A good online tutorial is Charan Langton's Coding and decoding with Convolutional Codes. (Fig. 10 seems incorrect, however, as three arrows go into one state.)

To visualize a Trellis on paper, I found the following useful:

Available as: .pdf and .svg

Some code (test.cpp) using the it++ library for C++ which illustrates the decoding example given in the tutotial:

// compile with 
//   g++ -Wall -o test test.cpp -litpp
// run with
//   ./test

#include <cstdio>
#include <cassert>

#include <itpp/itbase.h>
#include <itpp/itcomm.h>

// example program, following http://www.complextoreal.com/convo.htm

int main() {
    unsigned int invR = 2; // inverse rate
    unsigned int m = 4; // memory
            
    itpp::bvec u = "1 0 1 1 "; // input bits
                
    std::cout << "uncoded: " << u << "\n";
                    
    itpp::Convolutional_Code cc;
    itpp::BPSK bpsk;
                            
    itpp::ivec generators;
    generators.set_size(invR, false);
    generators(0) = 15; // polynomials
    generators(1) = 13; 
                                            
    printf("constraint length %u\n", m-1);
                                                
    cc.set_generator_polynomials(generators, m);
    itpp::bvec coded_bits = cc.encode_tail(u);
    std::cout << "coded: " << coded_bits << "\n";
                                                                
    itpp::vec symbols = bpsk.modulate_bits(coded_bits);
    printf("symbols %d\n", symbols.size());
                                                                            
    // channel here
    itpp::vec received_symbols = symbols + 0.3*itpp::randn(symbols.size());
                                   
    itpp::bvec decoded_bits = cc.decode_tail(received_symbols);
    std::cout << "decoded: " << decoded_bits << "\n";
}

posted at: 17:59 | path: /academic | permanent link