Critically subsampled filterbanks implementing Reed-Solomon codes: an algebraic point of view

The last decade shows a growing interest in soft decoding techniques, motivated by a soft decoding gain of roughly 2 dB. Most of the techniques are applied to concatenated codes, in particular to turbo codes. This is in strong contrast to many existing coding schemes where Reed-Solomon (RS) codes are common. Recently, we unveiled a filterbank structure behind the RS codes. Using this filterbank decomposition, a RS code is broken into many smaller subcodes that can consequently be used to build a soft-in soft-out (SISO) RS decoder. A limitation of this previous work is that it is only applicable to RS codes where the codeword and dataword length are not coprime. In this paper, this constraint is eliminated. A purely algebraic method is presented to construct a filterbank decomposition for any RS code, as long as a subfield exists in the Galois field in which the RS code operates. This method gives a lot of insight into the algebraic structure of RS codes and their corresponding filterbanks.