Linear Congruential Trellis Source Codes: Design and Analysis

Rate-distortion trellis source codes are developed for quantizing memoryless independent and identically distributed (i.i.d.) sources. The codes are generated by simple linear congruential recursions. The method generates codes at a variety of rates including fractional ones; reproducer sets can be large, a crucial advantage with certain sources. Axioms for good code construction are developed that are based on recursion properties and certain trellis symmetries. These axioms are justified by the outcome of random searches for good codes. It is found that the trellis code design breaks into two problems: the trellis labels should have certain properties regardless of the source distribution; and the reproducer values depend on the source. Encoders are simulated for a number of continuous amplitude sources. For the same computational complexity, the new codes, in most cases, perform better than the best codes in the literature, including trellis-coded quantization and fake process approaches.