On the viterbi decoding of linear block codes

This paper presents an overview of the trellis decoding of binary and non-binary linear block codes using of the Viterbi Algorithm (VA) in a variety of mobile channels. The construction of Bahl-Cocke-Jelinek-Raviv (BCJR) block code trellises is described, as well as the application of a block-wise VA to these trellises as an optimal Maximum-Likelihood (ML) decoder. Both hard and soft decision decoding is considered, as well as the incorporation of Channel State Information (CSD in the calculation of VA branch metrics. An extensive simulation study is presented to validate the VA as an efficient ML block code decoder. Simulation results are presented for hard and soft decision decoded binary Hamming and non-binary Reed-Solomon (RS) block codes under varying Additive White Gaussian Noise (AWGN) and flat fading channel conditions. The Bit Error Rate (BER) performances of reduced and unreduced trellises are also compared. Special attention is given to the influence of CSI on the BER performance of Viterbi decoded linear block codes. Unique contributions made by this paper in the field of linear block coding include: Novel techniques for binary and non-binary block code BCJR trellis expurgation and reduction. BER performance results for VA decoded non-linear RS block codes in flat fading channel conditions employing varying degrees of CSI, and simulation results for the VA decoding of a binary cyclic linear block code employing a reduced trellis structure.