Lossy Compression with Near-uniform Encoder Outputs

TL;DR

This paper investigates conditions for near-uniform encoder outputs in lossy compression scenarios, demonstrating their feasibility in Wyner-Ziv and distributed settings under certain information sharing conditions.

Contribution

It derives new conditions for near-uniform encoder outputs in Wyner-Ziv and distributed lossy compression, highlighting when such outputs are achievable.

Findings

Near-uniform outputs are possible in Wyner-Ziv at rates close to the limit.

Joint near-uniform outputs in distributed compression require shared Gács-Körner common information.

The work clarifies the role of randomness and source correlation in encoder output uniformity.

Abstract

It is well known that lossless compression of a discrete memoryless source with near-uniform encoder output is possible at a rate above its entropy if and only if the encoder is randomized. This work focuses on deriving conditions for near-uniform encoder output(s) in the Wyner-Ziv and the distributed lossy compression problems. We show that in the Wyner-Ziv problem, near-uniform encoder output and operation close to the WZ-rate limit is simultaneously possible, whereas in the distributed lossy compression problem, jointly near-uniform outputs is achievable in the interior of the distributed lossy compression rate region if the sources share non-trivial G\'{a}cs-K\"{o}rner common information.