Linear Coding for Gaussian Two-Way Channels

Abstract

Although user cooperation cannot improve the capacity of Gaussian two-way channels (GTWCs) with independent noises, it can improve communication reliability. In this work, we aim to enhance and balance the communication reliability in GTWCs by minimizing the sum of error probabilities via joint design of encoders and decoders at the users. We first formulate general encoding/decoding functions, where the user cooperation is captured by the coupling of user encoding processes. The coupling effect renders the encoder/decoder design non-trivial, requiring effective decoding to capture this effect, as well as efficient power management at the encoders within power constraints. To address these challenges, we propose two different two-way coding strategies: linear coding and learning-based coding. For linear coding, we propose optimal linear decoding and discuss new insights on encoding regarding user cooperation to balance reliability. We then propose an efficient algorithm for joint encoder/decoder design. For learningbased coding, we introduce a novel recurrent neural network (RNN)-based coding architecture, where we propose interactive RNNs and a power control layer for encoding, and we incorporate bi-directional RNNs with an attention mechanism for decoding. Through simulations, we show that our two-way coding methodologies outperform conventional channel coding schemes (that do not utilize user cooperation) significantly in sum-error performance. We also demonstrate that our linear coding excels at high signalto-noise ratios (SNRs), while our RNN-based coding performs best at low SNRs. We further investigate