#### Communications and Signal Processing Seminar

# Quantization of Multiple Sources Using Nonnegative Integer Bit

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 using optimal integer-valued bit

allocation from the mean-squared error 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.

Benjamin Farber earned his bachelors in Electrical Engineering from

Cornell University in 1999. He completed his PhD in Electrical and

Computer Engineering from the University of California, San Diego, in 2005

under the supervision of Professor Kenneth Zeger. His research is

focused on scalar quantization over noisy channels and the bit allocation

problem for a finite set of quantizers.