Sequential Decoding of Multiple Traces Over the Syndrome Trellis for Synchronization Errors

TL;DR

This paper introduces a novel joint decoding method using sequential decoders over the syndrome trellis for multiple sequences with synchronization errors, reducing complexity and improving performance in short blocklength regimes.

Contribution

It adapts sequential decoders for joint decoding over the syndrome trellis, extending to bidirectional decoding to handle erasures, offering a more efficient solution for synchronization errors.

Findings

Outperforms separate-BCJR decoding in certain conditions

Reduces decoding complexity for high-rate convolutional codes

Effective in short blocklength regimes

Abstract

Standard decoding approaches for convolutional codes, such as the Viterbi and BCJR algorithms, entail significant complexity when correcting synchronization errors. The situation worsens when multiple received sequences should be jointly decoded, as in DNA storage. Previous work has attempted to address this via separate-BCJR decoding, i.e., combining the results of decoding each received sequence separately. Another attempt to reduce complexity adapted sequential decoders for use over channels with insertion and deletion errors. However, these decoding alternatives remain prohibitively expensive for high-rate convolutional codes. To address this, we adapt sequential decoders to decode multiple received sequences jointly over the syndrome trellis. For the short blocklength regime, this decoding strategy can outperform separate-BCJR decoding under certain channel conditions, in addition to reducing decoding complexity. To mitigate the occurrence of a decoding timeout, formally called erasure, we also extend this approach to work bidirectionally, i.e., deploying two independent stack decoders that simultaneously operate in the forward and backward directions.