A State-Reduction Viterbi Decoder for Convolutional Codes with Large Constraint Lengths

A popular combination in modern coding system is the convolutional encoder and the Viterbi decoder [5]. With a proper design, they can jointly provide an acceptable performance with feasible decoding complexity. In such a combination, a tradeoff on the error performance and the decoding complexity resides on the choice of the code constraint length. Specifically, the probability of Viterbi decoding failure decreases exponentially as the code constraint length increases. However, an increment of code constraint lengths also exponentially increases the computational effort of the Viterbi decoder. Nowadays, the implementation technology on the Viterbi decoder can only accommodate convolutional codes with a constraint length no greater than nine, which somehow limits the achievable error performance. On the other hand, the construction of convolutional codes with very large constraint lengths are now possible in both theory and practice, yet Monte Carlo simulations of their resultant maximum-likelihood performance is technically infeasible. The authors of [10] then presented a new simulation technique called Important Sampling, which can accurately estimate the maximum-likelihood error performance of convolutional codes with constraint length up to 24 or higher. The authors proved by Important Sampling simulations that the error performance of convolutional codes with certain constraint length can actually be close to the Shannon limit although no feasible decoder can decode such codes. In this thesis, we propose a reduced-state Viterbi decoder with fixed decoding complexity for use of codes with large constraint lengths. Since, by [10], the maximum-likelihood error