On memory redundancy in the BCJR algorithm for nonrecursive shift register processes

For computation of a posteriori probabilities (APPs), the well-known Bahl, Cocke, Jelinek, and Raviv (1974) algorithm is often applied. If the underlying model is a nonrecursive shift register process, it is shown that this algorithm obtains a general memory redundancy if the computation is performed over a commutative semiring with an absorbing zero element. The result is of particular interest for the BCJR algorithm carried out in the max-log domain.