Metrics in the context of information theory and error correcting codes

Abstract

This post-doctoral project, associated with the FAPESP Thematic Project 2013 / 25977-7 "Security and reliability of information: Theory and Practice", have as a goal to approach metric problems in the context of theory of information and error correcting codes, which appear in different applications. Some of these problems include the characterization of perfect, quasi-perfect and dense codes, and the search for efficient decoding algorithms. We focus particularly pay special on the Lee and Chebyshev metrics for q-ary codes and associated lattices. Chebyshev and Kendall's tau metric for rank modulation codes will be studied in the context of error correction for flash memory. Grasmanian codes with the rank metric will also be analyzed. Within a general approach, will be considered problems related to matching of metrics and discrete memoryless channels. This proposal also includes some extensions of problems approached in the candidate PhD project FAPESP 2012/10600-2 and BEPE FAPESP 2014/04096-5, looking for new applications on topics of current interest in the field of error correcting codes, in constant interaction with the thematic project research group and experts in the area within and outside the country. (AU)