Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Coding for Gaussian Two-Way Channels: Linear and Learning-Based Approaches

Junghoon Kim, Taejoon Kim, Anindya Bijoy Das, Seyyedali Hosseinalipour, David J. Love, Christopher G. Brinton

TL;DR

The work tackles reliability optimization in Gaussian two-way channels by jointly designing encoders and decoders to minimize the sum of error probabilities under power constraints. It develops two complementary coding approaches: (i) a tractable linear coding framework with maximum-likelihood decoding and a systematic conversion to weighted-sum-power minimization, and (ii) a nonlinear learning-based scheme using interacting RNNs with state propagation, power control, and attention-based decoding, trained end-to-end as an autoencoder. Through extensive simulations, the authors show substantial sum-error improvements over non-cooperative baselines, with linear coding thriving at high SNR and RNN-based coding delivering robustness at low SNR and under varying block-lengths; they also reveal power- and rate-distribution insights and practical enhancements such as alternate channel uses. The results demonstrate the potential of two-way cooperation to balance reliability in GTWCs and highlight design principles guiding when to prefer linear versus learning-based methods in practical systems. The analysis and experiments provide a foundation for future practical GTWC codes that exploit feedback-like interactions to improve reliability under realistic power and delay constraints.

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 learning-based 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 signal-to-noise ratios (SNRs), while our RNN-based coding performs best at low SNRs. We further investigate our two-way coding strategies in terms of power distribution, two-way coding benefit, different coding rates, and block-length gain.

Coding for Gaussian Two-Way Channels: Linear and Learning-Based Approaches

TL;DR

The work tackles reliability optimization in Gaussian two-way channels by jointly designing encoders and decoders to minimize the sum of error probabilities under power constraints. It develops two complementary coding approaches: (i) a tractable linear coding framework with maximum-likelihood decoding and a systematic conversion to weighted-sum-power minimization, and (ii) a nonlinear learning-based scheme using interacting RNNs with state propagation, power control, and attention-based decoding, trained end-to-end as an autoencoder. Through extensive simulations, the authors show substantial sum-error improvements over non-cooperative baselines, with linear coding thriving at high SNR and RNN-based coding delivering robustness at low SNR and under varying block-lengths; they also reveal power- and rate-distribution insights and practical enhancements such as alternate channel uses. The results demonstrate the potential of two-way cooperation to balance reliability in GTWCs and highlight design principles guiding when to prefer linear versus learning-based methods in practical systems. The analysis and experiments provide a foundation for future practical GTWC codes that exploit feedback-like interactions to improve reliability under realistic power and delay constraints.

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 learning-based 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 signal-to-noise ratios (SNRs), while our RNN-based coding performs best at low SNRs. We further investigate our two-way coding strategies in terms of power distribution, two-way coding benefit, different coding rates, and block-length gain.
Paper Structure (63 sections, 7 theorems, 112 equations, 18 figures, 5 tables, 4 algorithms)

This paper contains 63 sections, 7 theorems, 112 equations, 18 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Optimization Problem for Coding
  3. Transmission Model
  4. Functional Form of Encoding and Decoding
  5. Encoding
  6. Decoding
  7. Optimization of Encoders and Decoders
  8. Linear Coding: Framework and Solution
  9. Signal Model for Linear Coding
  10. Maximum Likelihood Decoding
  11. Conversion of Optimization Problem
  12. Optimization Problem for Weighted Sum-Power Minimization
  13. Optimization Solution for Weighted Sum-Power Minimization
  14. First sub-problem for obtaining ${\bf q}_1$ and ${\bf F}_1$
  15. Second sub-problem for obtaining ${\bf F}_2$
  16. ...and 48 more sections

Key Result

Lemma 1

The optimal solutions of opt:linear:sum-error can be obtained by solving the following problem, defined as where $\mathcal{S} = \bigcup_{\eta_1, \eta_2 \in \mathbb{R}^+} \mathcal{S}_{(\eta_1, \eta_2)}$. Here, $\mathcal{S}_{(\eta_1, \eta_2)}$ is the set of solutions $({\bf g}_1, {\bf F}_1, {\bf g}_2, {\bf F}_2)$ of opt:linear:max-of-powers:SNR given $\eta_1$ and $\eta_2$, while satisfying ${\max}

Figures (18)

  • Figure 1: System model for Gaussian two-way channels. The goal is to successfully convey the messages ${\bf b}_i$ to each other by exchanging transmit symbols $x_i[k]$ between the users. The users employ encoders and decoders to ensure successful message transmissions, where the two-way interaction between the users should be captured.
  • Figure 2: Our proposed RNN-based encoding architecture for two-way channels. A pair of interactive RNNs captures the coupling effect caused by the encoding processes of the two users.
  • Figure 3: Our proposed RNN-based decoding architecture at User $i$, $i \in \{1,2\}$. Bi-directional RNNs with the attention mechanism are introduced to exploit correlations among receive symbols in which the encoders’ coupling behavior is captured. Here, $\bar{i}$ denotes the index of the counterpart of User $i$, i.e., $\bar{i}=2$ if $i=1$ while $\bar{i}=1$ if $i=2$.
  • Figure 4: Our proposed encoding/decoding architecture in a compact form for two-way channels.
  • Figure 5: Sum-BLER with short block-lengths of $L_1=L_2=6$ bits and $N_\text{L}=18$ channel uses with $r_1=r_2=1/3$. RNN-based coding shows robustness to high channel noises, while linear coding performs well in very low noise scenarios. Here, $\text{sum-BLER}$ of the channel coding schemes remains almost the same over $\text{SNR}^{\text{ch}}_2$, since $\text{sum-BLER}$ is dominated by $\text{BLER}_1$ and $\text{BLER}_1$ is constant due to a constant value of $\text{SNR}^{\text{ch}}_1$. The proposed linear and RNN-based schemes benefit from interactive two-way coding and yield a significant performance improvement.
  • ...and 13 more figures

Theorems & Definitions (18)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Lemma 2
  • Proposition 1
  • Proposition 2
  • Conjecture 1
  • Proposition 3
  • Corollary 1
  • Remark 3
  • ...and 8 more