This repository is designed to implement and simulate the work described in [1], which builds upon the work in [2]. The primary focus of this project is to present and demonstrate nested lattice quantization for matrix multiplication and accelerating decoding using small look up tables. The central implementation for this functionality resides in the HierarchicalNestedLatticeQuantizer.
There's also an efficient C implementation.
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Hierarchical Nested Lattice Quantizer: Implements a lattice quantization approach that supports successive refinement, enabling a broad range of results with minimal LUT sizes. This is the main implementation, designed to showcase the flexibility and efficiency of the method.
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Nested Lattice Quantizer: A "classic" reference quantizer for comparison purposes, implementing standard Voronoi code quantization.
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Closest Point Algorithms: Algorithms for finding the closest lattice points for well known lattices such as
$D_n$ ,$A_2$ and$E_8$ . Algorithms are from [3].
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I. Kaplan and O. Ordentlich, “High-Rate Nested-Lattice Quantized Matrix Multiplication with Small Lookup Tables”, to be presented in ISIT 2025, arXiv:2505.13164, 2025.
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O. Ordentlich and Y. Polyanskiy, “Optimal quantization for matrix multiplication”, arXiv preprint arXiv:2410.13780, 2024.
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J. Conway and N. Sloane, "Fast quantizing and decoding and algorithms for lattice quantizers and codes", in IEEE Transactions on Information Theory, vol. 28, no. 2, pp. 227-232, March 1982, doi: 10.1109/TIT.1982.1056484.
For a full list of references, please see the "References" section of our published work.
Feel free to open issues or submit pull requests for any suggestions or improvements!