Channel-Aware Optimal Transport: A Theoretical Framework for Generative Communication

TL;DR

This paper develops a theoretical framework for channel-aware optimal transport in generative communication, showing how to minimize distortion over communication channels with and without shared randomness, and proposing hybrid coding schemes.

Contribution

It introduces a novel channel-aware optimal transport problem, analyzes the asymptotic optimality of source-channel separation, and proposes a hybrid coding scheme that outperforms existing methods.

Findings

Source-channel separation is asymptotically optimal with unlimited common randomness.

Hybrid coding scheme outperforms separation-based and uncoded schemes.

The framework applies to generative communication with minimal end-to-end distortion.

Abstract

Optimal transport has numerous applications, particularly in machine learning tasks involving generative models. In practice, the transportation process often encounters an information bottleneck, typically arising from the conversion of a communication channel into a rate-limited bit pipeline using error correction codes. While this conversion enables a channel-oblivious approach to optimal transport, it fails to fully exploit the available degrees of freedom. Motivated by the emerging paradigm of generative communication, this paper examines the problem of channel-aware optimal transport, where a block of i.i.d. random variables is transmitted through a memoryless channel to generate another block of i.i.d. random variables with a prescribed marginal distribution such that the end-to-end distortion is minimized. With unlimited common randomness available to the encoder and decoder, the source-channel separation architecture is shown to be asymptotically optimal as the blocklength approaches infinity. On the other hand, in the absence of common randomness, the source-channel separation architecture is generally suboptimal. For this scenario, a hybrid coding scheme is proposed, which partially retains the generative capabilities of the given channel while enabling reliable transmission of digital information. It is demonstrated that the proposed hybrid coding scheme can outperform both separation-based and uncoded schemes.