EEM quantization revisited: asymptotic optimality for variable rate coding
Thomas Richter · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
Equal-Expectation Magnitude Quantization (EEM) aims at minimizing the distortion of a quantizer with defined reconstruction points by shifting the deadzone parameter such that the expectation value of the signal equals the reconstructed value. While intuitively clear, this argument is not sufficient to prove rate-distortion optimality. In this work, it is show that the EEM quantizer is rate-distortion optimal up to third order in an expansion in powers of the quantization bucket size in the high-bitrate appoximation, and the approximating series for the optimal quantizer is computed. This result is compared to an even simpler quantization strategy based on the LLoyd-Max quantizer which selectively sets coefficients to zero. It is shown that both strategies lead to the same asymptotic expansion for the threshold parameter, but zeroing coefficients provides optimality in one additional order in the quantization bucket size.