MDS Product Code Performance Estimations Under Header CRC Check Failures and Missing Syncs

Abstract

Data storage systems that use removable media heavily rely on strong concatenated error correction coding (ECC) architectures in order to guarantee very low target data loss rates. Particularly, tape drives and optical disk drives (e.g., CD, DVD, and BD) employ powerful ECC schemes based on a concatenation of an outer maximum distance separable (MDS) code called C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and an inner MDS code called C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> in order to achieve this performance. In addition to data, these storage systems employ header and synchronization appends (i.e., sync patterns) for appropriate allocation of user information on the physical storage medium. Since headers and sync patterns are subject to channel errors as well, accurately retrieved data may be regarded useless if an error occurs in either of these fields. In order to predict very low target C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> failure rates (which is typically on the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> ) in the presence of header and synchronization errors, we propose a semianalytical method in this paper that incorporates the effects of the header and synchronization errors in the output error rate expressions. We use our proposed model with linear tape open (LTO) data examples to both show the effectiveness of the estimation results and draw some interesting conclusions.