Perturbations in optimal trellis source code design

Given a fixed source model, a fixed trellis, and a fixed finite set of quantizer levels, one obtains a trellis source code for coding the given source by assigning each trellis edge a label from the set of quantizer levels. We consider the problem of finding which edge label assignment gives an optimal (or near optimal) trellis source code, i.e., a code yielding minimum (or near minimum) expected distortion per source sample. Group structures are imposed on the set of edges of the trellis and the set of quantizer levels, and the edge label assignment is required to be a group homomorphism. We define a trellis source code to be a perturbation of a given trellis source code if the set of edges where the edge label mappings of the two codes disagree is of smallest possible cardinality. We present the results of computer experiments showing that for a finite alphabet memoryless source model and Hamming distortion, an optimal or near optimal trellis source code may be found which is "intermediately perturbable" in the sense that the number of perturbations of the code is close to halfway between the minimum and maximum number of perturbations a trellis source code on the given trellis can have. This principle, where valid, can be used as a means to narrow the search for good trellis source codes