Achievability Performance Bounds for Integer-Forcing Source Coding

TL;DR

This paper analyzes the performance bounds of integer-forcing source coding, quantifying the probability of failure based on source covariance matrices and providing guarantees in Rayleigh fading environments.

Contribution

It offers a probabilistic analysis of when integer-forcing source coding succeeds or fails, extending understanding of its robustness across different source covariances.

Findings

Probability of failure depends on source covariance and rate

Performance guarantees are provided for Rayleigh fading scenarios

Most covariance matrices allow successful decoding with high probability

Abstract

Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for "most" but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, %in excess of the %Berger-Tung benchmark, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.