EPFL doctorate award 2013 - Eren Sasoglu
Polar Coding Theorems For Discrete Sysems. Thesis EPFL n°5219. Dir.: Prof. Emre Telatar
"For contributions to the theory of polar codes, in particular consolidating and simplifying the proof techniques, and for extending the polarization principle beyond error correction coding".
Abstract: One of the fundamental problems in communication theory is to find practical methods to transmit data reliably at optimal rates over noisy channels. Arikan's polar coding method is the first provably good solution to this problem for the class of symmetric binary-input memoryless channels. Polar codes are based on channel polarization, a principle that also yields efficient data compression schemes.
This dissertation studies the generality of the polarization principle. It is first shown that polarization by Arikan's method is not restricted to processes with binary alphabets. A family of low-complexity transforms is shown to polarize all discrete memoryless processes. This leads to coding theorems for all discrete memoryless channels and sources. Is then shown that memorylessness is not a condition for polarization to take place. Indeed, a large class of processes with memory can also be polarized with similar techniques. Then, it is shown that not only the original polarization transform, but in fact a very large class of transforms polarize all discrete channels and sources. This class contains transforms that outperform the original one at large coding lengths. Finally, it is shown that multiple processes can be jointly polarized using the same technique. This yields methods to communicate at optimal rates over channels with multiple senders.