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On Low-Complexity Maximum-Likelihood Decoding of Convolutional Codes

机译：卷积码的低复杂度最大似然译码

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摘要

This letter considers the average complexity of maximum-likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA), complexity reduction methods often use the sum log likelihood (SLL) of a Markov path as a bound to disprove the optimality of other Markov path sets and to consequently avoid exhaustive path search. In this letter, it is shown that SLL-based optimality tests are inefficient if one fixes the coding memory and takes the codeword length to infinity. Alternatively, optimality of a source symbol at a given time index can be testified using bounds derived from log likelihoods of the neighboring symbols. It is demonstrated that such neighboring log likelihood (NLL)-based optimality tests, whose efficiency does not depend on the codeword length, can bring significant complexity reduction. The results are generalized to ML sequence detection in a class of discrete-time hidden Markov systems.
机译：这封信考虑了卷积码最大似然（ML）解码的平均复杂度。可以将ML解码建模为找到通过马尔可夫图的最可能路径。与维特比算法（VA）集成在一起，降低复杂度的方法通常使用马尔可夫路径的总对数似然（SLL）作为边界，以证明其他马尔可夫路径集的最优性，从而避免详尽的路径搜索。在这封信中，表明如果固定编码存储器并将码字长度设为无穷大，则基于SLL的最优性测试效率低下。备选地，可以使用从相邻符号的对数似然得出的界限来证明给定时间索引处源符号的最优性。已经证明，这种基于效率的效率不取决于码字长度的基于邻对数似然（NLL）的最优性测试可以带来显着的复杂性降低。将结果推广到一类离散时间隐马尔可夫系统中的ML序列检测。

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