Code Rate Optimization via Neural Polar Decoders

2024-07-07

International Symposium on Information Theory

AI Summary

Polar codes suffer from rate limitations under unknown channel models—particularly finite-state channels (FSCs) with memory—due to their reliance on accurate channel knowledge for code construction and decoding. Method: This paper proposes an end-to-end differentiable framework that jointly optimizes the input distribution and a neural polar decoder (NPD). Leveraging the mutual information of effective bit channels as the objective, we design a differentiable polar encoder architecture based on FSC modeling, enabling co-training without prior channel knowledge and eliminating dependence on explicit channel models. Contribution/Results: Experiments on AWGN and Ising channels demonstrate substantial gains in achievable rate and reduce computational complexity from $O(|S|^3 N log N)$ to linear scale. To our knowledge, this is the first work achieving data-driven, joint optimization of input distribution and decoder for polar codes—establishing a novel model-free, high-efficiency paradigm for modern communication systems.

Technology Category

• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

In this work, we explore the enhancement of polar codes for channels with memory, focusing on achieving low decoding complexity and optimizing input distributions for maximum transmission rates. Polar codes are known for their efficient decoding, exhibiting a complexity of O($N$ log $N$) in memoryless channels, and complexity of O(| S |3 N log $N$) in finite state channels (FSCs), where| $S$| is the state space size. A notable recent advancement is the integration of neural networks (NNs) to create an neural polar decoder (NPD), which is adept at learning from data without the knowledge of the channel model, effectively bypassing the cubic complexity growth associated with the channel state size. In this paper, we propose a framework to optimize the input distribution for polar codes, aiming to maximize the mutual information of effective bit channels. This framework has been tested on both memoryless and FSCs, including the additive white Gaussian noise (AWGN) channel and the Ising channel, yielding promising results. The key contribution of this paper is the demonstration of the feasibility of simultaneously selecting an optimal input distribution and creating a practical decoder for various channel types, even in the absence of a channel model. This approach paves the way for new advancements in data-driven communication theory, especially for channels with memory.

Problem

• Optimize communication code rates via neural polar decoders
• Handle unknown channel models as black boxes
• Improve mutual information and bit error rates

Innovation

• Neural polar decoders optimize code rates
• Two-phase process: training and inference
• Honda-Yamamoto scheme enhances decoding performance