Efficient encoding and minimum distance bounds of Reed-Solomon-type array codes

Abstract

Array codes that are based on Reed-Solomon codes have been recognized to give a simple deterministic construction of binary low-density parity-check codes, which for moderate lengths and high rates achieve similar performance as randomly constructed codes. New sparse generator matrices for these quasi-cyclic codes are presented that lead to fast encoding schemes with linear complexity in the code length. From the low-density properties of these generator matrices upper bounds on the minimum Hamming distance of the codes are derived.