Neural Compress-and-Forward for the Relay Channel

TL;DR

The paper tackles the uncertainty in relay-channel capacity by developing a practical neural compress-and-forward (CF) scheme for a primitive relay channel with an out-of-band relay-to-destination link. It introduces end-to-end trainable one-shot Wyner--Ziv compressors at the relay and a neural demodulator at the destination, optimizing a loss that balances relay-rate usage and end-to-end mutual information. Results show the learned compressor naturally performs binning of quantized indices, achieving rates close to the Gaussian-input CF benchmark $C_{CF}$ with finite-order modulations, and provide interpretable visualizations of the binning behavior. This work offers a first proof-of-concept for a practical, interpretable neural CF relaying scheme and lays groundwork for extending to general relay channels and more complex relaying scenarios.

Abstract

The relay channel, consisting of a source-destination pair and 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. For CF, 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. In light of the recent advancements in neural network-based distributed compression, we revisit the relay channel problem, where we integrate a learned one-shot Wyner--Ziv compressor into a primitive relay channel with a finite-capacity and orthogonal (or out-of-band) relay-to-destination link. The resulting neural CF scheme demonstrates that our task-oriented 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. We show that the proposed neural CF scheme, employing finite order modulation, operates closely to the capacity of a primitive relay channel that assumes a Gaussian codebook. Our learned compressor provides the first proof-of-concept work toward a practical neural CF relaying scheme.

Figures (5)

• Figure 1: The primitive relay channel (PRC) under consideration. The red link denotes out-of-band relaying between relay and destination.
• Figure 2: The three proposed detection-oriented neural compress-and-forward relay schemes: (a) and (b) are based on marginal and conditional formulations respectively; (c) is the point-to-point 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.
• Figure 3: SER and mutual information results as a function of the relay-to-destination rate $R$, for the 4-PAM modulation with $\gamma = 13$ 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 lines provide baseline results without relaying ($R=0$) and with perfect relaying ($R\to\infty$).
• Figure 4: Mutual information results for the marginal model (Fig. \ref{['fig:marg_model']}) in case of BPSK and 4-PAM modulations with $\gamma = 3$ 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 Fig. \ref{['fig:rate_vs_overall_performance']}.
• Figure 5: Visualization (best viewed in color) of the learned CF strategy (marginal scheme in Fig. \ref{['fig:marg_model']}) and demodulation decisions for the 4-PAM modulation with $\gamma = 13$ and relay rate $R\approx 1$. The horizontal lines denote the quantization boundaries on $Y_R$, and the colors designate the transmitted index $\mathrm{e}_\theta(Y_R)$. The vertical lines denote the hard decision boundaries for the demodulator, and the markers represent the decisions. The transmitted symbols (denoted by cross, triangle, star, square) are also reported near the axis for reference.