Design of Binary and Nonbinary Codes from Lifting of Girth-8 Cycle Codes with Minimum Lengths

In this paper, some regular and irregular girth-8 cycle codes with arbitrarily high code rates are presented which have minimum lengths among all girth-8 cycle codes having parity-check matrices of the same row regularity. The paritycheck matrices of the constructed girth-8 cycle codes can be considered as the mother matrices of some quasi-cyclic (QC) cycle codes with maximum-achievable girth 24 having better rates rather than the girth-24 Geometric and Cylinder-type cycle codes. Simulation results show that the binary and nonbinary constructed cycle codes perform better than the repeat accumulate (RA) codes, progressive edge growth (PEG) codes and random-like LDPC codes of the same lengths and rates.

LDPC codes, Tanner graph, girth