Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/D4121C65-374C-44A4-963B-B2240D4FE6FC | ||
| Year | 2016 | ||
| Type of Item | Diploma Work | ||
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| Bibliographic Citation | Ioannis-Themistoklis Papoutsidakis, "Pascal-matrix polar coding for prime-input channels", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2016 https://doi.org/10.26233/heallink.tuc.66128 | ||
| Appears in Collections |
In 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.
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