Communicating Correlated Sources Over MAC and Interference Channels I: Separation-Based Schemes

Abstract

We consider the two scenarios of communicating a pair S 1 , S 2 of distributed correlated sources over 2−user multiple access (MAC) and interference channels (IC) respectively. While in the MAC problem, the receiver intends to reconstruct both sources losslessly, in the IC problem, receiver j intends to reconstruct S j losslessly. We undertake a Shannon theoretic study and focus on achievability, i.e., characterizing sufficient conditions. In the absence of a Gaćs-Körner-Witsenhausen common part, the current known single-letter (S-L) coding schemes are constrained to choosing X jt -the symbol input on the channel by encoder j at time t -based only S jt -the source symbol observed by it, at time t, resulting in the pmf p X1X2 of the inputs X 1 , X 2 constrained to the S-L long Markov Chain (LMC) X 1 − S 1 − S 2 − X 2 . Taking the lead of Dueck's example [1], we recognize that the latter constraint is debilitating, leading to sub-optimality of S-L coding schemes. The goal of our work is to design a coding scheme wherein (i) the choice of X jt is based on multiple source symbols S l j , and is yet ii) amenable to performance characterization via S-L expressions. In this article, we present the first part of our findings. We propose a new separation-based coding scheme comprising of (i) a fixed block-length (B-L) code that enables choice of X jt based on a generic number l of source symbols, thus permitting correlation of the input symbols X 1 , X 2 through a multiletter LMC X 1 − S l 1 − S l 2 − X 2 , (ii) arbitrarily large B-L codes superimposed on multiple sub-blocks of the fixed B-L code that communicate the rest of the information necessary for source reconstruction at the decoder(s), and (iii) a multiplexing unit based on the interleaving technique [2] that ensures the latter codes of arbitrarily large B-L experience a memoryless channel. This careful stitching of S-L coding techniques enables us to devise a multi-letter coding scheme that permits characterization of sufficient conditions via a S-L expression. We prove that the derived inner bound is strictly larger than the current known largest inner bounds for both the MAC and IC problems.Since the proposed coding scheme is inherently separation based, the derived inner bound does not subsume the current known largest. In the second part of our work, we propose to enlarge the inner bound derived in this article by incorporating the technique of inducing source correlation onto channel inputs [3].

Performance analysis of one‐source‐with‐one‐helper transmission over shadowed κ$\kappa$‐μ$\mu$ fading multiple access channels

“…In [8], the sufficient conditions and necessary conditions for the achievability of a certain distortion pair with Gaussian sources over a MAC with unidirectional conferencing encoders were presented, expressing the distortion pairs as a function of the channel signal‐to‐noise ratio (SNR) and of the source correlation. Padakandla characterized a set of sufficient conditions of transmitting two distributed correlated sources over MAC and interference channels [9], and extended to the performance analysis of joint source‐channel decoding [10].…”

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

“…In another line of work, superposition coding with Gacs Körner Witsenhausen (GKW) common part is used in ref. [ 22 ] to to describe the sufficient conditions lossless recoverability.…”