Adaptive Trellis Encoding of Discrete-Time Sources with a Distortion Measure

Abstract

An adaptive trellis-encoding scheme, using the Viterbi algorithm for trellis search and the Kalman algorithm for adaptive adjustment, is described. The encoder is comprised of a fixed precoder and a time-varying trellis coder in tandem. The source decoder is timevarying with the time-varying part being represented by a feed forward finite-state machine (FSM). Adaptive trellis encoding requires the presence of a local FSM to monitor the adaptive encoding operation. The absence of the source signal at the decoder requires the transmission of a side-information for the mechanization of the adaptive operation of the source decoder. The transmission rate of the proposed adaptive trellis-encoding scheme is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(1 + 1/K_{p})/M</tex> bits per source symbol, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> is the block size which the precoder maps source symbols onto an intermediate signal set before trellis coding and K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> is the update period. Results obtained in the encoding of iid binary, autoregressive, and video sources are presented.