Entropy coding of composite sources modeled by infinite Gaussian mixture distributions

A method for optimizing a multiple entropy coder system for coding of a memoryless mixture distribution is studied. The coding scheme is based on splitting the composite source into a finite number of subsources, followed by entropy coding of each subsource. A rate distortion optimal splitting scheme is found assuming an infinite Gaussian mixture distribution and one common infinite-level uniform threshold quantizer for all samples. Theoretical results quantifying the rate distortion performance for a Gaussian mixture distribution with an exponential mixing density are found for 1 to 5 entropy coders, and compared to the rate distortion function. At a signal-to-noise ratio of 30 dB the average entropy is reduced by 0.270 bits per sample, when using 5 entropy coders compared to coding of the composite source.