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

For computation of a posteriori probabilities (APP’s), the wellknown BCJR algorithm is often applied. If the underlying model is a nonrecursive shift register process, it will be 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.