Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors

摘要

Consider the transmission of a polar code of block length N and rate R over a binary memoryless symmetric channel W and let Pe be the block error probability under successive cancellation decoding. In this paper, we develop new bounds that characterize the relationship of the parameters R , N , Pe , and the quality of the channel W quantified by its capacity I(W) and its Bhattacharyya parameter Z(W) . In previous work, two main regimes were studied. In the error exponent regime, the channel W and the rate R