Decoding of Convolutional Codes

This chapter reviews general descriptions and analyses of important decoding algorithms for convolutional codes. The Viterbi algorithm that outputs the codeword maximizing the probability of the received sequence conditioned on the information sequence is analyzed. It has been shown that the Viterbi algorithm is an efficient decoding method, particularly when the advantage of soft decisions is fully exploited. The path weight enumerators and the extended path enumerators obtained from the state-transition diagram of the convolutional encoder are used to derive tight upper bounds on the decoding error probabilities for both hard and soft decisions. A Markovian technique is described for an exact calculation of the bit error probability for the Viterbi algorithm. The chapter considers an a posteriori probability (APP) decoding algorithm, and highlights that this symbol decoding algorithm outputs the a posteriori probability for each of the transmitted information symbols.