GRADE-AO: Towards Near-Optimal Spatially-Coupled Codes With High Memories

TL;DR

This paper introduces a probabilistic framework for designing high-memory spatially-coupled codes that outperform existing codes by optimizing partitioning matrices, enabling near-optimal performance in data storage and streaming applications.

Contribution

It proposes a gradient descent-based method to optimize partitioning matrices for high-memory SC codes, improving performance over uniform partitioning methods.

Findings

Codes outperform state-of-the-art SC codes with same constraint length

Optimized codes show significant performance gains in simulations

Method enables near-optimal high-memory SC code design

Abstract

Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their excellent performance. 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. While adopting higher memories results in improved SC code performance, obtaining optimal SC codes with high memory is known to be hard. In this paper, we investigate the relation between the performance of SC codes and the density distribution of partitioning matrices. We propose a 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 over the cycle properties to construct high memory, high performance quasi-cyclic SC codes. Simulation results show that codes obtained through our proposed method notably outperform state-of-the-art SC codes with the same constraint length and codes with uniform partitioning.