Learning-Based Compress-and-Forward Schemes for the Relay Channel

TL;DR

The paper tackles practical compress-and-forward relaying for the Gaussian primitive relay channel by introducing task-aware, neural Wyner--Ziv compressors that operate end-to-end with a demodulator, under a fixed relay-rate constraint. It demonstrates that these learned compressors naturally realize binning-like behavior and achieve rates close to the theoretical CF benchmark, even with finite-order modulations and without explicit source-statistics modeling. The authors provide multiple neural CF architectures, support their interpretability through visualization of binning and decision boundaries, and show robustness to SNR variations via training over SNR ranges. This work offers a first proof-of-concept toward practical, interpretable neural CF relaying, with potential extensions to general relay networks and MIMO settings benefiting from data-driven distributed compression.

Abstract

The relay channel, consisting of a source-destination pair along with a relay, is a fundamental component of cooperative communications. While the capacity of a general relay channel remains unknown, various relaying strategies, including compress-and-forward (CF), have been proposed. In CF, the relay forwards a quantized version of its received signal to the destination. Given the correlated signals at the relay and destination, distributed compression techniques, such as Wyner--Ziv coding, can be harnessed to utilize the relay-to-destination link more efficiently. Leveraging recent advances in neural network-based distributed compression, we revisit the relay channel problem and integrate a learned task-aware Wyner--Ziv compressor into a primitive relay channel with a finite-capacity out-of-band relay-to-destination link. The resulting neural CF scheme demonstrates that our compressor recovers binning of the quantized indices at the relay, mimicking the optimal asymptotic CF strategy, although no structure exploiting the knowledge of source statistics was imposed into the design. The proposed neural CF, employing finite order modulation, operates closely to the rate achievable in a primitive relay channel with a Gaussian codebook. We showcase the advantages of exploiting the correlated destination signal for relay compression through various neural CF architectures that involve end-to-end training of the compressor and the demodulator components. Our learned task-oriented compressors provide the first proof-of-concept work toward interpretable and practical neural CF relaying schemes.

Figures (12)

• Figure 1: The primitive relay channel (PRC) under consideration. The red link denotes out-of-band relaying between the relay and the destination.
• Figure 2: The three proposed neural CF schemes: (a) and (b) are based on marginal (marg.) and conditional (cond.) formulations, (coupled with classic either entropy or Slepian-Wolf (SW) coder) respectively; (c) is the point-to-point (p2p) scheme. The learned parameters are indicated in blue. Note that the schemes in (a) and (b) operationally correspond to task-aware neural Wyner--Ziv compressors, since the encoder can exploit the side information $Y_D$ at the receiver side. In (c), neither parameters of $\mathrm{e}_\theta$ and $\mathrm{q}_\zeta$ are updated during the fine-tuning step (only $\mathrm{p}_\phi$ is learned). In the split I-Q variants of each scheme (not depicted), we have two separate encoders that compress in-phase and quadrature components of the complex-valued signal independently. Wherever we present relevant experiments, we label the depicted respective scheme illustrated in this figure as joint I-Q, indicating a single encoder for both in-phase and quadrature components.
• Figure 3: Symbol error rate (SER) and mutual information as a function of the relay-to-destination rate $R$, for the 4-PAM modulation with $\gamma_D = \gamma_R = 13$ dB. The colored lines represent the performance of three neural CF relay architectures (Fig. \ref{['fig:sys']}), where each marker corresponds to a unique model trained for a particular value of $\lambda$ in \ref{['eq:loss_fn']}. The horizontal black lines provide baseline results without relaying ($R=0$) and with perfect relaying ($R\to\infty$).
• Figure 4: Symbol error rate (SER) and mutual information as a function of the relay-to-destination rate $R$, for the 16-QAM modulation with $\gamma_D = \gamma_R = 7$ dB. The colored lines illustrate the performance of three neural CF relay architectures depicted in Fig. \ref{['fig:sys']}, accompanied by their respective split I-Q variants (as introduced in Sec. \ref{['subsec:neural_cf_architectures']}). In the figure, each marker corresponds to a unique model trained for a specific value of $\lambda$ in \ref{['eq:loss_fn']}. The horizontal black lines indicate baseline results without relaying ($R=0$) and with perfect relaying ($R\to\infty$).
• Figure 5: Mutual information for the marginal model (Fig. \ref{['fig:marg_model']}) in case of BPSK, 4-PAM and 8-PAM modulations with $\gamma_D = \gamma_R = 3$ dB. The solid line represents $C_\text{CF}$ in \ref{['eq:C_CF-Simeone']}Simeone_2, obtained for Gaussian inputs. The dotted lines represent the perfect relay ($R\to\infty$) bounds for the respective curves, similar to Figs. \ref{['fig:rate_vs_overall_performance']} and \ref{['fig:rate_vs_overall_performance-QAM']}.