Unifying Views of Tail-Biting Trellises for Linear Block Codes

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.