A fast encoding method for lattice codes and quantizers 论文

摘要

In an earlier paper the authors described a very fast method which, for the root lattices <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{n}, D_{n}, E_{n}</tex> , their duals and certain other lattices, finds the closest lattice point to an arbitrary point of the underlying space. If the lattices are used as codes for a Gaussian channel, the algorithm provides a fast decoding procedure, or if they are used as vector quantizers the algorithm performs the analog-to-digital conversion efficiently. The present paper offers a solution to the inverse problem for the same lattices (the encoding problem for channel codes or the digital-to-analog part of quantizing), namely, given an integer <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> , to find the kth code vector, and to the closely related problem of finding the index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> of a given code vector.