Constraining the size of the instantaneous alphabet in trellis quantizers

A method is developed for decreasing the computational complexity of a trellis quantizer (TQ) encoder. We begin by developing a rate-distortion theory under a constraint on the average instantaneous number of quanta considered. This constraint has practical importance: in a TQ, the average instantaneous number of quanta is exactly the average number of multiplies required at the encoder. The theory shows that if the conditional probability of each quanta is restricted to a finite region of support, the instantaneous number of quanta considered can be made quite small at little or no cost in SQNR performance. Simulations of TQs confirm this prediction. This reduction in complexity makes practical the use of model-based TQs (MTQs), which had previously been considered computationally unreasonable. For speech, performance gains of several dB SQNR over adaptive predictive schemes at a similar computational complexity are obtained using only a first-order MTQ.