Algebraic Optimization of Binary Spatially Coupled Measurement Matrices for Interval Passing

TL;DR

This paper introduces algebraic methods to design binary spatially coupled measurement matrices that minimize harmful structures, enabling more reliable sparse signal reconstruction with the interval passing algorithm.

Contribution

It presents a novel algebraic lifting approach to construct SC measurement matrices with fewer termatiko sets, improving IPA performance for denser signals.

Findings

Reduced termatiko sets by eliminating length-12 cycles.

Almost error-free reconstruction for denser signals.

Enhanced performance of IPA with SC matrices.

Abstract

We consider binary spatially coupled (SC) low density measurement matrices for low complexity reconstruction of sparse signals via the interval passing algorithm (IPA). The IPA is known to fail due to the presence of harmful sub-structures in the Tanner graph of a binary sparse measurement matrix, so called termatiko sets. In this work we construct array-based (AB) SC sparse measurement matrices via algebraic lifts of graphs, such that the number of termatiko sets in the Tanner graph is minimized. To this end, we show for the column-weight-three case that the most critical termatiko sets can be removed by eliminating all length-12 cycles associated with the Tanner graph, via algebraic lifting. As a consequence, IPA-based reconstruction with SC measurement matrices is able to provide an almost error free reconstruction for significantly denser signal vectors compared to uncoupled AB LDPC measurement matrices.