Seminar: The Jacob Ziv Communication and Information Theory seminar
The Voronoi Spherical CDF for Lattices and Linear Codes: New Bounds for Quantization and Coding bbb
Lecturer:
Associate Prof. Or Ordentlich
Research Areas:
| For a lattice/linear code, we define the Voronoi spherical cumulative density function (CDF) as the CDF of the $\ell_2$-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 valid for any finite dimension and are quite close to a ball-based lower bound. They immediately translate to new non-asymptotic 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 new non-asymptotic upper bounds on the Hamming distortion and the error probability of a random linear code over the binary symmetric channel. In particular, we show that for most lattices in $\mathbb{R}^n$ the second moment is greater than that of a Euclidean ball with the same covolume only by a $\left(1+O(\frac{1}{n})\right)$ multiplicative factor. Similarly, for most linear codes in $\mathbb{F}_2^n$ the expected Hamming distortion is greater than that of a corresponding Hamming ball only by an additive universal constant. https://arxiv.org/pdf/2506.19791 |
| Or Ordentlich received the B.Sc. (cum laude), M.Sc (summa cum laude), and Ph.D. degrees from Tel Aviv University, Israel, in 2010, 2011, and 2016, respectively, all in electrical engineering. He is an Associate Professor with the School of Computer Science and Engineering, Hebrew University of Jerusalem. From 2015 to 2017, he was a Postdoctoral Fellow with the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology (MIT), and the Department of Electrical and Computer Engineering, Boston University. His research focuses on information theory, and its application to modern problems in communication, compression, and data science. His work on lattice covering has received the Frontiers of Science Award in 2025. He has been serving as an Associate Editor for Signal Processing and Source Coding in IEEE TRANSACTIONS ON INFORMATION THEORY since 2021.
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