Ordered Binary Decision Diagrams and Minimal Trellises
IEEE Transactions on Computers
Trellis Structure and Higher Weights of Extremal Self-Dual Codes
Designs, Codes and Cryptography
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Data detection and Kalman estimation for multiple space-time trellis codes
IEEE Transactions on Communications
On Trellis Structures for Reed-Muller Codes
Finite Fields and Their Applications
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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 dimension/length profile (DLP) bounds. Codes meeting these bounds minimize all the complexity measures simultaneously; conversely, a code attaining the bound for total span length, vertices, or edges, must likewise attain it for all the others. We define a notion of “uniform” optimality that embraces different domains of optimization, such as different permutations of a code or different codes with the same parameters, and we give examples of uniformly optimal codes and permutations. We also give some conditions that identify certain cases when no code or permutation can meet the bounds. In addition to DLP-based bounds, we derive new inequalities relating one complexity measure to another, which can be used in conjunction with known bounds on one measure to imply bounds on the others. As an application, we infer new bounds on maximum state and edge complexity and on total vertices and edges from bounds on span lengths