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. 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 associated with modulo 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 [5] is a special case for the path metric rescaling. Besides the fact that proposed technique saves design time considerably, we show through the complexity analysis that proposed technique saves the ACSU (Add-compareselect unit) complexity and reduces the critical path delay of decoder significantly.