/* 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		}	}}