdef	notdef
  /* The probability of a raw symbol error is the probability
   * that a 1-bit would be received as a sample with value
   * 0-128. This is the offset normal curve integrated from -Inf to 0.
   */
  printf("symbol Pe = %lg\n",normal(-1/noise));
#endif
  for(bit=0;bit<2;bit++){
    for(s=0;s<256;s++){
      /* Scale and round to nearest integer */
      mettab[bit][s] = floor(metrics[bit][s] * scale + 0.5);
#ifdef	notdef
      printf("metrics[%d][%d] = %lg, mettab = %d\n",
	     bit,s,metrics[bit][s],mettab[bit][s]);
#endif
    }
  }
}