Precision Bits Can Be Reduced by One in Max-Log-MAP-Based Decoder

The addition and taking the maximum (max) operations, as well as all the quantized data involved in the max-log-MAP turbo decoding algorithm form a commutative max-sum semiring. In this paper performance degradation of turbo decoding caused by shift operations using fixed-point data representation and unified precision bits is solved when the distributive law is properly applied to this semiring, with a bonus of considerable computational saving and precision bit reduction from 3 to 2 for all the pertinent variables with negligible performance degradation.