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This is a Quantitative Study study.

October 2, 2025Open Access

The Voronoi Spherical CDF for Lattices and Linear Codes: New Bounds for Quantization and Coding

Key Points

New lower bounds on the expected Voronoi spherical CDF enhance quantization techniques for lattices.
The bounds yield improved upper limits on the error probability of random lattices over Gaussian noise.
Jensen's inequality and the first moment method facilitate the development of new bounds for linear codes.
The results indicate a significant improvement in Hamming distortion estimates for random linear codes.

Abstract

For a lattice/linear code, we define the Voronoi spherical cumulative density function (CDF) as the CDF of the ₂-norm/Hamming weight of a random vector uniformly distributed over the Voronoi cell. Using the first moment method together with a simple application of Jensen's inequality, we develop lower bounds on the expected Voronoi spherical CDF of a random lattice/linear code. Our bounds are quite close to a trivial ball-based lower bound and immediately translate to improved upper bounds on the normalized second moment and the error probability of a random lattice over the additive white Gaussian noise channel, as well as improved upper bounds on the Hamming distortion and the error probability of a random linear code over the binary symmetric channel.

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Cite This Study

Or Ordentlich (Tue,) studied this question.

synapsesocial.com/papers/68de84c45b556a9128e1bfc8 https://doi.org/https://doi.org/10.48550/arxiv.2506.19791