Channel polarization: A method for constructing capacity-achieving codes

Abstract

Abstract-A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W ) of any given binary-input discrete memoryless channel (B-DMC) W . The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W , a second set of N binary-input channels fW

Power Efficient Design of Polar Code

“…Polar codes are recently invented in 2008 [7]. This code can achieve the symmetric capacity which is the highest capacity of the channel with same probabilities for any given Binary Discrete Memoryless Channel (B-DMC) [5].…”

“…A method is proposed to constrict code sequences that achieve the symmetric capacity of any given B-DMC is called channel polarization, [7]. It works with two operations, one is channel combining and other is channel splitting [1].…”

High-Speed Decoders for Polar Codes

“…Invented by Arıkan in 2008 [5] and further refined in 2009 [6], this new class of error-correcting codes, contrary to LDPC and turbo codes, have an explicit-non-random-construction making the implementation of their encoders and decoders simpler than that of LDPC or turbo codes. Polar codes exploit the channel polarization phenomenon by which the probability of correctly estimating codeword bits tends to either 1 (completely reliable) or 0.5 (completely unreliable).…”

“…The contributions of this paper are presented in Chapter 4. 5. P. Giard, G. Sarkis, C. Thibeault, and W. J.…”

Fast software polar decoders

“…Being the first error-correcting codes with an explicit construction to provably achieve the symmetric channel-capacity, polar codes have drawn significant attention since their introduction in [1,2]. Many hardware implementations of the successive-cancellation (SC) algorithm were able to exploit the regular structure of polar codes to reduce implementation complexity [3][4][5].…”