A novel metric representation for low-complexity log-MAP decoder

In this paper, we propose a novel state metric representation of log-MAP decoding which does not require any rescaling in both forward and backward path metrics and LLR (log-likelihood ratio). In order to guarantee the metric values to be within the range of precision, rescaling has been performed both for forward and backward metric computation, which requires considerable arithmetic operations and decoding delay. In this paper, by applying the homomorphism in a finite abelian group Z_b associated with modulo 2^b addition, we show that the proposed metric representation does not need any rescaling in metric and LLR computation. In this general observation, we show that the Hekstra´s scheme is a special case for the path metric rescaling. Besides the fact that the proposed technique saves design time considerably, we show through complexity analysis that proposed technique saves the ACSU (add-compare-select unit) complexity and reduces the critical path delay of the decoder significantly.