IIR critically subsampled filterbanks implementing systematic Reed-Solomon codes

The last decade shows a growing interest in soft decoding techniques, motivated by a soft decoding gain of roughly 2dB. Most of the techniques are applied to concatenated codes, with turbo codes as the most famous example. This is in strong contrast with many existing coding schemes where Reed-Solomon (RS) codes are common. Recently, we unveiled an (FIR) 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 SISO RS decoder. The aim of this paper is twofold: in the first part, an algebraic shortcut to construct the FIR filterbank is presented. This method gives a lot of insight into the algebraic structure of RS codes and their corresponding filterbanks. In the second part, motivated by the importance of systematic RS codes, a critically subsampled IIR filterbank structure implementing a systematic RS code is examined. The SISO RS decoder based on the IIR filterbank shows a lower computational complexity and better performance compared to the FIR counterpart.