A new code construction for polar codes using min-sum density

Abstract

Polar codes are capacity achieving codes for binary-input symmetric memoryless channels (B-SMCs) if the code word length tends to infinity. Its encoding and decoding complexity is low. However, low complexity in code construction holds only for some special B-SMCs like the binary erasure channel (BEC). For all other B-SMCs, the code construction becomes a trade off between low complexity and construction accuracy. This paper gives an overview on the most popular code construction methods including a new approach yielding to near optimum code construction while reducing the complexity and increasing robustness against numerical problems. In addition, we compare the performance of the presented methods in terms of frame error rates (FERs) for codes of length 2048.