Polarization and Polar Coding

Qingping Yu, Zhiping Shi, Li Juan DENG +1 more

Bit-channels of finite-length polar codes are not fully polarized, and the negative influences from semi-polarized channels are not negligible. In this letter, we consider the concatenated system of an inner polar code and an outer low-density parity-check (LDPC) code to improve the error correction performance of finite-length polar code with belief propagation (BP) decoding. We propose a bit mapping method between LDPC coded bits and polarized channels, aiming to match the coding protection of LDPC codes with polarization of polar codes. Simulation results show that, the concatenated polar codes with bit mapping outperform the pure polar codes with BP decoding and concatenated polar codes with traditional consecutive bit mapping.

Jochen Pade

Ryuhei Mori, Toshiyuki Tanaka

Polar codes, introduced by Arıkan, achieve symmetric capacity of any discrete memoryless channels under low encoding and decoding complexity. Recently, non-binary polar codes have been investigated. In this paper, we calculate error probability of non-binary polar codes constructed on the basis of Reed-Solomon matrices by numerical simulations. It is confirmed that 4-ary polar codes have significantly better performance than binary polar codes on binary-input AWGN channel. We also discuss an interpretation of polar codes in terms of algebraic geometry codes, and further show that polar codes using Hermitian codes have asymptotically good performance.

Jochen Pade

Bin Li, Hui Shen, David N. C. Tse

In this letter we propose a new hybrid code called RM-Polar codes. This new codes are constructed by combining the construction of Reed-Muller (RM) code and Polar code. It has much larger minimum Hamming distance than Polar codes, therefore it has much better error performance than Polar codes.