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- Ryuhei Mori, Toshiyuki Tanaka
- 2010 IEEE International Symposium on Information…
- 2010

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)

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 Şaşoğlu, Telatar, and Arıkan. In this paper, a necessary and sufficient condition of a matrix over… (More)

- Ryuhei Mori, Toshiyuki Tanaka
- IEEE Communications Letters
- 2009

Polar coding, proposed by Arıkan, makes it possible to construct capacity-achieving codes for symmetric binaryinput discrete memoryless channels, with low encoding and decoding complexity. Complexity of the originally proposed code construction method, however, grows exponentially in the blocklength unless a channel is the binary erasure channel. Recently,… (More)

- Ryuhei Mori, Toshiyuki Tanaka
- 2009 IEEE International Symposium on Information…
- 2009

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)

- Ryuhei Mori, Toshiyuki Tanaka
- 2010 IEEE Information Theory Workshop
- 2010

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)

- Toshiyuki Tanaka, Ryuhei Mori
- 2010 IEEE International Symposium on Information…
- 2010

A rate-dependent upper bound of the best achievable block error probability of polar codes with successive-cancellation decoding is derived.

- Ryuhei Mori
- ArXiv
- 2010

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)

- Ryuhei Mori
- 2011 IEEE International Symposium on Information…
- 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)

- Pravesh Kothari, Ryuhei Mori, Ryan O'Donnell, David Witmer
- STOC
- 2017

Let <i>P</i>:{0,1}<sup><i>k</i></sup> â {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 Î <i>n</i> constraints, each being <i>P</i> applied to <i>k</i> randomly chosen literals. Provided the constraint density satisfies Î â« 1, such… (More)

- Ryuhei Mori
- IEEE Transactions on Information Theory
- 2015

The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary variables by Chertkov and Chernyak. In this equality, the multiplicative error in the Bethe approximation is represented… (More)