TY - GEN
T1 - Shrink and stretch sequential scalar (S4) quantizers
AU - Meron, Eado
AU - Feder, Meir
PY - 2006
Y1 - 2006
N2 - A simple backward adaptation method for constructing adaptive scalar quantizers is presented. The method needs no excess memory apart from that used to describe the current state of the quantizer and its complexity is linear in the length of the sequence to be quantized. Furthermore, it is direct and does not go through auxiliary steps such as probability density function (PDF) estimations. The basic idea is that if the current value of the sequence belongs to a certain cell (the cell is "hit"), we shrink that cell by a certain factor (with a certain probability, assuming joint randomness) and stretch all the other cells to fill the remaining space. The probability of shrinking a cell is optimally set to be proportional to 1/length(cell) 2. In the high resolution limit, the equilibrium of the quantizer is reached when the length of the quantizer cells is proportional to 1/PDF(cell)1/3 which is the optimal density of a scalar quantizer. This method is shown to converge to the optimal quantizer even for probability density functions for which the Lloyd-Max algorithm converges to a local minimum, e.g., mixed gaussian with different weights.
AB - A simple backward adaptation method for constructing adaptive scalar quantizers is presented. The method needs no excess memory apart from that used to describe the current state of the quantizer and its complexity is linear in the length of the sequence to be quantized. Furthermore, it is direct and does not go through auxiliary steps such as probability density function (PDF) estimations. The basic idea is that if the current value of the sequence belongs to a certain cell (the cell is "hit"), we shrink that cell by a certain factor (with a certain probability, assuming joint randomness) and stretch all the other cells to fill the remaining space. The probability of shrinking a cell is optimally set to be proportional to 1/length(cell) 2. In the high resolution limit, the equilibrium of the quantizer is reached when the length of the quantizer cells is proportional to 1/PDF(cell)1/3 which is the optimal density of a scalar quantizer. This method is shown to converge to the optimal quantizer even for probability density functions for which the Lloyd-Max algorithm converges to a local minimum, e.g., mixed gaussian with different weights.
UR - http://www.scopus.com/inward/record.url?scp=39049124222&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2006.261783
DO - 10.1109/ISIT.2006.261783
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AN - SCOPUS:39049124222
SN - 1424405041
SN - 9781424405046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 582
EP - 586
BT - Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
T2 - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Y2 - 9 July 2006 through 14 July 2006
ER -