Coding for Channels with SNR Variation: Spatial Coupling and Efficient Interleaving.

In magnetic-recording systems, consecutive sections experience different signal to noise ratios (SNRs). To perform error correction over these systems, one approach is to use an individual block code for each section. However, a section affected by a lower SNR shows a weaker performance compared to a section affected by a higher SNR. A commonly used technique is to perform interleaving across blocks to alleviate negative effects of varying SNR. However, this scheme is typically costly to implement and does not result in the best performance. Spatially-coupled (SC) codes are a family of graph-based codes with capacity approaching performance and low latency decoding. An SC code is constructed by partitioning an underlying block code to several component matrices, and coupling copies of the component matrices together. The contribution of this paper is threefold. First, we present a new partitioning technique to efficiently construct SC codes with column weights 4 and 6. Second, we present an SC code construction for channels with SNR variation. Our SC code construction provides local error correction for each section by means of the underlying codes that cover one section each, and simultaneously, an added level of error correction by means of coupling among the underlying codes. Consequently, and because of the structure of SC codes, more reliable sections can help unreliable ones to achieve an improved performance. Third, we introduce a low-complexity interleaving scheme specific to SC codes that further improves their performance over channels with SNR variation. Our simulation results show that our SC codes outperform individual block codes by more than 1 and 2 orders of magnitudes in the error floor region compared to the block codes with and without regular interleaving, respectively. This improvement is more pronounced by increasing the memory and column weight.