TRELLIS-ORIENTED DECOMPOSITION AND TRELLIS COMPLEXITY OF COMPOSITE-LENGTH CYCLIC CODES

The trellis complexity of composite-length cyclic codes (CLCC's) is ad dressed. We first investigate the trellis properties of concatenated a nd product codes in general. Known factoring of CLCC's into concatenat ed subcodes is thereby employed to derive upper bounds on the minimal trellis size and state-space profile. New decomposition of CLCC's into product subcodes is established and utilized to derive further upper, bounds on the trellis parameters. The coordinate permutations that co rrespond to these bounds are exhibited. Additionally, new results on t he generalized Hamming weights of CLCC's are obtained. The reduction i n trellis complexity of many CLCC's leads to soft-decision decoders wi th relatively low complexity.