Polarization and Spatial Coupling: Two Techniques to Boost Performance
Ph.D. Dissertation, EPFL, September 2013

This thesis investigates two central topics: polar codes and spatial coupling for constraint satisfaction. Results on the first topic include bounds on the fraction of channels that remain unpolarized at a given blocklength, a tighter bound on error probability as a function of rate for rates below the symmetric capacity, a modification of the Tal & Vardy algorithm for efficiently determining the indices of the good channels after polarization with corresponding proofs that the computation remains efficient and that asymptotically no rate is lost through the approach, an investigation of polar codes for symmetric compound channels, and bounds on the rate loss of polar codes as a function of the precision of their implementation. Results on the second topic include techniques for transforming a K-SAT problem into a sequence of L coupled K-SAT problems such that properties of the former can be derived from the latter, which is apparently more amenable to heuristic solution. The results have significant implications both inside and outside the traditional communications applications of information theory.