Channel Coding and Source Coding with Increased Partial Side Information

TL;DR

This paper investigates the limits of channel and source coding with partial side information at both encoder and decoder, deriving capacity and rate-distortion functions for six cases, and establishing duality and computational methods.

Contribution

It introduces six new cases of coding problems with increased partial side information, providing capacity and rate-distortion characterizations and a tight lower bound on Wyner-Ziv solutions.

Findings

Derived capacity and rate-distortion functions for six cases.

Established duality between channel capacity and rate-distortion.

Developed numerical algorithms and tight bounds for solutions.

Abstract

Let (S1,i, S2,i), distributed according to i.i.d p(s1, s2), i = 1, 2, . . . be a memoryless, correlated partial side information sequence. In this work we study channel coding and source coding problems where the partial side information (S1, S2) is available at the encoder and the decoder, respectively, and, additionally, either the encoder's or the decoder's side information is increased by a limited-rate description of the other's partial side information. We derive six special cases of channel coding and source coding problems and we characterize the capacity and the rate-distortion functions for the different cases. We present a duality between the channel capacity and the rate-distortion cases we study. In order to find numerical solutions for our channel capacity and rate-distortion problems, we use the Blahut-Arimoto algorithm and convex optimization tools. As a byproduct of our work, we found a tight lower bound on the Wyner-Ziv solution by formulating its Lagrange dual as a geometric program. Previous results in the literature provide a geometric programming formulation that is only a lower bound, but not necessarily tight. Finally, we provide several examples corresponding to the channel capacity and the rate-distortion cases we presented.