A Low Complexity Method for Fixed rate Entropy coded Vector Quantization based on Integer Programming

This paper describes a new approach to Fixed rate Entropy coded Vector Quanti zation FEVQ for stationary memoryless sources where the structure of code words 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 Lagrangian formula tion which adjoins the constraint on the entropy codeword length to the distortion Unlike the previously known methods with a xed Lagrangian multiplier xed slope and variable rate output we use an iterative algorithm to optimize the underlying objective function while updating the Lagrange multiplier until the constraint on the overall rate is satis ed ensured to be xed rate This results in a chain of improving solutions which moves towards the op timum point as fast as possible in the sense that the changes in the objective function value at each step is maximized In order to achieve some packing gain we combine the process of Trellis Coded Quantization TCQ with that of FEVQ This results in an iterative application of the Viterbi algorithm on the underlying trellis for optimizing the Lagrangian multiplier Nu merical results are presented demonstrating substantial improvement in comparison with the alternative methods reported in the literature