Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

TL;DR

This paper introduces the linear transform network (LTN) model for analyzing compression and estimation of correlated signals over DAGs, providing algorithms for optimal linear coding and bounds on distortion.

Contribution

It proposes a novel LTN model, develops an iterative optimization algorithm for joint compression and estimation, and derives cut-set bounds for multi-source, multi-receiver networks.

Findings

The algorithm recovers regular and distributed Karhunen-Loeve transforms.

Cut-set lower bounds on distortion regions are established.

Illustrations demonstrate tradeoffs in various network configurations.

Abstract

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.