Synchronization recovery and state model reduction for soft decoding of variable length codes

TL;DR

This paper introduces an analytic method to evaluate the error resilience of variable length codes with trellis decoding and sequence length constraints, demonstrating that state aggregation maintains performance while reducing complexity.

Contribution

It presents a novel analytic approach to assess VLC error resilience and shows that state aggregation preserves performance with lower decoding complexity.

Findings

State aggregation does not significantly affect error resilience.

Performance of length-constrained Viterbi decoding is maintained with aggregated models.

Complexity can be further reduced by projecting onto smaller state models.

Abstract

Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence. If the number of symbols and/or bits transmitted are known by the decoder, termination constraints can be incorporated in the decoding process. All the paths in the trellis which do not lead to a valid sequence length are suppressed. This paper presents an analytic method to assess the expected error resilience of a VLC when trellis decoding with a sequence length constraint is used. The approach is based on the computation, for a given code, of the amount of information brought by the constraint. It is then shown that this quantity as well as the probability that the VLC decoder does not re-synchronize in a strict sense, are not significantly altered by appropriate trellis states aggregation. This proves that the performance obtained by running a length-constrained Viterbi decoder on aggregated state models approaches the one obtained with the bit/symbol trellis, with a significantly reduced complexity. It is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size.