Browsing by Subject "source coding"

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Open Access
Lossless data compression with polar codes
(2013) Çaycı, Semih
In this study, lossless polar compression schemes are proposed for finite source alphabets in the noiseless setting. In the first part, lossless polar source coding scheme for binary memoryless sources introduced by Arıkan is extended to general prime-size alphabets. In addition to the conventional successive cancellation decoding (SC-D), successive cancellation list decoding (SCL-D) is utilized for improved performance at practical block-lengths. For code construction, greedy approximation method for density evolution, proposed by Tal and Vardy, is adapted to non-binary alphabets. In the second part, a variable-length, zero-error polar compression scheme for prime-size alphabets based on the work of Cronie and Korada is developed. It is shown numerically that this scheme provides rates close to minimum source coding rate at practical block-lengths under SC-D, while achieving the minimum source coding rate asymptotically in the block-length. For improved performance at practical block-lengths, a scheme based on SCL-D is developed. The proposed schemes are generalized to arbitrary finite source alphabets by using a multi-level approach. For practical applications, robustness of the zero-error source coding scheme with respect to uncertainty in source distribution is investigated. Based on this robustness investigation, it is shown that a class of prebuilt information sets can be used at practical block-lengths instead of constructing a specific information set for every source distribution. Since the compression schemes proposed in this thesis are not universal, probability distribution of a source must be known at the receiver for reconstruction. In the presence of source uncertainty, this requires the transmitter to inform the receiver about the source distribution. As a solution to this problem, a sequential quantization with scaling algorithm is proposed to transmit the probability distribution of the source together with the compressed word in an efficient way.
Open Access
Polar codes for distributed source coding
(2014) Önay, Saygun
Polar codes were invented by Arıkan as the first “capacity achieving” codes for binary-input discrete memoryless symmetric channels with low encoding and decoding complexity. The “polarization phenomenon”, which is the underlying principle of polar codes, can be applied to different source and channel coding problems both in single-user and multi-user settings. In this work, polar coding methods for multi-user distributed source coding problems are investigated. First, a restricted version of lossless distributed source coding problem, which is also referred to as the Slepian-Wolf problem, is considered. The restriction is on the distribution of correlated sources. It is shown that if the sources are “binary symmetric” then single-user polar codes can be used to achieve full capacity region without time sharing. Then, a method for two-user polar coding is considered which is used to solve the Slepian-Wolf problem with arbitrary source distributions. This method is also extended to cover multiple-access channel problem which is the dual of Slepian-Wolf problem. Next, two lossy source coding problems in distributed settings are investigated. The first problem is the distributed lossy source coding which is the lossy version of the Slepian-Wolf problem. Although the capacity region of this problem is not known in general, there is a good inner bound called the Berger-Tung inner bound. A polar coding method that can achieve the whole dominant face of the Berger-Tung region is devised. The second problem considered is the multiple description coding problem. The capacity region for this problem is also not known in general. El Gamal-Cover inner bound is the best known bound for this problem. A polar coding method that can achieve any point on the dominant face of El Gamal-Cover region is devised.