Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

TL;DR

This paper explores optimal power allocation in layered broadcast coding for Gaussian sources over fading channels, minimizing expected distortion through convex optimization and differential equations, with insights on the benefits of CSI and diversity.

Contribution

It introduces a convex optimization framework for distortion minimization in layered coding and derives differential equations for the continuum of layers, advancing understanding of power allocation strategies.

Findings

Optimal power allocation involves a ceiling for higher layers.

Expected distortion minimized by solving convex optimization problems.

Diversity benefits surpass CSI at high SNR, especially with large bandwidth ratios.

Abstract

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.