Lossy Coding of Correlated Sources over a Multiple Access Channel: Necessary Conditions and Separation Results

TL;DR

This paper investigates lossy coding of correlated sources over a multiple access channel, establishing when separation of source and channel coding is optimal and deriving tighter necessary conditions for transmission without side information.

Contribution

It introduces new separation results with side information and provides tighter necessary conditions for correlated source transmission over MACs, including binary and Gaussian cases.

Findings

Separation is optimal with common observations or shared side information.

Derived tighter necessary conditions for transmitting correlated sources over MAC.

Provided a novel converse for binary and Gaussian source transmission over MAC.

Abstract

Lossy coding of correlated sources over a multiple access channel (MAC) is studied. First, a joint source-channel coding scheme is presented when the decoder has correlated side information. Next, the optimality of separate source and channel coding, that emerges from the availability of a common observation at the encoders, or side information at the encoders and the decoder, is investigated. It is shown that separation is optimal when the encoders have access to a common observation whose lossless recovery is required at the decoder, and the two sources are independent conditioned on this common observation. Optimality of separation is also proved when the encoder and the decoder have access to shared side information conditioned on which the two sources are independent. These separation results obtained in the presence of side information are then utilized to provide a set of necessary conditions for the transmission of correlated sources over a MAC without side information. Finally, by specializing the obtained necessary conditions to the transmission of binary and Gaussian sources over a MAC, it is shown that they can potentially be tighter than the existing results in the literature, providing a novel converse for this fundamental problem.