Adaptive error correction coding scheme for computations in the noisy min-sum decoder

With scaling of process technologies and increase in process variations, embedded memories will be inherently unreliable. In this paper, we propose redundancy-free adaptive error-correcting codes for the noisy min-sum decoder subject to memory errors. We consider the popular memory error model with a binary symmetric channel. We first revisit the density evolution analysis proposed by Balatsoukas-Stimming and Burg for the noisy min-sum decoder. Two important consequences of the density evolution analysis are: (a) after a large enough number of iterations, most of the messages have large magnitudes, and the residual errors are mostly from the sign bit flips due to memory failures, and (b) errors in the least significant bits in large-magnitude messages have a negligible effect on the residual error rate. We thus propose adaptive error-correcting codes to protect sign bits by least significant bits when the messages have large magnitudes. The proposed coding scheme does not require any further data storage (i.e., this code is redundancy-free). Density evolution analysis for the noisy min-sum decoder implementing the proposed coding scheme is derived, demonstrating that the proposed decoder achieves a residual error rate that is on the order of the square of the residual error rate achieved by the nominal min-sum decoder. Simulation results on the finite block length LDPC code also agree with this density evolution analysis.