1970results about "Cyclic codes" patented technology

The invention discloses a data validation, mirroring and error/erasure correction method for the dispersal and protection of one and two-dimensional data at the micro level for computer, communication and storage systems. Each of 256 possible 8-bit data bytes are mirrored with a unique 8-bit ECC byte. The ECC enables 8-bit burst and 4-bit random error detection plus 2-bit random error correction for each encoded data byte. With the data byte and ECC byte configured into a 4 bit×4 bit codeword array and dispersed in either row, column or both dimensions the method can perform dual 4-bit row and column erasure recovery. It is shown that for each codeword there are 12 possible combinations of row and column elements called couplets capable of mirroring the data byte. These byte level micro-mirrors outperform conventional mirroring in that each byte and its ECC mirror can self-detect and self-correct random errors and can recover all dual erasure combinations over four elements. Encoding at the byte quanta level maximizes application flexibility. Also disclosed are fast encode, decode and reconstruction methods via boolean logic, processor instructions and software table look-up with the intent to run at line and application speeds. The new error control method can augment ARQ algorithms and bring resiliency to system fabrics including routers and links previously limited to the recovery of transient errors. Image storage and storage over arrays of static devices can benefit from the two-dimensional capabilities. Applications with critical data integrity requirements can utilize the method for end-to-end protection and validation. An extra ECC byte per codeword extends both the resiliency and dimensionality.

Modern communication systems must cope with varying channel conditions and differing throughput constraints. Polar codes despite being the first error-correcting codes with an explicit construction to achieve the symmetric capacity of memoryless channels are not currently employed against other older coding protocols such as low-density parity check (LDPC) codes as their performance at short/moderate lengths has been inferior and their decoding algorithm is serial leading to low decoding throughput. Accordingly techniques to address these issues are identified and disclosed including decoders that decode constituent codes without recursion and/or recognize classes of constituent directly decodable codes thereby increasing the decoder throughput. Flexible encoders and decoders supporting polar codes of any length up to a design maximum allow adaptive polar code systems responsive to communication link characteristics, performance, etc. whilst maximizing throughput. Further, designers are provided flexibility in implementing either hardware or software implementations.

The present invention provides a distributed clustering method to allow multiple active instances of consistency management processes that apply the same encoding scheme to be cooperative and function collectively. The techniques described herein facilitate an efficient method to apply an erasure encoding and decoding scheme across dispersed data stores that receive constant updates. The technique can be applied on many forms of distributed persistent data stores to provide failure resiliency and to maintain data consistency and correctness.

Iterative decoder employing multiple external code error checks to lower the error floor and/or improve decoding performance. Data block redundancy, sometimes via a cyclic redundancy check (CRC) or Reed Solomon (RS) code, enables enhanced iterative decoding performance. Improved decoding performance is achieved during interim iterations before the final iteration. A correctly decoded CRC block, indicating a decoded segment is correct with a high degree of certainty, assigns a very high confidence level to the bits in this segment and is fed back to inner and/or outer decoders (with interleaving, when appropriate) for improved iterative decoding. High confidence bits may be scattered throughout inner decoded frames to influence other bit decisions in subsequent iterations. Turbo decoders typically operate relatively well at regions where the BER is high; the invention improves iterative decoder operation at lower BERs, lowering the ‘BER floor’ that is sometimes problematic with conventional turbo decoders.

Various embodiments of the present invention provide systems and methods for data processing. For example, a variable iteration data processing system is disclosed that includes at least a first detector, a second detector, a decoder, and a queuing buffer. The first detector is operable to perform a data detection on an input data set at a first time. The decoder receives a derivation of an output from the first detector and performs a decoding process. Where the decoding process fails to converge, the decoder output is passed to the second detector for a subsequent detection and decoding process at a second time.

A system for configuring solid-state storage devices comprises a solid-state storage device and an error correction code (ECC) selection system. The ECC selection system is configured to automatically select a set of error correction code based on an error rate of the storage device. The ECC selection system is further configured to install the selected set of error correction code in the solid-state storage device.

Transmitters, receivers, and coding schemes to increase data rate and decrease bit error rate of an optical data link are disclosed. Data is transmitted across the link with a less than nominal bit error rate (BER), by encoding the data using a forward error correction (FEC) code or by requesting retransmission of transmitted packets in error. Data is transmitted at a speed that introduces errors at a rate that is in excess of the nominal BER but that may be corrected using the FEC code or retransmission so that the data may be received with less than the nominal BER. The data rate is increased as the link operating speed is increased beyond the overhead required by the FEC codes or retransmission. High speed FEC encoders and decoders facilitating such transmission are disclosed.

An error correcting device for correcting erroneous data included in data read out from a nonvolatile memory includes a determining unit that determines whether the data read out from the nonvolatile memory include an error beyond an error correcting capability of the error correcting device. When the determining unit has determined that an error beyond the error correcting capability exists, the error correcting device does not perform the correction of the error.

A communications system can provide methods of dynamically interleaving streams, including methods for dynamically introducing greater amounts of interleaving as a stream is transmitted independently of any source block structure to spread out losses or errors in the channel over a much larger period of time within the original stream than if interleaving were not introduced, provide superior protection against packet loss or packet corruption when used with FEC coding, provide superior protection against network jitter, and allow content zapping time and the content transition time to be reduced to a minimum and minimal content transition times. Streams may be partitioned into sub-streams, delivering the sub-streams to receivers along different paths through a network and receiving concurrently different sub-streams at a receiver sent from potentially different servers. When used in conjunction with FEC encoding, the methods include delivering portions of an encoding of each source block from potentially different servers.

A disk drive is disclosed comprising a head actuated over a disk. A redundancy generator generates a plurality of redundancy symbols appended to user data to form a codeword C(x) written to a selected data sector on the disk. During a read operation, a syndrome generator generates a plurality of error syndromes in response to a received codeword C′(x) generated by reading the selected data sector. An error detector, responsive to the error syndromes, detects a number of errors in the received codeword C′(x), and a plurality of counters count a number of times the number of errors falls within a predetermined plurality of ranges to thereby provide a distribution of the errors. The error distribution is used, for example, for selecting a track density or ECC depth, or for failure prediction or defect mapping.

A computing system retrieves securely stored encrypted and encoded data from a dispersed data storage system. The computing system includes a processing module and a plurality of storage units. The processing module includes an error decoder and a decryptor and to decode and decrypt the encrypted and encoded data retrieved from the dispersed data storage system utilizing a read command to the storage units. The storage units retrieve the encrypted and encoded data and send the encrypted and encoded data to the processing module when receiving the read command.

A digital modulator which inputs a data stream to convert to a channel bit stream. The multiplexed data block is generated by multiplexing dummy data to any position within each data block cut out of the data stream one by one. The first Reed-Solomon code is generated by Reed-Solomon-encoding the multiplexed data block as an information part. A plurality of second Reed-Solomon codes are generated by adding a plurality of Reed-Solomon codes for scrambling each of which has identification data showing its scrambling pattern in the same position as that of the dummy data, and the code length of information part and parity part is the same as the first Reed-Solomon code. The second Reed-Solomon code in which the characteristics becomes desirable after modulation among the plurality of the second Reed-Solomon codes is set for output.

A method of printing digital data onto a photograph using infra-red ink and using an ink jet printing process is disclosed. The data can store the details of an image taken by a camera, which has been transformed by a proprietary image processing program, loaded separately into the camera, along with a copy of the program, the data being recorded in a fault tolerant form enabling the copying or recovery of the transformed photograph or of the original thereof notwithstanding damage thereto.

An algorithmic soft-decision decoding method for Reed-Solomon codes proceeds as follows. Given the reliability matrix Pi showing the probability that a code symbol of a particular value was transmitted at each position, computing a multiplicity matrix M which determines the interpolation points and their multiplicities. Given this multiplicity matrix M, soft interpolation is performed to find the non-trivial polynomial Q<HIL><PDAT>M</SB><PDAT>(X,Y) of the lowest (weighted) degree whose zeros and their multiplicities are as specified by the matrix M. Given this non-trivial polynomial Q<HIL><PDAT>M</SB><PDAT>(X,Y), all factors of Q<HIL><PDAT>M</SB><PDAT>(X,Y) of type Y-f(X) are found, where f(X) is a polynomial in X whose degree is less than the dimension k of the Reed-Solomon code. Given these polynomials f(X), a codeword is reconstructed from each of them, and the most likely of these codewords selected as the output of the algorithm. The algorithmic method is algebraic, operates in polynomial time, and significantly outperforms conventional hard-decision decoding, generalized minimum distance decoding, and Guruswami-Sudan decoding of Reed-Solomon codes. By varying the total number of interpolation points recorded in the multiplicity matrix M, the complexity of decoding can be adjusted in real time to any feasible level of performance. The algorithmic method extends to algebraic soft-decision decoding of Bose-Chaudhuri-Hocquenghem codes and algebraic-geometry codes.</PTEXT>

A coding system comprises pre-multiply the message u(x) by Xn−k. Obtain the remainder b(x), i.e. the parity check digits. And combine b(x) and Xn−ku(x) to obtain the code polynomial. A decoding method comprises calculating a syndrome; finding an error-location polynomial; and computing a set of error location numbers.

A method of encoding data for transmissions from a source to a destination over a communications channel is provided. The method operates on an ordered set of source symbols and may generate zero or more redundant symbols from the source symbols, wherein data is encoded in a first step according to a simple FEC code and in a second step, data is encoded according to a second FEC code, more complex than the first FEC code. The first FEC code and/or the second FEC code might comprise coding known in the art. These steps result in two groups of encoded data in such a way that a low-complexity receiver may make use of one of the groups of encoded data while higher complexity receivers may make use of both groups of encoded data.

A multiple protection group (MPG) erasure-resilient coding method for constructing MPG codes for encoding and decoding data. The MPG codes constructed herein protect data chunks of data in multiple protection groups and subgroups. In general, the MPG erasure-resilient codes are constructed by locating data chunks into multiple protection groups and assigning at least one parity chunk to each protection group. Basic MPG codes are constructed from existing Maximum Distance Separable (MDS) codes by splitting at least some of the parity chunks into local parities for each of the multiple protection groups and projecting local parities onto each of the groups. Generalized MPG codes have a Maximally Recoverable property that can be used to determine whether an erasure pattern is recoverable or unrecoverable. Generalized MPG codes can recover any erasure pattern that is recoverable.

This invention relates generally to a packet recovery algorithm for real-time (live) multi-media communication over packet-switched networks, such as the Internet. Such multi-media communication includes video, audio, data or any combination thereof. More specifically, the invention comprises a forward error correction (FEC) algorithm that addresses both random and burst packet loss and errors, and that can be adjusted to tradeoff the recoverability of missing packets and the latency incurred. The transmitter calculates parity packets for the rows, columns and diagonals of a block of multi-media data packets using the exclusive or (XOR) operation and communicates the parity packets along with the multi-media data packets to the receiver. The receiver uses the parity packets to recover missing multi-media data packets in the block. The FEC algorithm is designed to be able to recover long bursts of consecutive missing data packets. If some parity packets are missing, they too can be recovered using an extra single parity packet, so that they can be used to recover other missing data packets. The invention applies to both one-way real-time streaming applications and two-way real-time interactive applications, and to both wired and wireless networks. The invention retains backwards compatibility with existing standards governing FEC for professional video over IP networks.

A digital broadcast system having storing resistance to errors generated during the transmission of mobile service data, and a data processing method are disclosed. The digital broadcast system additionally encodes mobile service data. As a result, the mobile service data has strong resistance to a channel variation and noise, and at the same time the system can quickly cope with the channel variation.

A Reed-Solomon decoder includes a Chien search circuit to receive an error location polynomial function, performs Chien search, and finds an error location; a Forney algorithm circuit to receives an error pattern polynomial function and find an error pattern; and, a seed generator circuit to indicates a seed value corresponding to a codeword length for the input data. A Chien search is performed to obtain and outputs exponential terms related to variables for the polynomials, wherein the Chien search is performed in the same computational direction as an order for the input data.

PCT No. PCT/US97/04906 Sec. 371 Date Oct. 21, 1997 Sec. 102(e) Date Oct. 21, 1997 PCT Filed Mar. 27, 1997 PCT Pub. No. WO97/43835 PCT Pub. Date Nov. 20, 1997An apparatus and method for recovering from read errors detected by a read channel (70) in a sequence of data read from a disc (18) of a disc drive (10) by using read channel quality indicators to determine the appropriateness of using error correction in combination with other corrective actions utilized in the recovery process. Upon the detection of an uncorrected error in the retrieved data, the disc drive (10) enters a read error recovery routine wherein one or more corrective actions (102, 122) are applied in an effort to resolve the error. One of the channel quality indicators comprises a channel quality measurement (108, 128) determined as the sum of the square of the sampled data bit error values recovered during the read operation. When the channel quality measurement is at or below a threshold value indicative that the probability of passing undetected erroneous data is at an acceptable level (110, 130), error correction is applied to the data (112, 138); otherwise, error correction is disallowed (118, 140). Additional channel quality indicators comprise erasure pointers (132) which identify a particular set of symbols that are suspected of containing a read error. In such a case, the disc drive determines that the total number of symbols identified by the erasure pointers is below a predetermined erasure threshold before applying error correction (134, 136, 138), the erasure threshold selected to be within the correction capability of error correction circuitry 90.