Array-Code Ensembles -or- Two-Dimensional LDPC Codes

Probabilistic construction of codes on two-dimensional arrays is proposed and analyzed. Instead of a pure combinatorial erasure model used in traditional array codes, we propose a mixed combinatorial-probabilistic model of limiting the number of column failures, with assuming a binary erasure channel in each failing column. In addition, motivated by practical applications, we maintain an array with a fixed number of columns, while allowing the column size to grow to infinity. As a result, we obtain a framework that allows developing powerful constructions and analysis techniques previously only applicable in the theory of iteratively decoded one-dimensional low-density parity-check codes. The new array-code ensembles are shown to approach the performance of traditional MDS codes, with a simple decoder that offers better scalability in the number of column failures.