“…The most important part of PVQ schemes is an enumerative bijective mapping (3) which uniquely determines the codeword with length . It can be implemented by the recursive calculation of pyramid numbers [3], i.e., with 1 for all and 0 the is determined by (4) Let be defined as the number of pyramid points on all spheres with a radius not greater than , i.e., number of points in with (5) A can be calculated recursively [2], for fixed by (6) and for fixed by (7) with 1, 2 1, 1, 2 1, and 0 for each 0, 0. Finally, a fast coding and decoding PVQ algorithm for the points of a given pyramid encoding vector with an index can be calculated using the following algorithm.…”