LAUSR

Polar codes are linear block code with generator matrix GN = BNF ⊗log2N 2 , where N is code length and BN denotes bitreverse permutation matrix [1]. F2 = [ 1 0 1 1 ]. In this paper, a N 1 is used to denote row vector (a1, ..., aN ). With this notation, the encoding process can be expressed as x1 = u N 1 GN , where x N 1 = (x1, ..., xN ) is codeword and u N 1 = (u1, ..., uN ) is source bit sequence. u1 includes both information bits and frozen bits. Frozen bits are fixed to zero in this appendix. This work focuses on how to choose the index set of information bits in u1 under higher order modulation. Denote W a binary-input memoryless symmetric channel with input alphabet X = {0, 1} and output alphabet Y. W (y|x) is the transition probability of W , where x ∈ X and y ∈ Y. The Bhattacharyya parameter of W defined in [1] is