Lossy Compression via Sparse Regression Codes: Generalized Construction and Finite-length Bounds

2026-08-14

AI Summary

This study addresses the limited finite-length performance and distortion control challenges of Sparse Regression Codes (SPARCs) in lossy compression by proposing a universal construction of Additive Orthogonal Regression Codes. By tracking the evolution of encoding residuals, we derive non-asymptotic distortion bounds and optimize power allocation strategies to enhance compression efficiency. This approach significantly improves finite-length compression performance while providing rigorous theoretical distortion guarantees for low-complexity variants, including signed and k-sparse SPARCs. Ultimately, this work extends the applicability of sparse regression codes from both theoretical and algorithmic perspectives, establishing a novel paradigm for efficient lossy compression.

Abstract

We study sparse regression codes (SPARCs) for lossy compression under simple greedy encoding rules, including both correlation-based and distance-based methods. We generalize the SPARC construction, and consider the class of \emph{additive orthogonal} regression codes, of which standard SPARCs are a special case. For this class of codes, we derive nonasymptotic bounds on the squared-error distortion by tracking the evolution of the encoding residual across stages. Our results highlight the role of power allocation in controlling the distortion, allowing us to optimize the allocation based on the parameters of the code. The optimized allocation improves the finite-length compression performance of SPARCs, and our bounds provide distortion guarantees for lower complexity variants of SPARCs, like signed SPARCs and $K$-sparse SPARCs.

Problem

• Sparse Regression Codes
• Lossy Compression
• Finite-length Bounds
• Power Allocation
• Greedy Encoding

Innovation

• Sparse Regression Codes
• Additive Orthogonal Regression Codes
• Nonasymptotic Bounds
• Power Allocation Optimization
• Finite-length Performance