Showing papers by "Codex Corporation published in 1974"

Convolutional codes II. Maximum-likelihood decoding

Abstract: Convolutional codes are characterized by a trellis structure. Maximum-likelihood decoding is characterized as the finding of the shortest path through the code trellis, an efficient solution for which is the Viterbi algorithm. A universal asymptotic bounding technique is developed and used to bound error probability, free distance, list-of-2 error probability, and other subsidiary quantities. The bounds are dominated by what happens at a certain critical length N erit . Termination of a convolutional code to length N erit or shorter results in an optimum block code. In general, block code exponents can be related to convolutional code exponents and vice versa by a graphical construction, called the concatenation construction. It is shown that termination is unnecessary with the Viterbi algorithm.

Convolutional codes III. Sequential decoding

Abstract: Sequential decoding is characterized as a sequential search for the shortest path through a trellis. An easily analyzed algorithm closely related to the stack and Fano algorithms is described. Martingale techniques are used to find the distribution of computation on totally symmetric channels. For general channels, our universal bounding technique yields the well-known Pareto distribution of computation, as well as a bound on error probability that is asymptotically optimum in the high-rate range. The performance-complexity relation is shown to be asymptotically Pareto for both sequential and maximum-likelihood (Viterbi) decoding, with the same exponent in either case. A semisequential list-of-L Viterbi algorithm is introduced to extend the analogies below Rcomp.

Convolutional codes. II - Maximum-likelihood decoding. III - Sequential decoding

Abstract: Maximum-likelihood decoding is characterized as the determination of the shortest path through a topological structure called a trellis. Aspects of code structure are discussed along with questions regarding maximum-likelihood decoding on memoryless channels. A general bounding technique is introduced. The technique is used to obtain asymptotic bounds on the probability of error for maximum-likelihood decoding and list-of-2 decoding. The basic features of sequential algorithms are discussed along with a stack algorithm, questions of computational distribution, and the martingale approach to computational bounds.