Modulo Quantization Coding for Primitive Relay and Diamond Channels with Correlated Noises

2026-06-20

AI Summary

This work addresses communication over channels featuring a primitive relay link and correlated Gaussian noise between terminals. It proposes a modulo quantization (MQ) coding scheme that maps real-valued symbols to uniformly quantized indices under a modulo operation, thereby effectively exploiting the shared common noise component. The approach introduces modulo quantization for the first time to primitive relay and diamond channels under correlated noise. In the case of perfectly correlated noise, the scheme achieves the capacity of the Gaussian primitive relay channel. For the diamond channel, it establishes a new achievable rate region that improves upon existing results, significantly outperforming both compress-and-forward and decode-and-forward strategies at moderate signal-to-noise ratios. Moreover, under imperfectly correlated noise, the method substantially reduces computational complexity compared to conventional techniques.

Abstract

This paper proposes modulo quantization (MQ) coding as a simple, structured, and low-complexity scheme for channels with primitive (i.e., noiseless digital) relay links and correlated Gaussian noises across terminals. The key component of MQ coding is the modulo quantization operation, which maps a real-valued symbol to its uniform-quantization index taken modulo a fixed integer. This operation allows effective exploitation of the common noise component shared across the terminals. For the Gaussian primitive relay channel with perfectly correlated noises, where a relay has a finite-capacity link to the receiver, MQ coding can be shown to achieve the capacity of this channel. For the Gaussian primitive diamond channel with perfectly correlated noises, where two relays can forward information through finite-capacity links to a receiver that has no direct observation of the transmitted signal, MQ coding yields novel achievability bounds that improve upon previously known bounds and coincide with the cut-set upper bound in certain signal-to-noise ratio (SNR) regimes. In scenarios with highly but non-perfectly correlated noises, MQ coding can approach the performance of compress-forward (CF) at significantly lower complexity, while surpassing decode-forward (DF) for the Gaussian primitive relay channel in certain SNR ranges. For the Gaussian primitive diamond channel with non-perfectly correlated noises, MQ can outperform both CF and DF at moderate SNR.

Problem

• primitive relay channel
• diamond channel
• correlated noises
• Gaussian channel
• modulo quantization

Innovation

• Modulo Quantization
• Primitive Relay Channel
• Diamond Channel
• Correlated Noises
• Low-Complexity Coding