Design SNR Optimization of Polar Codes Over Block Rician Fading Channels

The performance of polar codes depends on its construction, and the code design process requires the knowledge of channel signal-to-noise power ratio (SNR), which will be used as a design SNR in several low-complexity construction algorithms under the assumption of successive cancellation (SC) decoding. In the case of fading channels, however, the instantaneous SNR may not be constant and thus the major challenge is how to select the design SNR in view of achieving best block error rate (BLER) performance. In this work, focusing on block Rician fading channels, we show that the straightforward use of average SNR as design SNR may lead to suboptimal BLER performance. We then propose a design SNR optimization algorithm based on the estimated average BLER of polar codes over Rician fading channels. Furthermore, we propose an alternative polar code construction algorithm based on the estimated average bit error rate (BER) over Rician fading channels whose complexity is much lower than that based on the BLER. Simulation results confirm that both approaches can achieve good BLER performance.

I. Introduction

Polar codes [1] can approach the capacity of a practical binary-input additive white Gaussian noise (BI-AWGN) channel as the codeword length N increases. Based on channel polarization, the reliability of the bit channels can become diverse. By selecting the channels with highest reliability for information bit transmission and the remaining channels as frozen, the information rate close to channel capacity can be achieved even with a simple successive cancellation (SC) decoding of complexity order O(N log N).