Abstract: 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.ltoreq.

Abstract: In a shift-correcting code which represents (d,k)-constrained run-length-limited (RLL) channel data as symbols drawn from GF(p.sup.m), the encoding process produces a set of redundant parity ternary GF(p.sup.m) symbols representing three shift error conditions: forward shift, backward shift and no shift, for p=3 and m=1 for example. The encoder of the invention transforms the parity symbols into (d,k)-constrained RLL channel bits to produce a binary data sequence that can be inserted in the RLL channel data stream without a large number of linking bits to maintain compliance with the (d,k) RLL constraints. A shift error in the RLL channel data representing parity symbols affects no more than one decoded parity symbol.

Abstract: A method for coding/decoding ternary symbols to d,k-constrained binary runs in a way that (i) associates (codes) a number of ternary symbols with a lesser number of d,k-constrained binary runs and (ii) provides that an individual single-shift error in any of the received binary runs that constitute a binary data codeword will cause at most one ternary symbol to be in error in the associated (decoded) ternary symbol codeword. This method allows shift-correction codeword parity checks to be transmitted (i.e., transformed to a d,k-constrained channel data sequence) with increased efficiency, so that the required number of channel bits needed to represent the parity checks is decreased.

Abstract: Channel encoded data (for example run length limited encoded data) is further encoded in accordance with a shift correction code prior to transmission. Upon reception, forward and backward shift errors present in the received channel encoded data are corrected by a shift correction decoder. The shift error correction is accomplished using a code, such as (for example) a BCH code over GF(p) or a negacyclic code, which treats each received symbol as a vector having p states. For a single shift error correction, p=3 and there are three states (forward shift, backward shift, no shift). In one embodiment, conventional error correction codewords which encode the user data may be interleaved within successive shift correction codewords prior to channel encoding, thereby enabling the error correction system to easily handle a high rate of randomly distributed shift errors (which otherwise would result in a high rate of short error bursts that exceed the capacity of the block error correction code).