ANract-The idea of thermodynamic depth put forth by Lloyd and Pagels requires the computation of the entropy of Markov trajecto-ries. Toward this end we consider an irreducible finite state Markov chain with transition matrix P and associated entropy rate H(X) =-c; j p;I';j log P;j, where p is the stationary distribution given by the solution of /I = MI'. A… (More)
Abstruct-In this partially tutorial paper, we examine minimal trellis representations of linear block codes and analyze several measures of trellis complexity: maximum state and edge dimensions , total span length, and total vertices, edges and mergers. We obtain bounds on these complexities as extensions of well-known dimensiodlength profile (DLP) bounds.… (More)
A Wald-like equation is proved for the entropy of a ran-db@y, stopped sequence of independent identically distributed discrete random variables XI, X2,. with a nonanticipating stopping time N.
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity for a fixed permutation of the code. We examine constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code. We identify the primitive structures that can appear in a minimal… (More)
Absftact-The idea of thermodynamic depth put forth by Lloyd and Pageh requires the computation of the entropy af Markov tqjecto-rim Toward this end we consider an irreducible finite state Markov chain with transition matrix P and pssoeiated entropy rate H (X) = solution of p = p P. A w e c t o r y T,, of the Markov chain is a path with initial state I, 6 4… (More)