Universal Coding for Lossless and Lossy Complementary Delivery Problems

TL;DR

This paper introduces universal coding schemes for complementary delivery problems, enabling efficient lossless and lossy data transmission using existing Slepian-Wolf and Wyner-Ziv codes, with proven bounds on performance.

Contribution

It presents novel universal coding schemes for both lossless and lossy complementary delivery, combining existing codes and providing performance guarantees.

Findings

Universal lossless code constructed from two Slepian-Wolf codes.

Error probability of the lossless code is exponentially tight.

Rate-loss in lossy coding is bounded by a universal constant.

Abstract

This paper deals with a coding problem called complementary delivery, where messages from two correlated sources are jointly encoded and each decoder reproduces one of two messages using the other message as the side information. Both lossless and lossy universal complementary delivery coding schemes are investigated. In the lossless case, it is demonstrated that a universal complementary delivery code can be constructed by only combining two Slepian-Wolf codes. Especially, it is shown that a universal lossless complementary delivery code, for which error probability is exponentially tight, can be constructed from two linear Slepian-Wolf codes. In the lossy case, a universal complementary delivery coding scheme based on Wyner-Ziv codes is proposed. While the proposed scheme cannot attain the optimal rate-distortion trade-off in general, the rate-loss is upper bounded by a universal constant under some mild conditions. The proposed schemes allows us to apply any Slepian-Wolf and Wyner-Ziv codes to complementary delivery coding.