Filterbank decompositions for BCH-codes with applications to soft decoding and code division multiple acces systems

Multirate systems and filterbanks are known to be powerful tools in image and audio applications. Recently, they are also recognised to play an important role in communication systems. This paper covers the use of filterbanks in a coding context. It is shown that their inherent periodically time varying character matches remarkably well with the cyclic properties of the family of Bose-Chaudhuri-Hochquenghem (BCH) codes. In this paper, the important subclass of Reed-Solomon (RS) codes is dealt with first. This section of the paper proves that an RS code can be implemented by a critically subsampled filterbank. The redundancy is added by the subbandfilters, which are shown to be variants of non-primitive BCH codes. The second part of the paper deals with BCH codes. In this part, a BCH code is decomposed as a sum of critically subsampled filterbanks. The critical subsampling is an important aspect in a number of applications. The use of these filterbanks in a CDMA system and in a soft-in soft-out (SISO) decoding context is briefly discussed