Coding Theory (Dagstuhl Seminar 11461)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 11461
``Coding Theory''. A (channel) code is typically a set of vectors of the same length n over a finite alphabet \Sigma. By choosing a fixed codebook, binary
strings of appropriate length are injectively mapped into the elements of   the code. These  elements are then transmitted over a communications channel which induces errors on the codeword.
Depending on how well the original code is designed, and which algorithms are used,  the result of this transmission  and attempts to recover the original vector after transmission can be anywhere between disastrous to excellent. Coding  theory is all  about the  design of excellent codes as  a function of the communications  channel, and the design of efficient algorithms  for choosing the codebook vectors, and more importantly, for recovering the original
vector  after  transmission.  As such, successful design of codes requires knowledge and tools in a number of areas such as combinatorics, algorithms   design, probability theory and complexity theory, to name a few.
The purpose of this workshop is to bring together researchers in the field to
discuss recent theoretical advances in algebraic coding, codes on graphs, and
network coding, as well as new and emerging applications of coding methods to
real-world problems.