Robust error correction for real-valued signals via message-passing decoding and spatial coupling

TL;DR

This paper introduces a robust error correction method for real-valued signals using message-passing decoding and spatial coupling, significantly improving performance over traditional convex relaxation techniques.

Contribution

It combines approximate message passing with spatially-coupled measurement matrices to enhance error correction robustness in noisy, real-valued signals.

Findings

Outperforms convex-relaxation decoders even at small sizes

Achieves significant robustness improvements with spatial coupling

Validated through state evolution analysis and numerical simulations

Abstract

We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and the spatially-coupled measurement matrix in compressed sensing we show that the error correction and its robustness towards noise can be enhanced considerably. We discuss the performance in the large signal limit using previous results on state evolution, as well as for finite size signals through numerical simulations. Even for relatively small sizes, the approach proposed here outperforms convex-relaxation-based decoders.