Divergence-Minimizing Distribution Matching for Parallel Channels and Channels with Memory

2026-09-28

AI Summary

This study addresses the lack of distribution matching (DM) theory for parallel and channels with memory, as well as the rate loss incurred at short blocklengths. It extends DM theory to distributions with memory by establishing, for the first time, a minimum-divergence DM framework and deriving the corresponding divergence scaling laws. Furthermore, this work proposes a joint enumeration sphere shaping (ESS) method based on weighted energy constraints, which is integrated with 5G-NR LDPC codes to achieve probabilistic amplitude shaping. Both theoretical analysis and simulations demonstrate that the proposed approach substantially reduces short-blocklength rate loss in multi-channel scenarios, thereby significantly enhancing overall transmission performance.

Abstract

Theory for distribution matchers (DMs) is extended to distributions with memory. The divergence-minimizing DM is shown to select the sequences with the highest target probability, as in the memoryless case. A scaling law for divergence is extended to distributions driven by innovation processes. The theory is applied to parallel additive white Gaussian noise channels. A modified enumerative sphere-shaping (ESS) method with a weighted energy constraint is used in implementations. An illustrative example with three channels shows that joint ESS across channels reduces the rate loss by a large factor compared to product DMs at short blocklengths. The gains are confirmed by simulations with probabilistic amplitude shaping and a 5G-NR low-density parity-check code.

Problem

• distribution matching
• channels with memory
• parallel channels
• rate loss
• probabilistic shaping

Innovation

• Distribution Matching
• Enumerative Sphere Shaping
• Parallel Channels
• Probabilistic Amplitude Shaping
• Divergence Minimization