Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording

This paper introduces a combinatorial construction of a class of iteratively decodable codes, an approach diametrically opposed to the prevalent practice of using large, random-like codes. Our codes are well-structured and, unlike random codes, can lend themselves to a very low complexity implementation. A systematic way of constructing codes based on Steiner systems and the Z_ν, group is presented, and a hardware efficient encoding algorithm is proposed. A substantial performance improvement of high-rate Steiner codes over the existing schemes used in magnetic recording systems is demonstrated