This paper considers the use of polar codes to enable secure transmission over parallel relay channels. By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based on Channel State Information (CSI) between the legitimate transmitter (Alice) and the legitimate receiver (Bob). Different from existing secure transmission schemes, the proposed scheme does not require CSI between Alice and the eavesdropper (Eve). The proposed scheme is proven to be reliable and shown to be capable of transmitting information securely under Amplify-and-Forward (AF) relay protocol, thereby providing security against passive and active attackers.

Polar codes have become the channel coding scheme for control channel of enhanced mobile broadband in the fifth generation (5G) communication systems. Belief propagation (BP) decoding of polar codes has the advantage of low decoding latency and high parallelism but suffers from high complexity. In this paper, a low complexity BP decoder is proposed for polar codes. We reduce the computational complexity by two steps. First, the cyclic redundancy check is concatenated to the decoder in order to decrease the number iterations of the BP algorithm. Then, a threshold is proposed based on Gaussian approximation to save the computational complexity of BP nodes. If the log-likelihood ratio of a node in the tanner graph is larger than the threshold, this node is no longer updated during the rest of the decoding process. The simulation results show that the proposed scheme has a similar block error rate performance with the original BP decoder, while the computational complexity is reduced significantly. INDEX TERMS Polar codes, belief propagation, low complexity decoding, eMBB.

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Polar codes have become the channel coding scheme for control channel of enhanced mobile broadband in the 5G communication systems. Belief propagation (BP) decoding of polar codes has advantages of low decoding latency and high parallelism but achieves worse bit error ratio (BER) performance compared with the successive cancellation list (SCL) decoding scheme. In this paper, an improved BP list (IBPL) decoding algorithm is proposed with comparable BER performance to SCL algoritm. Firstly, the optimal permuted factor graph is analyzed for polar codes, which improves the performance of the BP decoder without path extension. Furthermore, based on the optimal graph, the bit metric and decoding path metric are proposed to extend and prune the decoding path. The proposed IBPL decoder is focused on not only the permutation of polar codes but also the reliabilities of decoded codewords during each iteration of BP decoding, which has a more accurate decoding path list. The simulation results show that the proposed IBPL decoder improves the BER performance compared with the original BP decoder significantly, and can approach the performance of the SCL decoder at low signal to noise ratio regions.

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