Title :
Variable-rate trellis source encoding
Author :
Yang, En-Hui ; Zhang, Zhen
Author_Institution :
Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada
fDate :
3/1/1999 12:00:00 AM
Abstract :
The fixed slope lossy algorithm derived from the kth-order adaptive arithmetic codeword length function is extended to finite-state decoders or trellis-structured decoders. When this algorithm is used to encode a stationary, ergodic source with a continuous alphabet, the Lagrangian performance converges with probability one to a quantity computable as the infimum of an information-theoretic functional over a set of auxiliary random variables and reproduction levels, where λ>0 and -λ are designated to be the slope of the rate distortion function R(D) of the source at some D; the quantity is close to R(D)+λD when the order k used in the arithmetic coding or the number of states in the decoders is large enough, An alternating minimization algorithm for computing the quantity is presented; this algorithm is based on a training sequence and in turn gives rise to a design algorithm for variable-rate trellis source codes. The resulting variable-rate trellis source codes are very efficient in low-rate regions. With k=8, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Gaussian sources is comparable to that afforded by trellis-coded quantizers; with k=8 and the number of states in the decoder=32, the mean-squared error encoding performance at the rate 1/2 bits/sample for memoryless Laplacian sources is about 1 dB better than that afforded by the trellis-coded quantizers with 256 states, with k=8 and the number of states in the decoder=256, the mean-squared error encoding performance at the rates of a fraction of 1 bit/sample for highly dependent Gauss-Markov sources with correlation coefficient 0.9 is within about 0.6 dB of the distortion rate function
Keywords :
Gaussian processes; Markov processes; adaptive codes; arithmetic codes; decoding; mean square error methods; memoryless systems; rate distortion theory; source coding; trellis codes; variable rate codes; 1 dB; Gauss-Markov sources; Lagrangian performance; arithmetic coding; auxiliary random variables; continuous alphabet; finite-state decoders; fixed slope lossy algorithm; infimum; information-theoretic functiona; kth-order adaptive arithmetic codeword length function; mean-squared error encoding performance; memoryless Gaussian sources; memoryless Laplacian sources; minimization algorithm; rate distortion function; reproduction levels; stationary ergodic source; training sequence; trellis-coded quantizers; trellis-structured decoders; variable-rate trellis source codes; variable-rate trellis source encoding; Algorithm design and analysis; Arithmetic; Decoding; Encoding; Gaussian processes; Lagrangian functions; Laplace equations; Minimization methods; Random variables; Rate-distortion;
Journal_Title :
Information Theory, IEEE Transactions on