No abstract

No abstract

It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q (n-k) states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer than q n-k. For a binary (n,rz-1) single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm.

We consider a windowed decoding scheme for LDPC convolutional codes that is based on the belief-propagation (BP) algorithm. We discuss the advantages of this decoding scheme and identify certain characteristics of LDPC convolutional code ensembles that exhibit good performance with the windowed decoder. We will consider the performance of these ensembles and codes over erasure channels with and without memory. We show that the structure of LDPC convolutional code ensembles is suitable to obtain performance close to the theoretical limits over the memoryless erasure channel, both for the BP decoder and windowed decoding. However, the same structure imposes limitations on the performance over erasure channels with memory.

No abstract