Unifying Views of Tail-Biting Trellises for Linear Block Codes - Nori, Aditya (2005)
This thesis presents new techniques for the construction and specication of linear tail-biting trellises. Tail-biting trellises for linear block codes are combinatorial descriptions in the form of layered graphs, that are somewhat more compact than the corresponding conventional trellis descriptions. Conventional trellises for block codes have a well understood underlying theory. On the other hand, the theory of tail-biting trellises appears to be somewhat more involved, though several advances in the understanding of the structure and properties of such trellises have been made in recent years. Of fundamental importance is the observation that a linear tail-biting trellis for a block code corresponds to a coset decomposition of the code with respect to a subcode. All constructions seem to use this property in some way; in other words, this is the unifying factor in all our constructions. The constructions yield the conventional trellis when the subcode is the whole code. We list the main contributions of this thesis.