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000228453 001__ 228453 000228453 005__ 20190317000723.0 000228453 0247_ $$2doi$$a10.5075/epfl-thesis-7751 000228453 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis7751-1 000228453 02471 $$2nebis$$a10906474 000228453 037__ $$aTHESIS 000228453 041__ $$aeng 000228453 088__ $$a7751 000228453 245__ $$aCoding for Communications and Secrecy 000228453 260__ $$aLausanne$$bEPFL$$c2017 000228453 269__ $$a2017 000228453 300__ $$a251 000228453 336__ $$aTheses 000228453 502__ $$aProf. Bixio Rimoldi (président) ; Prof. Emre Telatar (directeur de thèse) ; Prof. Rüdiger Urbanke, Prof. Erdal Arikan, Prof. Yury Polyanskiy (rapporteurs) 000228453 520__ $$aShannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, Arikan discovered polar codes; the only class of explicitly constructed low-complexity codes that achieve the capacity of any binary-input memoryless symmetric-output channel. Arikan's polar transform turns independent copies of a noisy channel into a collection of synthetic almost-noiseless and almost-useless channels. Polar codes are realized by sending data bits over the almost-noiseless channels and recovering them by using a low-complexity successive-cancellation (SC) decoder, at the receiver. In the first part of this thesis, we study polar codes for communications. When the underlying channel is an erasure channel, we show that almost all correlation coefficients between the erasure events of the synthetic channels decay rapidly. Hence, the sum of the erasure probabilities of the information-carrying channels is a tight estimate of the block-error probability of polar codes when used for communication over the erasure channel. We study SC list (SCL) decoding, a method for boosting the performance of short polar codes. We prove that the method has a numerically stable formulation in log-likelihood ratios. In hardware, this formulation increases the decoding throughput by 53% and reduces the decoder's size about 33%. We present empirical results on the trade-off between the length of the CRC and the performance gains in a CRC-aided version of the list decoder. We also make numerical comparisons of the performance of long polar codes under SC decoding with that of short polar codes under SCL decoding. Shannon's framework also quantifies the secrecy of communications. Wyner, in 1975, proposed a model for communications in the presence of an eavesdropper. It was shown that, at rates below the secrecy capacity, there exist reliable communication schemes in which the amount of information leaked to the eavesdropper decays exponentially in the block-length of the code. In the second part of this thesis, we study the rate of this decay. We derive the exact exponential decay rate of the ensemble-average of the information leaked to the eavesdropper in Wyner's model when a randomly constructed code is used for secure communications. For codes sampled from the ensemble of i.i.d. random codes, we show that the previously known lower bound to the exponent is exact. Our ensemble-optimal exponent for random constant-composition codes improves the lower bound extant in the literature. Finally, we show that random linear codes have the same secrecy power as i.i.d. random codes. The key to securing messages against an eavesdropper is to exploit the randomness of her communication channel so that the statistics of her observation resembles that of a pure noise process for any sent message. We study the effect of feedback on this approximation and show that it does not reduce the minimum entropy rate required to approximate a given process. However, we give examples where variable-length schemes achieve much larger exponents in this approximation in the presence of feedback than the exponents in systems without feedback. Upper-bounding the best exponent that block codes attain, we conclude that variable-length coding is necessary for achieving the improved exponents. 000228453 6531_ $$acapacity-achieving error-correction codes 000228453 6531_ $$apolar codes 000228453 6531_ $$asuccessive-cancellation decoding 000228453 6531_ $$asuccessive-cancellation list decoding 000228453 6531_ $$awiretap channel 000228453 6531_ $$achannel resolvability 000228453 6531_ $$arandom-coding secrecy exponents 000228453 6531_ $$arandom-coding resolvability exponents 000228453 6531_ $$afeedback resolvability exponents 000228453 6531_ $$avariable-length resolvability codes 000228453 700__ $$0246556$$aBastaniparizi, Mani$$g191230 000228453 720_2 $$0240929$$aTelatar, Emre$$edir.$$g131639 000228453 8564_ $$s4831921$$uhttps://infoscience.epfl.ch/record/228453/files/EPFL_TH7751.pdf$$yn/a$$zn/a 000228453 909C0 $$0252180$$pLTHI$$xU10430 000228453 909CO $$ooai:infoscience.tind.io:228453$$pthesis-bn2018$$pDOI$$pIC$$pthesis$$qDOI2$$qGLOBAL_SET 000228453 917Z8 $$x108898 000228453 917Z8 $$x108898 000228453 918__ $$aIC$$cIINFCOM$$dEDIC 000228453 919__ $$aLTHI 000228453 920__ $$a2017-6-9$$b2017 000228453 970__ $$a7751/THESES 000228453 973__ $$aEPFL$$sPUBLISHED 000228453 980__ $$aTHESIS