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2009

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Korada, Satish Babu, Sasoglu, Eren, Urbanke, Rudiger

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Polar codes were recently introduced by Ar\i kan.

They achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy.
The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the $2 \times 2$ matrix $\bigl[ 1 &0 1& 1 \bigr]$.
It was shown by Ar\i kan and Telatar that this construction achieves an error exponent of $\frac12$, i.e., that for sufficiently large blocklengths the error probability decays exponentially in the square root of the length.

Polar Codes: Characterization of Exponent, Bounds, and Constructions · Around

Built on

R. E. Blahut, Theory and Practice of Error Control Codes . Addison-Wesley, 1983
1983
Earlier work this paper cites.
I. Sutskover, S. Shamai, and J. Ziv, “Extremes of information combining,” IEEE Trans. Inform. Theory , vol. 51, no. 4, pp. 1313 – 1325, Apr. 2005
2005
Earlier work this paper cites.

Similar

I. Land, S. Huettinger, P. A. Hoeher, and J. B. Huber, “Bounds on information combining,” IEEE Transactions on Information Theory , vol. 51, no. 2, pp. 612–619, 2005
Original
2005
Cited alongside, same era.
E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” submitted to IEEE Trans. Inform. Theory , 2008
2008
Cited alongside, same era.

Then

E. Arıkan and E. Telatar, “On the rate of channel polarization,” July 2008, available from “http://arxiv.org/pdf/0807.3917”
Original
2008
Later among the works it cites.
J.A. Bondy and U.S.R. Murty, Graph Theory . Springer, 2008
2008
Later among the works it cites.

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