ASYMPTOTIC BOUNDS ON OPTIMAL NOISY CHANNEL QUANTIZATION VIA RANDOM CODING

Citation
K. Zeger et V. Manzella, ASYMPTOTIC BOUNDS ON OPTIMAL NOISY CHANNEL QUANTIZATION VIA RANDOM CODING, IEEE transactions on information theory, 40(6), 1994, pp. 1926-1938
Citations number
15
Categorie Soggetti
Information Science & Library Science","Engineering, Eletrical & Electronic
ISSN journal
00189448
Volume
40
Issue
6
Year of publication
1994
Pages
1926 - 1938
Database
ISI
SICI code
0018-9448(1994)40:6<1926:ABOONC>2.0.ZU;2-C
Abstract
Asymptotically optimal zero-delay vector quantization in the presence of channel noise is studied using random coding techniques. First, an upper bound is derived for the average rth-power distortion of channel optimized k-dimensional vector quantization at transmission rate R on a binary symmetric channel with bit error probability epsilon. The up per bound asymptotically equals 2-rRg(epsilon,k,r), where k/(k + r) [1 - log2(1 + 2square-rootepsilon(1 - epsilon))] less-than-or-equal-to g (epsilon,k,r) less-than-or-equal-to 1 for all epsilon greater-than-or- equal-to 0, lim(epsilon --> 0) g(epsilon,k,r) = 1, and lim(k --> infin ity) g(epsilon,k,r) = 1. Numerical computations of g(epsilon,k,r) are also given. This result is analogous to Zador's asymptotic distortion rate of 2-rR for quantization on noiseless channels. Next, using a ran dom coding argument on nonredundant index assignments, a useful upper bound is derived in terms of point density functions, on the minimum m ean squared error of high resolution, regular, vector quantizers in th e presence of channel noise. The formula provides an accurate approxim ation to the distortion of a noisy channel quantizer whose codebook is arbitrarily ordered. Finally, it is shown that the minimum mean squar ed distortion of a regular, noisy channel VQ with a randomized nonredu ndant index assignment, is, in probability, asymptotically bounded awa y from zero.