Yingxian Zhang

Polar-LDPC Concatenated Coding for the AWGN Wiretap Channel

In this paper, a concatenated coding scheme based on polar codes and LDPC codes is proposed for the additive white Gaussian noise (AWGN) wiretap channel. We first analyze the bit error rate (BER) performance of the proposed coding scheme through the density evolution (DE). Then, the security gap that our coding scheme can achieve is investigated. Finally, to adapt to the dynamic environments, we present a transmission scheme using rate compatible Polar-LDPC codes. Numerical results suggest that the proposed coding scheme is more effective and flexible than other existing secure coding schemes.

A Modified Belief Propagation Polar Decoder

In this paper, a modified belief propagation (BP) polar decoder is proposed. Unlike the orignal BP polar decoders, a check node is added to each node of the proposed decoder. In the BP decoding, the propagated messages of the nodes are modified by multiplying the messages from the check nodes, so as to enhance the reliability of these propagated messages. Numerical results show that the proposed decoder achieves better performance than that of the original BP decoders, only at cost of some additional multiplications, which indicates its effectiveness.

A Practical Construction Method for Polar Codes

In this paper, a practical construction method is proposed for polar codes over binary-input channels. Unlike the existing construction methods, we use a Bhattacharyya parameter bound to select the bit-channels over which the information bits are transmitted. We first derive the expression of the Bhattacharyya parameter bound, and introduce a method to achieve its exact value. Then, we present our construction method for different binary-input channels. Numerical results show that, the achievable rate of our method approaches the theoretical value, and its performance is better than that of some existing methods, while the complexity is O(N log N) (N is codeword length), which indicates its effectiveness.

Practical Design and Decoding of Parallel Concatenated Structure for Systematic Polar Codes

In this paper, a parallel concatenated structure is proposed to improve the performance of polar codes in finite length in which multiblocks systematic polar codes (SPC) and recursive systematic convolutional codes (RSC) are combined. We first design a weighted iterative decoding algorithm for the proposed structure such that better bit error rate performance can be obtained. Then, a deliberated interleaver is optimized for the new scheme. Thereafter, we introduce a strategy to estimate the minimum distance of the concatenation codeword, where an asymptotic performance and convergence behavior analysis are elaborated. Finally, the error performance of the proposed scheme is evaluated via simulations. The results show that our scheme almost outperforms all the existed concatenation ones using polar codes, making the codes more practical.

Symbol-Based Belief Propagation Decoder for Multilevel Polar Coded Modulation

In this letter, symbol-based belief propagation decoder is proposed for multilevel polar coded modulation (MLPCM) scheme. Unlike the traditional multi-stage detection (MSD) strategy by decoding polar codes level by level after demapping, we directly calculate the probabilities of symbols and do demapping after the symbol decoding process so as to decrease the decoding delay and improve the performance of MLPCM. The lower bound of frame error rate for MLPCM is also estimated using the union bound technique. Numerical results show that the performance of proposed decoder well matches the estimated bound for pulse amplitude modulation (PAM) modulation and outperforms the MSD strategy about 0.5−1 dB with lower decoding delay, only at the cost of some additional computational complexity, which indicates its effectiveness.

Concatenated polar codes based on selective polarization

In this paper, we propose a selectively polarized concatenation structure for polar codes. We first divide the polarized bit-channels into three types, i.e., good, intermediate and bad bit-channels according to their Bhattacharyya parameter. Then, through combining several information blocks, the intermediate bit-channels are further polarized to enhance polarization rate. Theoretical and numerical results indicate that the proposed scheme achieves the same capacity as original polar codes at the same length, while the bit error rate (BER) performance is better than that of original polar codes as same decoding delay is considered. The polar codes can be used in the cognitive radio system.

A Generalization Belief Propagation Decoding Algorithm for Polar Codes Based on Particle Swarm Optimization

We propose a generalization belief propagation (BP) decoding algorithm based on particle swarm optimization (PSO) to improve the performance of the polar codes. Through the analysis of the existing BP decoding algorithm, we first introduce a probability modifying factor to each node of the BP decoder, so as to enhance the error correcting capacity of the decoding. Then, we generalize the BP decoding algorithm based on these modifying factors and drive the probability update equations for the proposed decoding. Based on the new probability update equations, we show the intrinsic relationship of the existing decoding algorithms. Finally, in order to achieve the best performance, we formulate an optimization problem to find the optimal probability modifying factors for the proposed decoding algorithm. Furthermore, a method based on the modified PSO algorithm is also introduced to solve that optimization problem. Numerical results show that the proposed generalization BP decoding algorithm achieves better performance than that of the existing BP decoding, which suggests the effectiveness of the proposed decoding algorithm.

Codes design based on EXIT chart for polar coded BICM-ID

Polar codes are applied to bit-interleaved coded modulation system with iterative decoding (BIPCM-ID) system. To optimize the iterative decoding performance, conventional polar coding construction is modified by extrinsic information transfer (EXIT) chart methodology. Simulation results show that BIPCM-ID system based on the proposed technique can outperforms BIPCM over 16-ary quadrature-amplitude with 1 dB.

An ARQ-aided polar coding scheme for security transmission of the wiretap channel

In this paper, an Automatic Repeat Request (ARQ)-aided secure polar coding scheme for the wiretap channel is proposed, where the frozen bits of the codes are obtained through the feedback of the legitimate recipient. Then, security of the proposed scheme is investigated, and analytical work proves that, both the reliability condition and security condition can be satisfied, specifically for the non-degraded wiretap channel. Finally, some simulation results reveal that the proposed scheme can transmit confidential messages reliably and securely.

Analysis and Adaptive Design of Polar Coded HARQ Transmission Under SC-List Decoding

A novel polar coded hybrid-ARQ (PC-HARQ) transmission with chase combining utilizing powerful successive cancellation list decoder (HARQ-CC-SCL) is explored. We propose that by applying the distance spectrum of polar code to evaluate its frame error rate, the bounds of throughput and average transmission number can be derived. Then, this letter proposes an adaptive scheme combining the list size-manageable SCL decoding with ARQ protocol. Simulations indicate that the proposed HARQ-CC-SCL obtains a considerable throughput improvement of PC-HARQ-CC system, and approaches those of HARQ schemes with incremental redundancy through less transmission times for each packet. Meanwhile, the adaptive version achieves high throughput and good flexibility in practical applications without significant increase of complexity.