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—Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this paper, a new construction method for arbitrary symmetric binary memoryless channel (B-MC) with linear complexity in the(More)
—A method of channel polarization, proposed by Arıkan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of q-ary channel polarization is considered by S ¸ as¸o˘ glu, Telatar, and Arıkan. In this paper, we consider more general channel(More)
—Polarization phenomenon over any finite field Fq with size q being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arıkan for the binary field, as well as its extension to a prime field by S ¸ as¸o˘ glu, Telatar, and Arıkan. In this paper, a necessary and sufficient condition of a(More)
—Recently, Vontobel showed the relationship between Bethe free energy and annealed free energy for protograph factor graph ensembles. In this paper, annealed free energy of any random regular, irregular and Poisson factor graph ensembles are connected to Bethe free energy. The annealed free energy is expressed as the solution of maximization problem whose(More)
Recently, Arıkan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm of polar codes, called successive cancellation decoding, can be regarded as belief propagation decoding, which has been(More)
—Polar codes, introduced by Arıkan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is(More)
For a binary-input memoryless symmetric channel W , we consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over W. In particular, we study the asymptotics of the cumulative distribution P(Zn ≤ z), where {Zn} is the Bhattacharyya process defined from W , and its dependence on the rate of(More)
—Polarization phenomenon over any finite field Fq with size q being a power of a prime is considered. This problem is a generalization of the original proposal of channel polarization by Arıkan for the binary field, as well as its extension to a prime field by S ¸ as¸o˘ glu, Telatar, and Arıkan. In this paper, a necessary and sufficient condition of a(More)