Mismatched Decoding in Information Theory with Applications to Channel Modelling

Marie Curie Career Integration Grant, 2012-2016

The recent trend to communicate over short temporal durations undermines two key assumptions in the underlying communication-theoretic analysis, namely: 1) perfect knowledge of the stochastic nature of the channel may be difficult to acquire, a state of affairs which renders impossible the use of optimum decoding rules; 2) efficient analytical techniques valid for infinitely long transmission durations, such as large-deviation theory, are loose and of difficult theoretical justification and ought therefore to be replaced by tools valid for arbitrary transmission lengths. Similarly, the coding schemes used to attain the entropy or capacity limits often turn out to be inefficient. This projects aims at addressing these challenges by devising new tools, theoretical and practical, which expand the validity and usefulness of previous communication-theoretic methods. These new tools are inspired by common practice in two adjacent disciplines, i.e. physics (electromagnetic and quantum electrodynamics) and probability, and besides have the potential to impact not only the field of information theory, but quantum information theory and applied probability.
More specifically, the work plan covers the study (both theoretical and practical) of phase noise and time-varying channels in general, energy-modulation as a possible alternative for non-coherent transmission; the study of general achievable rates with mismatched decoding, with special emphasis to the performance of source and channel codes at finite block-lengths and with applications to decoder design.