|| Channel Combining for Nonstationary Polarization on Erasure Channels
||Hanwen Yao, University of California, San Diego, United States; Hessam Mahdavifar, University of Michigan, United States; Arman Fazeli, Alexander Vardy, University of California, San Diego, United States|
||D4-S4-T2: Polar Codes II
||Thursday, 15 July, 23:00 - 23:20
||Thursday, 15 July, 23:20 - 23:40
The problem of channel polarization for an arbitrary sequence of n independent channels, referred to as a non-stationary sequence of channels, is considered. Also, each of the channels is used only once for communication. We consider a general framework for polarization of non-stationary channels and aim at optimizing the framework toward obtaining the best polarization. This framework includes permuting channels before Arıkan’s pairwise channel combining operations are applied at each polarization level and skipping certain combining operations. We define an explicit optimization problem with the objective of finding the best permutation and indices of skipped operations in order to minimize a certain measure of polarization in one-level polarization. We then provide a complete solution to this optimization problem in the case of non-stationary binary erasure channels (BECs). We also propose a greedy method for polarizing non-stationary BECs, based on our solution for one-level polarization. Numerical results confirm the superiority of our method, in terms of various performance metrics, for constructing polar codes in non-stationary settings compared to prior work.