Implementation of Viterbi algorithm

Matlab implementation of Viterbi algorithm with early decision for binary encoding. The code containes several files:

• trellis.m: returns the trellis structure for the encoding;
• viterbi_algorithm.m: carries out the choice of the less cost path for the sequence of bits in the window considered, by calling the function get_cost_enter() and then selecting the bits associated with the less cost path with the function backtrack();
• run.m: randomly generates a signal mapped with the function trellis() and adds some noise. Then call the function viterbi_algorithm() to reconstruct the original signal. This operation is repeted until the Signal-To-Noise rate is below a certain threshold;
• get_cost_enter.m: computes the cost for a sequence of 2 mapped bits;
• backtrack.m: reconstructs the original signal from the trellis considered in the trellis() function.

Usage

Choose three window lenghts and the confidence interval size in terms of minimum number of wrong bits in the file run.m: the file plots the trends of the Bit Error Rate over the Signal-To-Noise rate for the three windows chosen.

As displayed in the image, the higher is the delay, the more the BIR of the signal is close to a Viterbi algorithm without windows and consequently, the quickly BIR decreases while SNR increases.