Abstract:
WHEREIN I is the identity element and A1, A2,...AK are distinct nonzero elements of Galois Field (2b), wherein the indicated multiplication and addition are the Galois Field defined operations, and wherein b is an integer > 1, and K is an integer 2 Apparatus including an encoder adapted for encoding blocks of data into a sent message and a decoder adapted for recovering the data from a received message corresponding to the sent message but which may be in error wherein the blocks of data consist of K-bytes of data (D1, D2,...DK) each of b bits. The sent message comprises the K-bytes of data plus two check bytes C1 and C2, each of b bits. The decoder is effective in recovering the data without error when not more than a single byte of the received message is in error no matter how many bits may be in error in the single byte. The encoder computes the check bytes according to the relationships
Abstract:
This specification describes an error correction system for a high density memory made up of a number of monolithic wafers each containing a plurality of arrays that are addressed thru circuitry and wiring contained on that wafer. The storage bits on the wafers are functionally divided into a number of blocks each containing a plurality of words. The words of each block are on several wafers with each word made up of a plurality of arrays on a single array wafer. Each word in a block is protected by a similar error correction double multiple error detection code. The block is further protected by two additional check words made up using a b-adjacent code. Each byte in the check words protects one byte position of the words of the block. When a single error is detected in any word by the SEC-MED code the code corrects the error. If a multiple error is detected, the multiple error signal points to the word in error to be corrected by the b-adjacent code check words.
Abstract:
Apparatus including a decoder adapted for recovering the data from a received message corresponding to the sent message but which may be in error wherein the blocks of data consist of k bytes of data (D0, D1, D2,...Dk 1) each of b bits. The sent message comprises the k bytes of data plus two check bytes C1 and C2, each of b bits. The decoder is effective in recovering the data without error when not more than two of the bytes are in error no matter how many bits may be in error in the two bytes. Pointers are required which indicate the two bytes containing errors. In the absence of the pointers or in the presence of a single false pointer, the decoder is effective in recovering the data without error when not more than a single byte is in error no matter how many bits may be in error in the single byte. The message is encoded by computing the check bytes according to the relationship: C1 ID0 + ID1 +...+ IDk 1 C2 ID0 + T D1 + T2 D2 +...+ Tk 1 Dk 1 WHEREIN I is the identity element and T, T2,...,Tk 1 are distinct non-zero elements of Galois Field (2b) wherein the indicated multiplication and addition are the Galois Field defined operations, and wherein b is an integer > 1 and k is an integer 2
Abstract:
An error correction and detection circuit includes a modular encoder that provides the minimum number of check bits for encoding a particular number of data bits. Means is provided for combining several units to produce the minimum number of code bits when a larger data word is to be encoded. A storage hierarchy system using this error correction circuit is also disclosed.
Abstract:
In apparatus for correcting an error in a codeword according to a syndrome, means is provided for transforming the computed syndrome through a succession of syndrome sequences or values and for counting the number of syndrome sequences in the succession. The values of each syndrome sequence are sensed to detect a distinct predetermined value and the bit in error is located from the count of the number of syndrome sequences and inverted for correction. The preferred embodiment uses a shortened BoseChaudhuri codeword and uses a linear feedback shift register to transform the syndrome values.
Abstract:
This specification describes a system for preventing the catastrophic loss of data in one storage unit of a storage system comprised of a plurality of such storage units. In this system one of the plurality of storage units is used to store parity bits for the storage system, bit position by bit position. To be more specific, if the data in each of the storage units is considered to be a linear string of bits the storage unit containing the parity bits would contain a parity or Exclusive OR sum of all the first bits of all the storage units or, in a more general case, the j.sup.th bit of the check storage unit is the parity or Exclusive OR sum of all the j bits of all the storage units.
Abstract:
Errors in parallel binary data produced by a plurality of data track, e.g., a plurality of parallel shift registers, are corrected by a system in which the shift registers which are stuck, i.e., inalterable, are determined and counted. By single Hamming error detection means, the presence of a Hamming error and an indication of the bit position of a single Hamming error is made. Comparison means determine if the indicated Hamming error is coincident with a stuck track. Then, dependent on the parity condition of the data as well as the count of stuck tracks, apparatus is provided for complementing one or more of the stuck tracks and/or correcting the indicated Hamming error.
Abstract:
A multiple error correcting system for correcting t (t 2) errors in message of k data bits, m2 k (m+1)2, where m is an integer of at least three, comprises encoding means and decoding means. The encoding means adds r check bits, each check bit corresponding to a number of data bits; each data bit is represented by 2t check bits; these 2t check bits have only the one data bit in common; and, the number, r, of check bits is: 2mt r 2(m+1)t. The decoding means for each data bit has an error correcting circuit receiving 2t+1 inputs from input circuitry, the inputs being the data bit itself, and 2t combinations of check bits and other data bits representing the data bit. The error correcting circuit is capable of producing an output signal correctly corresponding to a data bit if no more than t inputs thereto for that data bit were in error. A coding system for generating these r check bits by augmenting Latin square codes is described.
Abstract:
The error correcting system is capable of correcting multiple random errors in data messages of k m2 data bits where m is an integer. The message is encoded by adding 2m check bits for each additional error correcting capability. The encoded message after data transfer and storage is decoded by parity checking and threshold logic decision circuits. The parity checking circuits are constructed in modular form. Each additional module adds a further error correcting capability. The outputs from each module form inputs to the threshold logic decision circuit where the error correction is made. Detection of an additional error can be simply achieved by an overall parity circuit.