A low-complexity method for fixed-rate entropy-constrained vector quantization

This paper describes a new approach to fixed-rate entropy-constrained vector quantization (FEVQ) for stationary memoryless sources where the structure of codewords are derived from a variable-length scalar quantizer. We formulate the quantization search operation as a zero-one integer-optimization problem, and show that the resulting integer program can be closely approximated by solving a simple linear program. The result is a Lagrange formulation which adjoins the constraint on the entropy (codeword length) to the distortion. Unlike the previously known methods with a fixed Lagrange multiplier, we use an iterative algorithm to optimize the underlying objective function, while updating the Lagrange multiplier until the constraint on the overall rate is satisfied. The key feature of the new method is the substantial reduction in the number of iterations in comparison with previous related methods. In order to achieve some packing gain, we combine the process of trellis-coded quantization with that of FEVQ. This results in an iterative application of the Viterbi algorithm on the underlying trellis for selecting the Lagrange multiplier. Numerical results are presented which demonstrate substantial improvement in comparison with the alternative methods reported in the literature.