Algebraic Design of a Class of Rate 1/3 Quasi-Cyclic LDPC Codes

Abstract

An algebraic design procedure is given for constructing rate 1/3 quasi-cyclic LDPC codes with Tanner graphs with girth 6. Parity check matrices consist of 2 × 3 block matrices of circulants of size p, a prime, exhibiting invariance under the action of a subgroup of the multiplicative group mod p. The group invariance converts the problem of avoiding short cycles into that of choosing orbits to solve connectivity constraints. A series of very low density H matrix codes constructed show surprisingly good minimum distances.