Neural Compress-and-Forward for the Primitive Diamond Relay Channel

TL;DR

This work extends neural compress-and-forward to the primitive diamond relay channel with two oblivious relays that must compress their noisy observations without inter-relay communication. It introduces an end-to-end framework where each relay uses a one-shot neural quantizer and entropy model, paired with a learned destination demodulator, to realize Berger–Tung-like distributed coding under rate constraints. The distributed scheme outperforms a point-to-point baseline and approaches theoretical bounds across multiple modulation orders, illustrating scalable, interpretable neural CF for multi-relay networks. The results highlight learned binning regions and joint decoding as mechanisms for achieving efficient distributed compression in relay networks.

Abstract

The diamond relay channel, where a source communicates with a destination via two parallel relays, is one of the canonical models for cooperative communications. We focus on the primitive variant, where each relay observes a noisy version of the source signal and forwards a compressed description over an orthogonal, noiseless, finite-rate link to the destination. Compress-and-forward (CF) is particularly effective in this setting, especially under oblivious relaying where relays lack access to the source codebook. While neural CF methods have been studied in single-relay channels, extending them to the two-relay case is non-trivial, as it requires fully distributed compression without any inter-relay coordination. We demonstrate that learning-based quantizers at the relays can harness input correlations by operating remote, yet in a collaborative fashion, enabling effective distributed compression in line with Berger-Tung-style coding. Each relay separately compresses its observation using a one-shot learned quantizer, and the destination jointly decodes the source message. Simulation results show that the proposed scheme, trained end-to-end with finite-order modulation, operates close to the known theoretical bounds. These results demonstrate that neural CF can scale to multi-relay systems while maintaining both performance and interpretability.

Figures (6)

• Figure 1: Primitive diamond relay channel model under consideration. Red links indicate orthogonal (or out-of-band) relaying between the two relays and the destination.
• Figure 2: Neural compress-and-forward (CF) schemes for the diamond relay channel (DRC). (a) In the distributed scheme, each relay separately but collaboratively compresses its observation. (b) In the point-to-point (p2p) scheme, a single relay encoder and demodulator are pre-trained, and a new demodulator is fine-tuned to jointly process compressed signals coming from the two relays.
• Figure 3: SER and mutual information as a function of average relay rate $R = \frac{\tilde{R}_{1}+\tilde{R}_{2}}{2}$, for 4-PAM where $\gamma_{R_{1}} = \gamma_{R_{2}} = 10$dB. Solid and dashed horizontal black lines represent cases with two perfect relays (equivalent to $R_{1} \rightarrow \infty, R_{2} \rightarrow \infty$) and the single perfect relay (equivalent to $R_{1} \rightarrow \infty$, $R_{2}=0$), respectively. The green lines correspond to results from ozyilkan2024learning, which considered a single-relay setting with where side information is fully available at the demodulator. Therefore, the setting studied in ozyilkan2024learning is operationally equivalent to $R = \tilde{R}_{1}$ and $R_{2} \rightarrow \infty$. Each marker on all curves represents a training run with a specific value of $\lambda$.
• Figure 4: Mutual information for the distributed scheme (Fig. \ref{['fig:dist_model']}) under BPSK, 4-PAM, and 8-PAM modulations with $\gamma_{R_{1}} = \gamma_{R_{2}} = 5$ dB. For the bounds obtained from ayfer2019newkatz2024gaussian, we choose the rates for both relays as $R = R_{1} =R_{2}$. Dashed horizontal lines represent performance of two perfect relays (i.e., $R_{1} \rightarrow \infty$, $R_{2} \rightarrow \infty$) for the respective curves, similar to Fig. \ref{['fig:multistep']}.
• Figure 5: Mutual information for the distributed scheme (Fig.\ref{['fig:dist_model']}) under 4-QAM and 16-QAM with $\gamma_{R_{1}} {=} \gamma_{R_{2}} {=} 5$dB. For the bounds obtained from ayfer2019newkatz2024gaussian, we choose the rates for the relays as $R {=} R_{1} {=} R_{2}$. Dashed horizontal lines represent the case of perfect relays, i.e., $R_{1} {\rightarrow} \infty$, $R_{2} {\rightarrow} \infty$ under its corresponding modulation scheme.