Breaking the Computational Bottleneck: Design of Near-Optimal High-Memory Spatially-Coupled Codes

Abstract

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an underlying block code, followed by rearranging and concatenating the partitioned components in a convolutional manner. The number of partitioned components determines the memory of SC codes. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. While adopting higher memories results in improved SC code performance, obtaining finite-length, high-performance SC codes with high memory is known to be computationally challenging. We break this computational bottleneck by developing a novel probabilistic framework that obtains (locally) optimal density distributions via gradient descent. Starting from random partitioning matrices abiding by the obtained distribution, we perform low-complexity optimization algorithms that minimize the number of detrimental objects to construct high-memory, high-performance quasi-cyclic SC codes. We apply our framework to various objects of interests, from the simplest short cycles, to more sophisticated objects such as concatenated cycles aiming at finer-grained optimization. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and optimized SC codes with uniform partitioning. The performance gain is shown to be universal over a variety of channels, from canonical channels such as additive white Gaussian noise and binary symmetric channels, to practical channels underlying flash memory and magnetic recording systems.

arXiv comment26 pages, 30 figures, 2 tables, the manuscript has been submitted to IEEE Transactions on Information Theory. arXiv admin note: substantial text overlap with arXiv:2101.09962

References in corpus (7)

• Spatially Coupled LDPC Codes Constructed from Protographs
• Threshold Saturation for Spatially-Coupled LDPC and LDGM Codes on BMS Channels
• Searching for Voltage Graph-Based LDPC Tailbiting Codes with Large Girth
• Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length
• A Combinatorial Methodology for Optimizing Non-Binary Graph-Based Codes: Theoretical Analysis and Applications in Data Storage
• Design of Non-Binary Quasi-Cyclic LDPC Codes by ACE Optimization
• Minimizing the Number of Detrimental Objects in Multi-Dimensional Graph-Based Codes