Neural Polar Codes for Source Coding
Abstract
This paper presents a data-driven approach to lossless and lossy source compression using polar codes. Classical polar source coding achieves fundamental limits with low complexity for binary memoryless sources. However, for unknown q-ary sources with memory, successive-cancellation (SC) decoding requires an explicit source model and can be computationally prohibitive. We present analytical SC recursions and show that exact implementations scale quadratically with alphabet size and cubically with state-space size. To overcome these limitations, we develop neural polar decoders trained directly from data to approximate conditional distributions of synthetic polar coordinates without requiring an explicit source model. These learned distributions enable estimation of entropy rates, mutual information, and rate-distortion functions, and support explicit polar compression schemes. For lossless compression, we identify high-entropy polarized coordinates and reconstruct the remaining coordinates using the learned SC recursion. For lossy compression, we combine neural polar decoders with a neural test channel to estimate and optimize the mutual information-distortion tradeoff and construct an explicit lossy polar code. We also extend the framework to Wyner-Ziv compression with decoder side information by learning conditional polarized distributions and a reconstruction mapping. Experiments on memoryless sources, sources with memory, and real genomic data show that the learned decoders closely match analytical SC decoders when available and remain applicable when conventional methods are computationally infeasible or the source model is unavailable.
Related
- Polar Complexity: A New Descriptive Complexity with Applications to Source and Joint Source-Channel Coding
- OSD-JSCC: Neural Joint Source-Channel Coding with One-Step Diffusion
- Log Density Spectrum Based Decoding of Polar Codes for Channels with Strong Phase Noise
- PMR-Aided Shifted-Pruning SCL-Flip Decoding for CRC-Aided Polar Codes
- Semantic SCL Decoding for Polar Codes
BibTeX
@misc{huleihel2026neural,
title = {{Neural Polar Codes for Source Coding}},
author = {Bashar Huleihel and Ziv Aharoni and Haim H. Permuter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13554},
eprint = {2610.13554},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13554},
}
RIS
TY - UNPB
TI - Neural Polar Codes for Source Coding
AU - Bashar Huleihel
AU - Ziv Aharoni
AU - Haim H. Permuter
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13554
UR - https://arxiv.org/abs/2610.13554
AB - This paper presents a data-driven approach to lossless and lossy source compression using polar codes. Classical polar source coding achieves fundamental limits with low complexity for binary memoryless sources. However, for unknown q-ary sources with memory, successive-cancellation (SC) decoding requires an explicit source model and can be computationally prohibitive. We present analytical SC recursions and show that exact implementations scale quadratically with alphabet size and cubically with state-space size. To overcome these limitations, we develop neural polar decoders trained directly from data to approximate conditional distributions of synthetic polar coordinates without requiring an explicit source model. These learned distributions enable estimation of entropy rates, mutual information, and rate-distortion functions, and support explicit polar compression schemes. For lossless compression, we identify high-entropy polarized coordinates and reconstruct the remaining coordinates using the learned SC recursion. For lossy compression, we combine neural polar decoders with a neural test channel to estimate and optimize the mutual information-distortion tradeoff and construct an explicit lossy polar code. We also extend the framework to Wyner-Ziv compression with decoder side information by learning conditional polarized distributions and a reconstruction mapping. Experiments on memoryless sources, sources with memory, and real genomic data show that the learned decoders closely match analytical SC decoders when available and remain applicable when conventional methods are computationally infeasible or the source model is unavailable.
ER -