The BCJR trellis and trellis decoders for some BCH codes

This paper provides an overview of trellis descriptions for block codes. The design and implementation of efficient trellis decoders for the (32, 26) and the (32, 21) BCH codes is then considered in some detail. Minimum edge and vertex counts for the (32, 26) code are derived, and then generalized for arbitrary extended Hamming codes. A subcode analysis technique is used to tighten the lower bound on edge complexity for the (32, 21) code. A trellis is then found that satisfies the optimized lower bound with equality.