Optimum non-integer rate allocation using integer programming

Rate allocation is the problem of distributing a given quota of bits among a number of different quantizers such that the total distortion of all the quantizers is minimized. Conventionally, the problem of rate allocation is handled by limiting the number of levels allocated to each quantizer to be an integer power of two. Traditional methods are also based on assuming that the quantizer distortion curves have certain convexity property. we discuss a new method for the optimum rate allocation using an integer programming formulation, which unlike the conventional methods, does not make any assumption on either the integrality of the allocated bit rate, or on the convexity of the distortion curves. We apply this method to a fixed rate and also to a variable rate coding schemes. Numerical results are presented for the DCT coding of still images showing a noticeable improvement in the performance with no increase in the complexity.