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//
// scramble_example.c
//
// Data-scrambling example. Physical layer synchronization of
// received waveforms relies on independent and identically
// distributed underlying data symbols. If the message sequence,
// however, is '00000....' and the modulation scheme is BPSK,
// the synchronizer probably won't be able to recover the symbol
// timing. It is imperative to increase the entropy of the data
// for this to happen. The data scrambler routine attempts to
// 'whiten' the data sequence with a bit mask in order to achieve
// maximum entropy. This example demonstrates the interface.
//
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "liquid.h"
float compute_entropy(unsigned char * _x,
unsigned int _n);
int main() {
unsigned int n=32; // number of data bytes
unsigned char x[n]; // input data
unsigned char y[n]; // scrambled data
unsigned char z[n]; // unscrambled data
unsigned int i;
// generate data
for (i=0; i<n; i++)
x[i] = rand() % 2 ? 0x0f : 0xc8;
// scramble input
memmove(y,x,n);
scramble_data(y,n);
// unscramble result
memmove(z,y,n);
unscramble_data(z,n);
float Hx = compute_entropy(x,n);
float Hy = compute_entropy(y,n);
// print results
printf("i\tx\ty\tz\n");
printf("--\t--\t--\t--\n");
for (i=0; i<n; i++)
printf("%u\t%.2x\t%.2x\t%.2x\n", i, x[i], y[i], z[i]);
printf("H(x) = %12.8f\n", Hx);
printf("H(y) = %12.8f\n", Hy);
printf("done.\n");
return 0;
}
// raw entropy calculation, orders 1, 2, 4, 8
float compute_entropy(unsigned char * _x,
unsigned int _n)
{
unsigned int i;
unsigned int j;
// initialize counter arrays
unsigned int c1[2]; // 1-bit symbols
unsigned int c2[4]; // 2-bit symbols
unsigned int c4[16]; // 4-bit symbols
unsigned int c8[256]; // 8-bit symbols
for (i=0; i<2; i++) c1[i] = 0;
for (i=0; i<4; i++) c2[i] = 0;
for (i=0; i<16; i++) c4[i] = 0;
for (i=0; i<256; i++) c8[i] = 0;
for (i=0; i<_n; i++) {
// b:1
for (j=0; j<8; j++) c1[ (_x[i] >> j) & 0x01 ]++;
// b:2
for (j=0; j<8; j+=2) c2[ (_x[i] >> j) & 0x03 ]++;
// b:4
for (j=0; j<8; j+=4) c4[ (_x[i] >> j) & 0x0f ]++;
// b:8
c8[ _x[i] ]++;
}
// compute entropy
float H1 = 0.0f;
float H2 = 0.0f;
float H4 = 0.0f;
float H8 = 0.0f;
float p;
for (i=0; i<2; i++) {
p = (float) c1[i] / (float)(8*_n);
H1 -= p * log2f(p+1e-12f);
}
H1 /= 1.0f;
for (i=0; i<4; i++) {
p = (float) c2[i] / (float)(4*_n);
H2 -= p * log2f(p+1e-12f);
}
H2 /= 2.0f;
for (i=0; i<16; i++) {
p = (float) c4[i] / (float)(2*_n);
H4 -= p * log2f(p+1e-12f);
}
H4 /= 4.0f;
for (i=0; i<256; i++) {
p = (float) c8[i] / (float)(_n);
H8 -= p * log2f(p+1e-12f);
}
H8 /= 8.0f;
#if 0
printf("H1 : %12.8f\n", H1);
printf("H2 : %12.8f\n", H2);
printf("H4 : %12.8f\n", H4);
printf("H8 : %12.8f\n", H8);
#endif
// not sure if product is truly the entropy, but
// it is a fair assessment
return H1 * H2 * H4 * H8;
}
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