Critically Subsampled Filterbanks for SISO Reed–Solomon Decoding

In the last decade, there has been a growing interest in soft decoding techniques. These techniques are used in the context of concatenated codes, with Turbo codes as the main example, but are almost never applied to existing classical codes. In this paper, the family of Reed-Solomon (RS) codes is considered, and the complexity problem of soft-in soft-out (SISO) RS decoding is tackled by breaking RS codes into several smaller subcodes. Finally, the decoders of these subcodes work together in a Turbo-like fashion (Gallager's algorithm) to find an approximate maximum a posteriori (MAP) solution. The decomposition that is presented here is based on critically subsampled filterbanks, with one subcode in each subband. A critically subsampled filterbank allows us to define a number of parallel independent subcodes. Furthermore, noncritically subsampled filterbanks have a larger number of subband variables than the codeword length, causing a message passing decoder (Gallager's algorithm) to fail. This paper focuses on the construction of such filterbanks, starting from noncritically subsampled filterbanks, it gradually evolves towards a critically subsampled filterbank