Computationally-efficient iterative decoding for storage system design: Min-Sum refined

In this paper we propose a computationally-efficient, iterative decoding algorithm that is well-suited for storage systems with very stringent reliability constraints and low redundancy/high code rate requirements. The proposed Dual-Scaling Min-Sum (DS-MSA) overcomes certain deficiencies of the Min-Sum approximation when used for decoding graph-based codes. We observe that a small but non-negligible fraction of check-to-variable messages is underestimated by the Normalized Min-Sum algorithm in the low error rate region. By carefully adjusting the scaling factor for the variable-to-check message with the smallest magnitude, we develop the DS-MSA algorithm characterized by two scaling parameters. The proposed algorithm (1) outperforms Sum-Product and (Normalized) Min-Sum algorithms in the very low error rate regime, (2) maintains the low-complexity feature of the Min-Sum, and (3) can be easily combined with existing decoder implementations.