2012/12/14 by Heide Gluesing-Luerssen, Gluesing-Luerssen, Heide, G. David Forney +1
Computer Science · #94B05 #Coding theory and cryptography #Cryptographic Implementations and Security #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1212.3621
openalex publication_date 2012/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates tail-biting trellis realizations for linear block codes. Intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis. It proves beneficial to always consider the trellis and its dual simultaneously. A major role is played by trellis properties that amount to observability and controllability for fragments of the trellis of various lengths. For fragments of length less than the minimum span length of the code it is shown that fragment observability and fragment controllability are equivalent to irreducibility. For reducible trellises, a constructive reduction procedure is presented. The considerations also lead to a characterization for when the dual of a trellis allows a product factorization into elementary ("atomic") trellises.