Construction of Regular and Irregular LDPC Codes using (n, {k1, k2}, 1) Block Design

In this paper, we construct regular and irregular LDPC codes using (n, {k ₁, k ₂}, 1)block design. The problem of designing regular and irregular structured LDPC codes that have good overall error performance for wide range of code rates and block sizes with attractive storage requirements is attempted. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Further we analyze the constructed codes based on number of short cycles of the corresponding Tanner graph. The analysis shows that codes having small number of short cycles and a cycle structure which is not overly regular in their Tanner graph perform better. The presented codes are well structured and unlike random codes can lend themselves to a very low-complexity encoder and decoder implementation.