Recursive Algorithm for Maximum Likelihood Decoding of Non-Binary Codes

The maximum likelihood (ML) decoding is essential for error-correcting codes, but the ML decoding problem is NP-hard in general. This suggests that there is no single universal ML decoding algorithm that works efficiently for an arbitrary code. Therefore researchers developed many ML decoding algorithms with different characteristics so that they can be used complementary. This study is intended to propose an ML decoding algorithm that can be used for general non-binary linear codes. The algorithm proposed in this paper is a generalization of the adaptive and recursive ML decoding algorithm that was studied for binary codes. This paper shows that the structure and properties of linear codes that helped realizing the decoding algorithm for binary codes can be generalized to nonbinary cases, and reports the implementation results of the soft-decision ML decoding alogorithm for several non-binary linear codes.