Title: "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels"
Speaker: Beryl Sui, Department of ECE, UCLA
Date: Thursday, November 30, 2023 at 9:00 am in Los Angeles, Pacific Standard Time
Abstract: This is a tutorial presentation of the paper “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels” by Erdal Arıkan. In Arıkan’s paper, 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 {W_N^{i}: i <= i <= N} such that, as N becomes large, the fraction of indices i for which I(W_N^(i)) is near 1 approaches I(W) and the fraction for which I(W_N^(i)) is near 0 approaches 1-I(W). The polarized channels {W_N^(i)} are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R << I(W), there exists a sequence of polar codes {C_n; n >=1} such that C_n has block-length N=2^n, rate >= R, and probability of block error under successive cancellation decoding bounded as P_e(N,R) <= O(N^-1/4) independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N logN) for each.
Speaker Biography: Wenhui Sui (Student Member, IEEE) received the B.S. and M.S. degrees in electrical engineering from the University of California at Los Angeles (UCLA) in 2023, where she is currently pursuing the Ph.D. degree with the Communications Systems Laboratory. Her research interests include convolutional codes, LDPC codes, and channel coding theory. Her honors include 2022 UCLA ECE Fast Track to Success Honors and 2023 UCLA ECE Departmental Scholar.
Related References: E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels,” in IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051-3073, July 2009, doi: 10.1109/TIT.2009.2021379.