Theoretical estimation of defect management reliability

Data integrity is one of the most important performance of the optical disk. Long Distance Code (LDC) is used in the optical disk conforms to ISO/IEC standard to correct the read data error. This article shows the LDC format of ISO/IEC IS15041 as an example. The sector size is 2048 bytes. There are 20 interleaved Reed Solomon codes whose minimum weight are 17. When there are errors which exceed pre-determined criteria at verify, whole data of the sector is rewritten in the spare sector. The address of original sector and that of the replaced sector is written in Secondary Defect List (SDL) area. The sector replacement criteria is based on the number of errors in one Reed Solomon Code (RSC). The reliability of the defect management depends on the detection probability of the errors by RSCs. This paper describes the theoretical estimation of upper bound probability of the mis-detection of error at verify mode.