Performance of Polar Codes with the Construction using Density Evolution

Polar coding, proposed by Arikan, makes it possible to construct capacity-achieving codes for symmetric binary-input discrete memoryless channels, with low encoding and decoding complexity. Complexity of the originally proposed code construction method, however, grows exponentially in the blocklength unless a channel is the binary erasure channel. Recently, the authors have proposed a new capacity-achieving code construction method with linear complexity in the blocklength for arbitrary symmetric binary-input memoryless channels. In this letter, we evaluate performance of polar codes designed with the new construction method, and compare it with that of the codes constructed with another heuristic method with linear complexity proposed by Arikan.