Shift correction code system for correcting additive errors and synchronization slips

摘要

In a shift correction decoder which processes d,k-constrained RLL data that is encoded in accordance with a shift correction code whose symbols in GF(p) comprise modulo p reductions of cumulative sums of successive run symbols of the RLL data (where p is an odd prime), additive errors (i.e., drop-out and drop-in errors) in the received RLL data are corrected by relying in part on information pertaining to the sequence of the polarities of successive 1-bits in the received RLL data. The polarity information is used to either insert missing 1-bits (due to drop-outs) or delete spurious 1-bits (due to drop-ins) and specify to the shift correction decoder the location of an additive error as an erasure. Synchronization slips are corrected by pre-multiplying the received codeword polynomial by a factor which reduces to two the number of errors created by a single synchronization slip. GF(p) is selected such that p