[IEEE Trans. on Information Theory, November 2006, pp. 4945-4964 ]
Quantization of Multiple Sources Using Nonnegative Integer Bit Allocation
Benjamin Farber and Kenneth Zeger
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 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.