Integer-Forcing Source Coding

TL;DR

This paper introduces Integer-Forcing source coding, a low-complexity distributed lossy compression scheme for correlated Gaussian sources that leverages lattice codes and integer linear combinations to improve compression efficiency.

Contribution

It applies the integer-forcing framework to source coding, proposing a novel scheme that enhances compression by recovering integer combinations of signals rather than individual signals.

Findings

The scheme achieves smaller average powers for linear combinations, enabling higher lattice densities.

It reduces compression rates compared to traditional methods.

A one-shot version suggests potential for new analog-to-digital converter designs.

Abstract

Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. 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. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.