[IEEE Trans. on Information Theory, January 1998, pp. 79-94]
Binary Lattice Vector Quantization with Linear Block Codes
and Affine Index Assignments
András Méhes and Kenneth Zeger
Abstract
We determine analytic expressions for the performance of some low-complexity
combined source-channel coding systems. The main tool used is the Hadamard
transform. In particular, we obtain formulas for the average distortion of
binary lattice vector quantization with affine index assignments, linear block
channel coding, and a binary symmetric channel. The distortion formulas are
specialized to non-redundant channel codes for a binary symmetric channel, and
then extended to affine index assignments on a binary asymmetric channel.
Various structured index assignments are compared. Our analytic formulas
provide a computationally efficient method for determining the performance of
various coding schemes. One interesting result shown is that for a uniform
source and uniform quantizer, the Natural Binary Code is never optimal for a
nonsymmetric channel, even though it is known to be optimal for a symmetric
channel.