Huffman-coded Sphere Shaping and Distribution Matching Algorithms via Lookup Tables

TL;DR

This paper introduces Huffman-coded sphere shaping (HCSS) and alternative distribution matching algorithms that improve amplitude shaping efficiency in probabilistic amplitude shaping, achieving near-optimal performance with reduced complexity and LUT-based implementations.

Contribution

The paper presents HCSS with a LUT-based approach and compares it to existing methods, demonstrating performance close to sphere shaping with lower complexity and flexible channel adaptation.

Findings

HCSS closes the performance gap with enumerative sphere shaping.

MR-HCSS and SR-HCSS achieve similar performance to ESS at medium to long block lengths.

Shaping gains of 0.5 dB and 1 dB are demonstrated with small LUTs in AWGN simulations.

Abstract

In this paper, we study amplitude shaping schemes for the probabilistic amplitude shaping (PAS) framework as well as algorithms for constant-composition distribution matching (CCDM). Huffman-coded sphere shaping (HCSS) is discussed in detail, which internally uses Huffman coding to determine the composition to be used and relies on conventional CCDM algorithms for mapping and demapping. Numerical simulations show that HCSS closes the performance gap between distribution matching schemes and sphere shaping techniques such as enumerative sphere shaping (ESS). HCSS is based on an architecture that is different from the trellis-based setup of ESS. It allows to tailor the used HCSS compositions to the transmission channel and to take into account complexity constraints. We further discuss in detail multiset ranking (MR) and subset ranking (SR) as alternatives to arithmetic-coding (AC) CCDM. The advantage of MR over AC is that it requires less sequential operations for mapping. SR operates on binary alphabets only, which can introduce some additional rate loss when a nonbinary-to-binary transformation is required. However, the binomial coefficients required for SR can be precomputed and stored in a lookup table (LUT). We perform an analysis of rate loss and decoding performance for the proposed techniques and compare them to other prominent amplitude shaping schemes. For medium to long block lengths, MR-HCSS and SR-HCSS are shown to have similar performance to ESS. SR-HCSS and uniform 64QAM are compared in additive white Gaussian noise simulations and shaping gains of 0.5 dB and 1 dB are demonstrated with 1 kbit and 100 kbit LUT size, respectively.