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A method of channel polarization, proposed by Arikan, 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 Şaşoğlu, Telatar, and Arikan. In this paper, we consider more general(More)
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)
—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)
  • Ryuhei Mori
  • 2011
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 factor graph ensembles are connected to Bethe free energy. The annealed free energy is expressed as the solution of maximization problem whose stationary condition(More)
Let <i>P</i>:{0,1}<sup><i>k</i></sup> &#226;†’ {0,1} be a nontrivial <i>k</i>-ary predicate. Consider a random instance of the constraint satisfaction problem (<i>P</i>) on <i>n</i> variables with &#206;” <i>n</i> constraints, each being <i>P</i> applied to <i>k</i> randomly chosen literals. Provided the constraint density satisfies &#206;” &#226;‰« 1, such(More)
  • Ryuhei Mori
  • 2015
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is represented by an inner product of two high-dimensional vectors both of which can be decomposed to tensor products of(More)
Polar codes, introduced by Ar&#x0131;kan, 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)
We consider the asymptotic behavior of the polarization process in the large block-length regime when transmission takes place over a binary-input memoryless symmetric channel <i>W</i>. In particular, we study the asymptotics of the cumulative distribution P(<i>Zn</i> &#x2264; <i>z</i>), where {<i>Zn</i>} is the Bhattacharyya process associated with(More)