Rate-Compatible Shortened Polar Codes Based on RM Code-Aided

Chunjie Li, Haiqiang Chen, Zelin Wang, Youming Sun, Xiangcheng Li

Abstract: The minimum Hamming distance is not considered for the traditional rate-compatible shortened polar (RCSP) codes, which may cause performance degradations. In this paper we propose a hybrid algorithm to construct RCSP codes based on Reed-Muller (RM) code-aided. The shortened bits and pre-frozen bits are jointly designed by the row weight property of the common generator matrix \(G_N\) for the RM/Polar code. First, the selected shortened bits are guaranteed to be uniquely depended upon the pre-frozen bits, which makes them completely be known by the decoder. Second, the proposed construction method is designed in such way, so that the minimum row weight of \(G_N\) can be maximized. More specifically, when multiple candidate positions satisfy the conditions (weight-1 column constraint), those rows having less weights are deleted to form the shortened/pre-frozen bits, which can reduce the number of rows with small weight and naturally, make the resulting RCSP codes have larger minimum Hamming distance in average. Simulation results show that the proposed RCSP codes perform better than the traditional shortened codes at low code rates. While at high code rates, the proposed RCSP codes can achieve better performance than that of the quasi uniform punctured (QUP) polar codes, especially at large signal-to-noise ratio (SNR) region. The proposed RCSP codes can find applications in future communications, such as the beyond 5th generation (B5G) and 6th generation (6G) systems.