Nonbinary quantum codes derived from finite geometries

Jian‐Zhang Chen, Jianping Li, Fan Yang +1 more

Juane Li, Keke Liu, Shu Lin +1 more

This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.

Xueqin Hu, Guanghui Zhang, Bocong Chen

Pradeep Kiran Sarvepalli, Andreas Klappenecker

Lisheng Zhang, Fanxin Zeng, Lirui Tan

In this paper, a family of nonbinary LDPC codes over a finite field GF(q) is presented and its properties are derived. In comparison with the second method presented by Ref. [4], the simulation results show that in 16-ary (75,150), 64-ary (441,882) and 128-ary (1270,2540) LDPC code, the proposed LDPC codes have a slight higher coding gain, 0.25dB, 0.2dB, and 0.15 dB at the BER= 10-4, respectively, which demonstrates that the proposed nonbinary LDPC codes are valid.

Haiyang Liu, Hao Zhang, Lianrong Ma +1 more

In this letter, the structural analysis of nonbinary cyclic and quasi-cyclic (QC) low-density parity-check (LDPC) codes with α-multiplied parity-check matrices (PCMs) is concerned. Using analytical methods, several structural parameters of nonbinary cyclic and QC LDPC codes with α-multiplied PCMs are determined. In particular, some classes of nonbinary LDPC codes constructed from finite fields and finite geometries are shown to have good minimum and stopping distances properties, which may explain to some extent their wonderful decoding performances.