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Interpreting Deepcode, a learned feedback code

Yingyao Zhou, Natasha Devroye, Gyorgy Turan, Milos Zefran

TL;DR

The paper addresses understanding how a deep-learned feedback code (Deepcode) operates on AWGN channels with passive feedback by developing an interpretable framework. It combines dimension reduction, pruning, influence-length analysis, and nonlinear map approximations to derive a compact encoder/decoder that preserves BER while revealing how feedback is utilized for error correction. By constructing a 5-state (and extended 7-state) interpretable encoder and a corresponding decoder, the work achieves BER comparable to Deepcode in many regimes, including noisy feedback, and demonstrates that a small, well-structured model can capture the essential feedback dynamics. The findings offer trust and guidance for designing nonlinear feedback codes, highlighting the role of influence length, outliers, and knee-point adaptation in robust performance.

Abstract

Deep learning methods have recently been used to construct non-linear codes for the additive white Gaussian noise (AWGN) channel with feedback. However, there is limited understanding of how these black-box-like codes with many learned parameters use feedback. This study aims to uncover the fundamental principles underlying the first deep-learned feedback code, known as Deepcode, which is based on an RNN architecture. Our interpretable model based on Deepcode is built by analyzing the influence length of inputs and approximating the non-linear dynamics of the original black-box RNN encoder. Numerical experiments demonstrate that our interpretable model -- which includes both an encoder and a decoder -- achieves comparable performance to Deepcode while offering an interpretation of how it employs feedback for error correction.

Interpreting Deepcode, a learned feedback code

TL;DR

The paper addresses understanding how a deep-learned feedback code (Deepcode) operates on AWGN channels with passive feedback by developing an interpretable framework. It combines dimension reduction, pruning, influence-length analysis, and nonlinear map approximations to derive a compact encoder/decoder that preserves BER while revealing how feedback is utilized for error correction. By constructing a 5-state (and extended 7-state) interpretable encoder and a corresponding decoder, the work achieves BER comparable to Deepcode in many regimes, including noisy feedback, and demonstrates that a small, well-structured model can capture the essential feedback dynamics. The findings offer trust and guidance for designing nonlinear feedback codes, highlighting the role of influence length, outliers, and knee-point adaptation in robust performance.

Abstract

Deep learning methods have recently been used to construct non-linear codes for the additive white Gaussian noise (AWGN) channel with feedback. However, there is limited understanding of how these black-box-like codes with many learned parameters use feedback. This study aims to uncover the fundamental principles underlying the first deep-learned feedback code, known as Deepcode, which is based on an RNN architecture. Our interpretable model based on Deepcode is built by analyzing the influence length of inputs and approximating the non-linear dynamics of the original black-box RNN encoder. Numerical experiments demonstrate that our interpretable model -- which includes both an encoder and a decoder -- achieves comparable performance to Deepcode while offering an interpretation of how it employs feedback for error correction.
Paper Structure (26 sections, 9 equations, 14 figures, 6 tables)

This paper contains 26 sections, 9 equations, 14 figures, 6 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Model Reduction
  4. Dimension Reduction
  5. Pruning
  6. Opening the black box
  7. Influence Length
  8. Nonlinear Dynamics
  9. Interpretable model of a Deepcode-like encoder and decoder
  10. Encoder Interpretation
  11. Reduced Deepcode ($5$)
  12. Reduced Deepcode ($7$)
  13. Decoder Interpretation
  14. Training
  15. Equivalent Codes
  16. ...and 11 more sections

Figures (14)

  • Figure 1: AWGN channel with passive noisy feedback.
  • Figure 2: Deepcode encoder (above) and decoder (below). Here, $i \in \{1, \ldots, K + 1\}$ because the message bits are padded with a zero. When $i = 1$, the initial value for phase 2 noises is $0$.
  • Figure 3: BER performance vs. forward SNR, different dimensions (number of hidden states in RNNs), noiseless feedback
  • Figure 4: Outlier values of hidden states (left) and their impact on parity bit $c_{i,1}$ (right). The outliers cause deviations in the parity bits from the regular values in the right figure.
  • Figure 5: Outlier analysis of the "blue" portions in \ref{['eq:intparity1']} and \ref{['eq:intparity2']}.
  • ...and 9 more figures