Title :
Quantization of Multiple Sources Using Nonnegative Integer Bit Allocation
Author :
Farber, Benjamin ; Zeger, Kenneth
Author_Institution :
Fair Isaac Corp., San Diego, CA
Abstract :
Asymptotically optimal real-valued bit allocation among a set of quantizers for a finite collection of sources was derived in 1963 by Huang and Schultheiss, and an algorithm for obtaining an optimal nonnegative integer-valued bit allocation was given by Fox in 1966. We prove that, for a given bit budget, the set of optimal nonnegative integer-valued bit allocations is equal to the set of nonnegative integer-valued bit allocation vectors which minimize the Euclidean distance to the optimal real-valued bit-allocation vector of Huang and Schultheiss. We also give an algorithm for finding optimal nonnegative integer-valued bit allocations. The algorithm has lower computational complexity than Fox´s algorithm, as the bit budget grows. Finally, we compare the performance of the Huang-Schultheiss solution to that of an optimal integer-valued bit allocation. Specifically, we derive upper and lower bounds on the deviation of the mean-squared error (MSE) using optimal integer-valued bit allocation from the MSE using optimal real-valued bit allocation. It is shown that, for asymptotically large transmission rates, optimal integer-valued bit allocations do not necessarily achieve the same performance as that predicted by Huang-Schultheiss for optimal real-valued bit allocations
Keywords :
computational complexity; mean square error methods; source coding; vector quantisation; Euclidean distance; MSE; computational complexity; mean-squared error method; multiple source quantization; nonnegative integer bit allocation; optimal real-valued bit-allocation vector; Bit rate; Computational complexity; Context; Euclidean distance; Helium; Optimization methods; Quantization; Source coding; Speech coding; Video coding; Data compression; high-resolution quantization; source coding;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2006.883630