Design of LDPC codes using degree distributions of Tanner graphs

Kenya Sugihara, Hideo Yoshida

Huang–Chang Lee, Jyun-Ching Wang, Yi-Tsun Huang +1 more

This letter presents a construction flow for rate-compatible LDPC (RC-LDPC) codes, collaboratively using both extension and splitting schemes. In addition to the decoding threshold used for selecting the degree distribution, a new metric, known as the Average ACE (A2CE) value, is introduced in order to estimate the Tanner graph connectivity. The proposed collaborative scheme provides more flexibility in the designs of the degree distribution and graph connectivity, both of which are critical for RC LDPC codes that have short and/or moderate lengths. The designed LDPC codes achieve a comparable or better error rate performance compared to existing codes.

Yongyi Mao, Amir H. Banihashemi

For a given block length and given degree sequences of the underlying Tanner graph (TG), the ensemble of short low-density parity-check (LDPC) codes can have considerable variation in performance. We present an efficient heuristic method to find good LDPC codes based on what we define as the girth distribution of the TG. This method can be used effectively to design short codes for applications where delay and complexity are of major concern.

好一 坂庭, KOHICHI SAKANIWA

Guojun Han, Yong Liang Guan, Lingjun Kong +2 more

Non‐binary low‐density parity‐check (NB‐LDPC) codes can be directly constructed by using algebraic methods, or indirectly constructed by mapping well‐designed binary parity‐check matrices to non‐binary parity‐check matrices. Given the Tanner graph (TG) of a NB‐LDPC code, the selection of edge weights in the TG significantly affects the performance of the NB‐LDPC code. The authors introduce an edge weight distribution (EWD) parameter for the TG of NB‐LDPC codes. By utilising particle swarm optimisation (PSO), the EWD is optimised and it has been demonstrated that the optimal EWD approaches a two‐element distribution for large field size and high average variable‐node degree. With the optimised EWD, the authors construct a class of field‐compatible LDPC (FC‐LDPC) codes over GF( q ) whose parity‐check matrices only include elements 0, 1 and 2, and can be encoded and decoded over different field sizes. The simulations demonstrate that the performance of the proposed FC‐LDPC codes improves monotonically with increasing field size, and significantly outperforms that of the corresponding algebraic NB‐LDPC codes or NB‐LDPC codes generated with uniform distribution of non‐zero elements over GF( q ).

M. Ahmadi, H. Dehghani, ‎Saeid Alikhani +1 more