On Coding for 2-D Storage Systems

Abstract

In this paper we compare some aspects of the design and analysis of one-dimensional (1-D) and two-dimensional (2-D) storage systems. We show that for modulation codes and for the detection of signals corrupted by intersymbol interference and additive white Gaussian noise, the design and analysis is much more complicated in the 2-D case as compared with the 1-D case. However, we show that the reverse is true for the design of burst error correcting cyclic codes. That is, we show that one must carefully choose the generator polynomial to obtain a good 1-D burst error correcting code but using a cyclic product code, any arbitrary generator polynomials for the row code and for the column code can produce a good 2-D burst error correcting code.