init commit

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
+// Updated March 2014 (!)
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+extern int Verbose;
+
+// Normal function integrated from -Inf to x. Range: 0-1
+static double normal(double x){
+  return 0.5 + 0.5*erf(x/M_SQRT2);
+}
+
+// Generate log-likelihood metrics for 8-bit soft quantized channel assuming AWGN and BPSK
+void gen_met(
+     int mettab[2][256], // Metric table, [sent sym][rx symbol]
+     double signal,	 // Signal amplitude, units
+     double noise,	 // Noise amplitude, units (absolute, no longer relative!)
+     double bias,	 // Metric bias; 0 for viterbi, rate for sequential
+     double scale		 // Metric scale factor */
+){
+  int s;
+  double metrics0,metrics1,p0,p1;
+  double left0,left1,right0,right1;
+  double inv_noise;
+
+  inv_noise = 1./noise;
+
+  // Compute the channel transition probabilities, i.e., the probability of receiving each of the
+  // 256 possible values when 0s and 1s were sent.
+  // The bins are assumed to be centered on their nominal values:
+  // Bin 0; -infinity < v < -127.5
+  // Bin 1: -127.5 < v < -126.5
+  // Bin 128: -0.5 < v < +0.5
+  // Bin 255: +126.5 < v < +infinity
+  left0 = left1 = 0.0; // area below bin 0 is zero
+  for(s=0;s<256;s++){
+
+    // Find the area below and in this bin, subtract the area below and in the previous bin,
+    // leaving just the area of this bin.
+    // The area above bin 255 is zero.
+    right0 = (s != 255) ? normal((s - 128 + 0.5 + signal) * inv_noise) : 1.0;
+    right1 = (s != 255) ? normal((s - 128 + 0.5 - signal) * inv_noise) : 1.0;
+
+    p0 = right0 - left0;    // p0 = P(s|0), prob of receiving s given that a 0 was sent
+    p1 = right1 - left1;    // p1 = P(s|1), prob of recieving s given that a 1 was sent
+
+    left1 = right1;
+    left0 = right0;
+
+    // Compute log-likelihood ratios assuming even balance of 0's and 1's on channel
+    if(p0 == p1){
+      // At high SNR, extremal sample values may underflow to p0 == p1 == 0, giving
+      // infinitely bad metrics for what might actually be very good samples if
+      // actually encountered. Not sure what's right here, so I punt and treat both as erasures
+      metrics0 = metrics1 = -bias;
+    } else {
+      // The smallest value from log2() is about -32, so approximate log2(0) as -33.
+      // Alternatively I could represent it as -INT_MAX, the worst possible metric, but that seems excessive
+      metrics0 = (p0 == 0) ? -33.0 : log2(2*p0/(p1+p0)) - bias;
+      metrics1 = (p1 == 0) ? -33.0 : log2(2*p1/(p1+p0)) - bias;
+      // Equivalent:
+      metrics0 = (p0 == 0) ? -33.0 : 1 + log2(p0) - log2(p1+p0) - bias;
+      metrics1 = (p1 == 0) ? -33.0 : 1 + log2(p1) - log2(p1+p0) - bias;
+    }
+    // Scale and round for table
+    mettab[0][s] = lrint(metrics0 * scale);
+    mettab[1][s] = lrint(metrics1 * scale);
+    if(Verbose){
+      printf("s=%3d P(s|0) = %-12lg P(s|1) = %-12lg P(s) = %-12lg",
+	     s,p0,p1,(p1+p0)/2.);
+      printf(" metrics0 = %-12lg [%4d]",metrics0,mettab[0][s]);
+      printf(" metrics1 = %-12lg [%4d]\n",metrics1,mettab[1][s]);
+    }
+  }
+}