Efficient APP decoding of nonsystematic encoded block codes

We consider the problem of trellis-based symbol-by-symbol a posteriori probability (APP) decoding of information symbols of nonsystematic encoded 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 the block code. We introduce an extended trellis representation for block codes by inserting systematic symbols into the code. This enables the application of the BCJR algorithm as well as trellis based decoding in the dual code space. Complexity properties of the extended trellis are investigated.