/* 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 */intgen_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    }  }}