kiss.m

Lattice coding and decoding

function varargout = kiss(latt,element)

%KISS Lattice kissing number
%   TAU = KISS(L,P) counts the kissing number in the particular 
%   element's P Voronoi region. In order to eliminate the finite lattice
%   edge effects is better to use tracelatt function. This function
%   counts the Voronoi cell parameters as well as the kissing number
%   for all  lattice elements.
%
%   [TAU,SH] = KISS(L,P) also returns the kissing elements
%   coordinates stored in SH matrix.
%
%   Note: KISS function gives sensible results only for geometrically
%         uniform lattices.
%
%   See also TRACELATT, NBHOOD, SSHELL.

%   Copyright 2001-2003 Kamil Anis, [e-mail]
%   Dept. of Radioelectronics, 
%   Faculty of Electrical Engineering
%   Czech Technical University in Prague
%   $Revision: 0.2 $  $Date: 2003/09/28 11:31:21 $
%   --
%   <additional stuff goes here>

[npts,foo] = size(latt);

ord = 1;
thick = 1;

coord = latt(element,:);
center = repmat(coord,[npts 1]);
dist = abs(latt - center);

% find n-th smallest non-zero element
q = mapsto(dist,0,100);

% row norms
nn = dist .^ 2;
nn = sum(nn,2);
nn = nn .^ (1/2);
nn = single(nn);

% sort (unique) the shells
uu = unique(nn);

rho_lo = uu(1 + ord);
rho_hi = uu(ord + thick);

pos = find((nn >= rho_lo) & (nn <= rho_hi));
sh = latt(pos,:);
tau = length(pos);

varargout = {tau,sh};