Abstract: An improved cross-checking circuit is provided for use within a Reed-Solomon error correction and cross checking apparatus for performing error correction and cross checking upon a data block within an incoming stream of substantially contiguous data blocks flowing from a source to a destination. The circuit is based upon a distinguished primitive element, alpha.sup.1 (2B (Hex))=x.sup.5 +x.sup.3 +x+1, of a Galois field whose elements are represented by residue classes of binary polynomials modulo p(x)=x.sup.8 +x.sup.4 +x.sup.3 +x.sup.2 +1. The apparatus includes a microcontroller for supervising the flow of the data blocks and for making calculations related to error corrections, and a Galois field syndrome generator and remainder recovery circuit is connected to receive the incoming stream and recover therefrom plural error correction remainder bytes for each block and selectively to hold said bytes in a syndrome latch, the remainder bytes being related to syndrome bytes appended to the data block.

Abstract: This disclosure concerns for generating asymmetrically constrained run-length-limited encoded data from a serialized binary string of 1's and 0's. The method comprises the steps of encoding the input data bits using a run-length-limited constraint in the form of M/N (d,k), where M is the number of input data bits, N is the number of output bits associated therewith, d is the minimum number of 0 data bits between adjacent data bit 1's, and k is the maximum number of 0 data bits between adjacent 1's; and alternating the values of d and k between a set (d.sub.1, k.sub.1) and a set (d.sub.2, k.sub.2), respectively, where d.sub.1 .noteq.d.sub.2. The apparatus comprises means for generating N output data bits in response to M input data bits and for generating data bit 0's between data bit 1's based upon a run-length-limited coding constraints (d.sub.1, k.sub.1) and (d.sub.2, k.sub.2), where constraints (d.sub.1, k.sub.1) and (d.sub.2, k.sub.2) apply alternately to runs of zeroes between output data ones.

Abstract: A maximum-likelihood sequence decoder is used with a partial-response signaling system for processing sequences of sampled values from a communication channel or recording device. The partial-response signals can be duobinary, dicode, or partial-response class-IV. The maximum-likelihood decoding for each sequence can be based upon a two-state trellis. Instead of two survivor metrics for two states, only a difference metric is necessary.

Abstract: A maximum-likelihood sequence decoder is used with a partial-response signaling system for processing sequences of sampled values from a communication channel or recording device. The partial-response signals can be duobinary, dicode, or partial-response class-IV. The maximum-likelihood decoding for each sequence can be based upon a two-state trellis. Instead of two survivor metrics for two states, only a difference metric is necessary.