Modulo Quantization Coding for Primitive Relay and Diamond Channels with Correlated Noises
The work provides a low-complexity coding scheme that achieves or approaches capacity in relay networks with correlated noises, addressing a practical bottleneck in cooperative communication.
This paper introduces modulo quantization (MQ) coding for Gaussian primitive relay and diamond channels with correlated noises. MQ coding achieves capacity for the relay channel with perfect noise correlation and improves upon known bounds for the diamond channel, matching the cut-set bound in certain SNR regimes; for non-perfectly correlated noises, it outperforms compress-forward and decode-forward at moderate SNR with lower complexity.
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.