Sequential decoding, commonly applied to substitution channels, is a sub-optimal alternative to Viterbi decoding with significantly reduced memory costs. In this work, a sequential decoder for convolutional codes over channels that are prone to insertion, deletion, and substitution errors, is described and analyzed. Our decoder expands the code trellis by a new channel-state variable, called drift state, as proposed by Davey and MacKay. A suitable decoding metric on that trellis for sequential decoding is derived, generalizing the original Fano metric. The decoder is also extended to facilitate the simultaneous decoding of multiple received sequences that arise from a single transmitted sequence. Under low-noise environments, our decoding approach reduces the decoding complexity by a couple orders of magnitude in comparison to Viterbi's algorithm, albeit at slightly higher bit error rates. An analytical method to determine the computational cutoff rate is also suggested. This analysis is supported with numerical evaluations of bit error rates and computational complexity, which are compared with respect to optimal Viterbi decoding.

翻译：序列译码通常应用于替代信道，是维特比译码的一种次优替代方案，具有显著降低的内存成本。本文描述并分析了一种针对易受插入、删除和替代错误影响的信道上卷积码的序列译码器。我们的译码器采用Davey和MacKay提出的方法，引入一种称为漂移状态的新信道状态变量来扩展码格图。推导了适用于该格图序列译码的译码度量，推广了原始的Fano度量。该译码器还进行了扩展，以支持对单一传输序列产生的多个接收序列进行同时译码。在低噪声环境下，与维特比算法相比，我们的译码方法将译码复杂度降低数个数量级，尽管误码率略有升高。本文还提出了一种计算截止速率的分析方法。该分析以误码率和计算复杂度的数值评估作为支持，并与最优维特比译码进行了对比。