Designs of Bhattacharyya Parameter in the Construction of Polar Codes

Polar codes, introduced by Arikan recently, can achieve capacity of symmetric channel with low complexity successive cancellation decoding strategy. In this paper, we design efficient Bhattacharyya Parameters in Polar codes construction for common communications channels. We present the satisfactory recursive formula for the four conventional channels and discuss the initial value of each recursive equations. Numerical simulations show that Polar codes are channel-specific designing codes; they can approach their capacities by selecting the frozen bits in our proposed Bhattacharyya Parameter calculating method.