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Pascal-matrix polar coding for prime-input channels

Papoutsidakis Ioannis-Themistoklis

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Extent32 pagesen
TitlePascal-matrix polar coding for prime-input channelsen
TitleΠολικοί κώδικες βασισμένοι στον πίνακα Πασκάλ για prime-input κανάλιαel
CreatorPapoutsidakis Ioannis-Themistoklisen
CreatorΠαπουτσιδακης Ιωαννης-Θεμιστοκληςel
Contributor [Thesis Supervisor]Karystinos Georgiosen
Contributor [Thesis Supervisor]Καρυστινος Γεωργιοςel
Contributor [Committee Member]Liavas Athanasiosen
Contributor [Committee Member]Λιαβας Αθανασιοςel
Contributor [Committee Member]Τουμπακάρης Δημήτριοςel
Contributor [Committee Member]Toumpakaris Dimitriosen
PublisherΠολυτεχνείο Κρήτηςel
PublisherTechnical University of Creteen
Academic UnitTechnical University of Crete::School of Electrical and Computer Engineeringen
Academic UnitΠολυτεχνείο Κρήτης::Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστώνel
Content SummaryIn this thesis, first we present the original polar codes. We describe the basic polarization effect and present an efficient recursive formula to compute the best choices for frozen bits in the case of the binary erasure channel. Both the encoder and the decoder have log-linear complexity. We highlight that, by using the same construction as in binary polar codes, we can create polarized extreme (perfect or useless) channels for any prime-input channel. Then, we indicate the characteristics of the matrices that achieve channel polarization. We present a strict method that allows us to recursively construct generator matrices based on the Pascal matrix for prime alphabets. We observe their characteristics and properties. Finally, using the above-mentioned technique, we develop a new ternary kernel and an encoder and successive cancellation decoder with log-linear complexity. We also construct formulas that efficiently calculate the optimal choice of frozen symbols for a ternary erasure channel. It is shown that our construction polarizes the capacities of the channels relatively faster in comparison to the conventional polar construction. The latter is illustrated by considering the error-correction capability of both the conventional Polar code and our proposed code and simulating the symbol error rate for the TEC.en
Type of ItemΔιπλωματική Εργασίαel
Type of ItemDiploma Worken
Date of Item2016-07-25-
Date of Publication2016-
SubjectChannel codingen
Bibliographic CitationIoannis-Themistoklis Papoutsidakis, "Pascal-matrix polar coding for prime-input channels", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2016en
Bibliographic CitationΙωάννης-Θεμιστοκλής Παπουτσιδάκης, "Πολικοί κώδικες βασισμένοι στον πίνακα Πασκάλ για prime-input κανάλια", Διπλωματική Εργασία, Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών, Πολυτεχνείο Κρήτης, Χανιά, Ελλάς, 2016el

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