A study on channel polarization and polar coding

In 2006, Arikan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel (B-DMC). In this letter, we will give a description of the main ideas and mechanisms of this kind of codes. The codes construction, decoding algorithm as well as the probability of block error under successive cancellation (SC) decoding are also discussed.

[1]  E. Arkan,et al.  A performance comparison of polar codes and Reed-Muller codes , 2008, IEEE Communications Letters.

[2]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[3]  Erdal Arikan,et al.  Channel polarization: A method for constructing capacity-achieving codes , 2008, 2008 IEEE International Symposium on Information Theory.

[4]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.

[5]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[6]  Ryuhei Mori.  Properties and Construction of Polar Codes , 2010, ArXiv.

[7]  Erdal Arikan.  Channel combining and splitting for cutoff rate improvement , 2006, IEEE Transactions on Information Theory.