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Scalable Syndrome-based Neural Decoders for Bit-Interleaved Coded Modulations

Gastón De Boni Rovella, Meryem Benammar, Tarik Benaddi, Hugo Meric

TL;DR

This work addresses scalable neural decoding for high-order Bit-Interleaved Coded Modulations (BICM) by deriving an effective bit-LLR channel model and extending Syndrome-Based Neural Decoders (SBND) to operate on bit-LLRs. It establishes that the relevant statistics $|\\boldsymbol{L}|$ and $\\mathrm{H}\\boldsymbol{L}^b$ are sufficient for SBND in this setting, and evaluates two neural architectures—RNN (GRU-based) and Transformer—for polar codes $(64,32)$ and $(128,64)$. The results show the RNN-based SBND achieving BER performance close to near-optimal decoding (OSD), while the Transformer offers competitive performance at higher complexity, with larger gaps at lower Eb/N0. The findings demonstrate a practical, code-aware neural decoding approach for BICM in high-order modulation regimes, with clear implications for latency-complexity trade-offs in 5G-and-beyond physical layers.

Abstract

In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes $(64,32)$ and $(128,64)$, using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.

Scalable Syndrome-based Neural Decoders for Bit-Interleaved Coded Modulations

TL;DR

This work addresses scalable neural decoding for high-order Bit-Interleaved Coded Modulations (BICM) by deriving an effective bit-LLR channel model and extending Syndrome-Based Neural Decoders (SBND) to operate on bit-LLRs. It establishes that the relevant statistics and are sufficient for SBND in this setting, and evaluates two neural architectures—RNN (GRU-based) and Transformer—for polar codes and . The results show the RNN-based SBND achieving BER performance close to near-optimal decoding (OSD), while the Transformer offers competitive performance at higher complexity, with larger gaps at lower Eb/N0. The findings demonstrate a practical, code-aware neural decoding approach for BICM in high-order modulation regimes, with clear implications for latency-complexity trade-offs in 5G-and-beyond physical layers.

Abstract

In this work, we introduce a framework that enables the use of Syndrome-Based Neural Decoders (SBND) for high-order Bit-Interleaved Coded Modulations (BICM). To this end, we extend the previous results on SBND, for which the validity is limited to Binary Phase-Shift Keying (BPSK), by means of a theoretical channel modeling of the bit Log-Likelihood Ratio (bit-LLR) induced outputs. We implement the proposed SBND system for two polar codes and , using a Recurrent Neural Network (RNN) and a Transformer-based architecture. Both implementations are compared in Bit Error Rate (BER) performance and computational complexity.
Paper Structure (17 sections, 3 theorems, 22 equations, 6 figures, 1 table)

This paper contains 17 sections, 3 theorems, 22 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. System model and preliminaries
  3. Bit-Interleaved Coded Modulations (BICM)
  4. BICM equivalent channel models
  5. Channel distributions $P_{Y|C}$ and $P_{L|C}$
  6. Bit-LLRs binary channel distribution $P_{L^b|C}$
  7. Proposed system: SBND for BICM
  8. Decoding as a binary noise detection problem
  9. Previous works on SBND for BPSK and QPSK modulations
  10. Proposed solution: SBND for BICM
  11. Experiments
  12. Possible architectures and training
  13. Results
  14. Complexity analysis
  15. Conclusion
  16. ...and 2 more sections

Key Result

Lemma 1

An equivalent channel distribution of a classical BICM setting is given for all $\boldsymbol{y} \in \mathds{C}^{n^\prime}$, $\boldsymbol{l} \in \mathds{R}^n$, and $\boldsymbol{c} \in \{0,1\}^n$ by where, the distributions $P_{Y|C}$ and$P_{L|C}$ are given by and $\mathcal{X}_{c}^s$ is the set of symbols for which the $s$-th bit equals $c$.

Figures (6)

  • Figure 1: General system model.
  • Figure 2: BICM channel model extended to bit-LLRs.
  • Figure 3: Suggested SBND for higher-order modulations
  • Figure 4: Error rate studies for two rate $1/2$ polar codes: $(64,32)$ (left) and $(128,64)$ (right).
  • Figure 5: Decision regions of the 8-PSK constellation
  • ...and 1 more figures

Theorems & Definitions (6)

  • Lemma 1: BICM classical channel models Caire_1998Alvarado_2008
  • proof
  • Theorem 1: Bit-LLRs binary channel model
  • proof
  • Theorem 2: Sufficient statistics
  • proof