A Posteriory Probability Decoding of Nonsystematically Encoded Block Codes

We consider the problem of symbol-by-symbol a posteriori probability (APP) decoding for information symbols of nonsystematically encoded block codes. This problem arises at soft concatenated decoding of generalized concatenated block codes. The well-known BCJR algorithm for efficient APP decoding is not able to solve the problem if it runs on the minimal code trellis of a block code. We introduce an extended trellis representation for block codes, which includes encoding information and thus makes it possible to apply the BCJR algorithm as well as trellis-based decoding in the dual code space. Complexity properties of the extended trellis are investigated.