Leech lattice decoding
The Leech lattice is a very remarkable lattice in 24 dimensions. Its density and high degree of structure make it a very suitable candidate for error-correction.
This library aims to efficiently implement several different Leech lattice decoders.
For a discussion of the original, cryptographically safe integer implementation, please see my thesis at the Cryptology ePrint archive.
- leech.h: Header file containing constants and declarations of all integer decoders.
- leech.c: Non-vectorized, cryptographically safe, integer implementation of . If a tighter bound on the modulus
qcan be assumed, this implementation can be optimized further.
- leech_unsafe.c: Non-vectorized integer implementation of . Some minor optimizations are probably possible.
- Vectorized versions of both the above.
- Floating point versions of the unsafe version.
- Bounded distance decoder, based on .
Maximum likelihood decoding
Maximum likelihood decoding is equivalent to the Closest Vector Problem (CVP) on lattices. Given a point in space, it finds the closest lattice vector to this point. Alternatively, it maps every point in the Voronoi cell of a lattice point to that point, except those points on the boundary.
The most efficient decoder known is described in . This library contains a cryptographically secure implementation, and an unsafe version.
Bounded distance decoding
Bounded distance decoding is equivalent to maximum likelihood decoding, with the additional restriction that the input point lies within a certain distance to a lattice point. For the Leech lattice, this distance is equal to half the minimal distance. Essentially, it maps each point within a sphere packing of the Leech lattice to the relevant point.
The most efficient bounded distance decoder known is based on the same construction as . It is described in .
 Vardy and Be'ery, "Maximum Likelihood Decoding of the Leech lattice", Trans. on Information Theory, Vol. 39, No. 4, July 1993.
 Vardy, "Even More Efficient Bounded-Distance Decoding of the Hexacode, the Golay Code, and the Leech Lattice", Trans. on Information Theory, Vol. 41, No. 5, September 1995.