[2404.04776] Soft Demapping of Spherical Codes from Cartesian Powers of PAM Constellations

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Computer Science > Information Theory

arXiv:2404.04776 (cs)

[Submitted on 7 Apr 2024 (v1), last revised 20 Nov 2024 (this version, v2)]

Title:Soft Demapping of Spherical Codes from Cartesian Powers of PAM Constellations

Authors:Reza Rafie Borujeny, Susanna E. Rumsey, Stark C. Draper, Frank R. Kschischang<br>View a PDF of the paper titled Soft Demapping of Spherical Codes from Cartesian Powers of PAM Constellations, by Reza Rafie Borujeny and 3 other authors

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Abstract:For applications in concatenated coding for optical communications systems, we examine soft-demapping of short spherical codes constructed as constant-energy shells of the Cartesian power of pulse amplitude modulation constellations. These are unions of permutation codes having the same average power. We construct a list decoder for permutation codes by adapting Murty's algorithm, which is then used to determine mutual information curves for these permutation codes. In the process, we discover a straightforward expression for determining the likelihood of large subcodes of permutation codes called orbits. We introduce a simple process, called orbit demapping, that allows us to extract soft information from noisy permutation codewords. In a sample communication system with probabilistic amplitude shaping protected by a standard low-density parity-check code that employs short permutation codes, we demonstrate that orbit demapping provides a gain of about 0.3 dB in signal-to-noise ratio compared to the traditional symbol-by-symbol demapping. By using spherical codes composed of unions of permutation codes, we can increase the input entropy compared to using permutation codes alone. In one scheme, we consider a union of a small number of permutation codes. In this case, orbit demapping provides about 0.2 dB gain compared to the traditional method. In another scheme, we use all possible permutations to form a spherical code that exhibits a computationally feasible trellis representation. The soft information obtained using the BCJR algorithm outperforms the traditional symbol-by-symbol method by 0.1 dB. Using the spherical codes containing all possible permutation codes of the same average power and the BCJR algorithm, a gain of 0.5 dB is observed. Comparison of the achievable information rates of bit-metric decoding verifies the observed gains.

Subjects:

Information Theory (cs.IT)

Cite as:<br>arXiv:2404.04776 [cs.IT]

(or<br>arXiv:2404.04776v2 [cs.IT] for this version)

https://doi.org/10.48550/arXiv.2404.04776

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arXiv-issued DOI via DataCite

Submission history<br>From: Reza Rafie Borujeny [view email]<br>[v1]<br>Sun, 7 Apr 2024 01:37:00 UTC (639 KB)

[v2]<br>Wed, 20 Nov 2024 16:07:03 UTC (532 KB)

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