[Problems of Control and information Theory vol. 20, no. 6, 1991, pp. 475-484]

On asymptotically optimal companding quantization

Tamás Linder


The validity of Bennett's formula for companding quantizers is shown under precise conditions for $r$th power distortion measures. Using these conditions it is shown rigorously that certain companders are asymptotically optimal, i.e., their distortion and the distortion of the optimal quantizers decrease to zero at the same rate, as the number of quantization levels increases to infinity. Some defects in previous derivations concerning companders are pointed out.