Algorithmic complexity in coding theory and the minimum distance problem
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Ordered Binary Decision Diagrams and Minimal Trellises
IEEE Transactions on Computers
A Posteriory Probability Decoding of Nonsystematically Encoded Block Codes
Problems of Information Transmission
Computing Weight Distributions of Convolutional Codes via Shift Register Synthesis
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Minimal Tail-Biting Trellises for Certain Cyclic Block Codes Are Easy to Construct
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
On the Many Faces of Block Codes
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Package for the Implementation of Block Codes as Finite Automata
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
Graph Configurations and Decoding Performance
Proceedings of the 8th IMA International Conference on Cryptography and Coding
On viewing block codes as finite automata
Theoretical Computer Science
On maximum length convolutional codes under a trellis complexity constraint
Journal of Complexity - Special issue on coding and cryptography
On Viterbi-like algorithms and their application to Reed-Muller codes
Journal of Complexity - Special issue on coding and cryptography
Iterative decoding algorithms for turbo product codes
ELECTROSCIENCE'07 Proceedings of the 5th conference on Applied electromagnetics, wireless and optical communications
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Low-floor decoders for LDPC codes
IEEE Transactions on Communications
Data detection and Kalman estimation for multiple space-time trellis codes
IEEE Transactions on Communications
IEEE Transactions on Wireless Communications
Low-floor detection/decoding of LDPC-coded partial response channels
IEEE Journal on Selected Areas in Communications
New constructions of low-complexity convolutional codes
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
New constructions of high-performance low-complexity convolutional codes
IEEE Transactions on Communications
Low-floor tanner codes via hamming-node or RSCC-Node doping
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Trellis Structures for Reed-Muller Codes
Finite Fields and Their Applications
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In this semi-tutorial paper, we will investigate the computational complexity of an abstract version of the Viterbi algorithm on a trellis, and show that if the trellis has e edges, the complexity of the Viterbi algorithm is Θ(e). This result suggests that the “best” trellis representation for a given linear block code is the one with the fewest edges. We will then show that, among all trellises that represent a given code, the original trellis introduced by Bahl, Cocke, Jelinek, and Raviv in 1974, and later rediscovered by Wolf (1978), Massey (1978), and Forney (1988), uniquely minimizes the edge count, as well as several other figures of merit. Following Forney and Kschischang and Sorokine (1995), we will also discuss “trellis-oriented” or “minimal-span” generator matrices, which facilitate the calculation of the size of the BCJR trellis, as well as the actual construction of it