Fundamental study on theory and applications of channel polarization

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Polar codes combined with successive-cancellation decoding, that were newly proposed in 2008, have been attracting attentions of researchers as error-correcting codes that have been proven to saturate the symmetric capacity for any memoryless channel in the limit of long codelength, while requiring relatively low computational complexity in encoding and decoding. In this research project, aiming at obtaining understandings that will be useful in constructing codes with better performance, we have elucidated the phenomenon of channel polarization, which lays the mathematical basis for high performance of polar codes. We have obtained a result on asymptotic decoding error probability in a coderate-dependent form, by refining existing asymptotic results on decoding error probability. We have also studied channel polarization over non-binary alphabet, and have obtained a necessary and sufficient condition for an invertible ?×? matrix on Fq to induce channel polarization.