An adaptive PCM system designed for noisy channels and digital implementations

We propose a new adaptive quantization scheme for digitally implementing PCM and DPCM structures. The arithmetics we develop for the digital processing are useful as well in the implementation of previously existing schemes for adaptive quantization. Two objectives are stressed here: (i) The system must be robust in the presence of noise in the transmission channel which causes the synchronization between quantizer adaptations in the transmitter and receiver to deteriorate. (ii) It must also minimize the complexity of the digital realization. In addition to the above objectives, we require, of course, good fidelity of the processed speech waveform. The problem of synchronization in digital implementations where the constraint of finite precision arithmetic exists has not been addressed previously. We begin by examining an existing, idealized adaptation algorithm which contains a leakage parameter for the purpose of deriving robustness. We prove that, to provide the necessary synchronization capability without impairing the quality of speech reproduction, it is necessary to use a minimum, unexpectedly large, number of bits in the machine words and, additionally, to carefully specify the internal arithmetic, as is done here. The new scheme that we propose here uses an order of magnitude less memory in an ROM-based implementation. The key innovations responsible for the improvement are: (i) modification of the adaptation algorithm to one where leakage is interleaved infrequently but at regular intervals into the adaptation recursion; (ii) a specification of the internal machine arithmetic that guarantees synchronization in the presence of channel errors. A detailed theoretical analysis of the statistical behavior of the proposed system for random inputs is given here. Results of a simulation of a realistic 16-level adaptive quantizer are reported.