A Unified, SNR-Aware SC-LDPC Code Design With Applications to Magnetic Recording

Spatially coupled (SC)-low-density parity-check (LDPC) codes are known to have outstanding error-correction performance and low decoding latency, which make them an excellent choice for high-density magnetic recording (MR) technologies. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, we propose a unified framework for jointly optimizing the codes' thresholds and cycle counts to address both regimes. We focus on circulant-based (CB) SC-LDPC code family as a representative, high-performance exemplar of structured SC-LDPC codes. The framework is based on efficient traversal and pruning of the code search space, building on the fact that the performance of a CB SC-LDPC code depends on some characteristics of the code's partitioning matrix, which by itself is much smaller than the code's full parity-check matrix. We then propose an algorithm that traverses all non-equivalent partitioning matrices and outputs a list of codes, each offering an attractive point on the trade-off between asymptotic and finite-length performance. Our simulations show that our framework results in SC-LDPC codes that outperform the state-of-the-art constructions, over both additive white Gaussian noise (AWGN) and partial response (PR) channel models, and that it offers the flexibility to choose low-signal-to-noise ratio (SNR), high-SNR, or in- between SNR region considering system requirements, e.g., that of the MR device.