Abstract: An embodiment of the invention provides a method of correcting 2 bits and detecting three bit using an extended bidirectional Hamming code. A data word with length K=2m?1 is received. A code word with length N=2m?1+2m+1 is generated from the data word in accordance with the extended bidirectional Hamming code defined by the following parity check matrix: H = [ 1 1 … 1 1 ? … ? N - 1 1 ? - 1 … ? - N + 1 ] . The number of parity bit is given by (2m+1).

Abstract: A data processing apparatus is provided having error code generation circuitry configured to generate an error code associated with a received data value, such that a bit change in the received data value can be known about by reference to the error code. Stored data values are stored in a data store and associated error codes are stored in an error code store. Error checking circuitry performs a verification operation on a stored data value and an associated error code to determine if an error has occurred in at least one of the stored data value and the associated error code during storage. The received data value comprises at least one additional bit with respect to the stored data value and the error checking circuitry is configured to reconstruct the at least one additional bit by reference to the stored data value and the associated error code.

Abstract: The invention relates to a method of probabilistic symmetric encryption of a plaintext message element with the aid of a secret key that can be represented in the form of a matrix. It comprises an operation of encrypting the plaintext message element, with the aid of the matrix parametrized by a random vector, so as to obtain an encrypted message element coupled to the random vector. Furthermore, there is envisaged a step of encoding the plaintext message element as a code word with the aid of an error correcting code having a given correction capacity and a step of adding a noise vector. The error correcting code and the noise vector are adapted so that the Hamming weight of the noise vector is less than or equal to the correction capacity of the correcting code.

Abstract: Positions holding different bit values between a first code word, which is obtained by coding an information bit sequence based on a coding method utilizing quasi-cyclic codes, and a second code word, which has the close Hamming distance from the first code word and satisfies a parity check of the coding method, are identified. Thereafter, a code word is generated by inserting bit values known to the transmitter and receiver into the identified positions of the information bit sequence and coding the information bit sequence. Upon reception of a signal based on the generated code word, the receiver judges whether known bit values held by corresponding positions in a code word obtained by decoding the received signal are the same as preset bit values. If the judgment result is negative, the code word based on the received signal is judges as erroneous even when it satisfies the parity check.

Abstract: To derive a Hamming code to manage data errors a set of at least four parity bit positions is selected for parity bits which will protect a set of data bits (where each data bit has a data bit position in the data bit set). A syndrome is determined for each data bit position. This involves selecting a unique sub-set of at least three parity bit positions. The unique sub-set shares at least one parity bit position with at least one other unique sub-set of at least three parity bit positions. A parity bit value may then be calculated for each parity bit position based on the determined syndromes. The header of a packet may be provided with a word which defines the length of the packet and an error management code generated utilizing this word so that errors in the word may be detected and, possibly, corrected.

Abstract: Some embodiments include apparatus and methods to prevent at least one of misidentifying and ignoring multiple-bit errors if the multiple-bit errors include a plurality of erroneous data bits that belong to only one specific group of a plurality of groups of data bits and if none of the other groups of the plurality of groups have errors.

Abstract: If the number of bits at which 64-bit width data has changed at the same time has exceeded a threshold, the data is outputted, with the polarity of each bit inverted. Otherwise, the data is outputted. A 7-bit width error correcting code is given to the outputted data and the inversion instruction signal indicating whether the number of the changed bits has exceeded the threshold. Error code correction is performed for the data and the inversion instruction signal with the use of the transmitted error correcting code. If the inversion instruction signal for which the error code correction has been performed indicates that the number of the changed bits has exceeded the threshold, the data for which the error code correction has been performed is outputted, with the polarity of each bit inverted. Otherwise, the data for which the error code correction has been performed is outputted.

Abstract: Methods are described that facilitate the detection and correction of data in memory systems or devices by encoding the data bits of a memory row or block in a non-systematic ECC code. Reduced complexity error detection and correction hardware and/or routines detect and correct corrupted user data in a segment of memory, such as a sector, word line row, or erase block. User data is not stored in a plaintext format in the memory array. The ECC code is distributed throughout the stored data in the memory segment.

Abstract: Unrecoverable electronic correction code (ECC) errors in memory storage devices are usually preceded by recoverable ECC errors. A memory storage device controller is provided notice of the recoverable errors and associated information. The memory storage device controller can cause the data having the recoverable information to be rewritten on the memory storage device. Rewriting the data on the memory storage device (often in a different location) normally reduces the probability of encountering data with unrecoverable data errors.

Abstract: Systems and methods for processing and decoding TCM/BCM-coded signal vectors. A multi-dimensional signal vector is received by, for example, a TCM or BCM decoder. The TCM/BCM decoder identifies the closest signal points in the signal constellation set, or “nearest neighbors,” for each dimension of the received signal vector. The TCM/BCM decoder then forms a test set that includes a plurality of multi-dimensional test vectors, where each dimension of each test vector is based on an identified nearest neighbor. In particular, each test point in the test set is based on a different combination of the nearest neighbors. The TCM/BCM decoder can compute branch metrics based on only the test points in the test set, and can make detection decisions using the computed branch metrics.

Abstract: A data encoding scheme for transmission of data from one circuit to another circuit considers the Hamming Weight of combined multiple words to determine whether to invert or not invert an individual word to be transmitted. The multi-word data encoding scheme performs DBI encoding with data inversion conducted based on the total HW in the combined multiple words. The decision to invert or not invert each of the multiple words is made based on the sum of the individual Hamming Weights of each of the words. Such encoding has the advantage that SSO noise is dramatically reduced when the encoded data has a large number of words transmitted from one circuit to another circuit over a wide parallel bus.

Abstract: A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.

Abstract: Some embodiments include apparatus and methods to prevent at least one of misidentifying and ignoring multiple-bit errors if the multiple-bit errors include a plurality of erroneous data bits that belong to only one specific group of a plurality of groups of data bits and if none of the other groups of the plurality of groups have errors.

Abstract: Various embodiments of the present invention provide systems and methods for generating a code format. One method discussed includes: Various embodiments of the present invention provide methods for generating a code format. Such methods include: receiving an indication of a low weight codeword having a trapping set; selecting an initial value for a base matrix; testing the low weight codeword after modification by the initial value to determine an updated weight of the low weight codeword; and testing the low weight codeword after modification by the initial value to determine whether the trapping set remains.

Abstract: In a method, by a first circuit, a plurality of bits is converted in a first format to a second format. By a second circuit, the plurality of bits in the second format is used to program a plurality of memory cells corresponding to the plurality of bits. The first circuit and the second circuit are electrically coupled together in a first chip. The plurality of bits is selected from the group consisting of 1) address information, cell data information, and program information of a memory cell that has an error; and 2) word data information of a first word and error code and correction information corresponding to the word data information of the first word.

Abstract: An error correction encoding device is provided that combines redundancy data with source data, said device including: at least three encoding stages and at least two permutation stages. Each encoding stage implements at least one set of three basic encoding modules, in which a first encoding stage receives said source data and a last encoding stage provides said redundancy data. Each encoding module implements a basic code and includes c inputs and c outputs, c being an integer. The permutation stages are inserted between two consecutive encoding stages and each permutation stage implements a c-cyclic permutation.

Abstract: The present invention relates to coding method and coding device that allow Rate-Compatible LDPC (low-density parity-check) codes to have favorable BER performance both with a low code rate and with a high code rate. In coding of LDPC codes that have plural code rates and whose all parity check matrices are composed of plural cyclic matrices, a coder 121 performs the coding in such a way that 1<w0 and w1<w0 are satisfied when the maximum column weight of the cyclic matrices in the check matrix of a certain code whose code rate is not the minimum value among the LDPC codes is defined as w0 and the maximum column weight of the cyclic matrices in the check matrix of a code having a code rate lower than that of the certain code is defined as w1.

Abstract: A parallel interleaver that operates to interleave convolutionally and turbo encoded data packets is described. Packets are divided into subpackets and interleaved in parallel for improved performance. The Pruned Bit Reversal Interleaver (PBRI) function used to generate interleaver addresses is invertible such that its inverse function can be used to generate de-interleaver addresses. For convolutionally encoded subpackets, encoder output bits are demultiplexed into three sequences V0, V1, V2 with the first bit going to V0, the second bit going to V1, the third going to V2, and the fourth to V0, etc. Next, each of the three sequences is bit-permuted independently using PBRIs to generate the sequences ?(V0), ?(V1), ?(V2). For turbo encoded subpackets, the encoder NT output data bits are demultiplexed into five sequences U, V0, V1, V?0, V?1. Next, the demultiplexed sequences are bit-permuted using five PBRIs into three separate interleaved blocks, denoted as ?(U), ?(V0/V?0), and ?(V1/V?1).

Abstract: In bus communications methods and apparatus, a first set of physical signals representing the information to be conveyed over the bus is provided, and mapped to a codeword of a spherical code, wherein a codeword is representable as a vector of a plurality of components and the bus uses at least as many signal lines as components of the vector that are used, mapping the codeword to a second set of physical signals, wherein components of the second set of physical signals can have values from a set of component values having at least three distinct values for at least one component, and providing the second set of physical signals for transmission over the data bus in a physical form.

Abstract: The present invention is related to systems and methods for applying two or more data decode algorithms to a processing data set.

Abstract: Methods include receiving data and an ECC code read from a memory array, generating an ECC code from the received data, and determining whether the received data is corrupted by evaluating the generated ECC code against the ECC code read from the memory array. If the received data is determined to be corrupted, a correction algorithm and a recorded likely state of a known bad/questionable bit of the received data may be used to correct error in the received data. Alternatively, if the received data is determined to be corrupted, the correction algorithm and a recorded location of a known bad/questionable bit of the received data may be used to correct error in the received data.

Abstract: Described herein are a method and apparatuses for providing customizable error correction for memory arrays. In one embodiment, an apparatus includes a memory device having a memory array to store data and an analog to digital sense unit coupled to the memory array. The analog to digital sense unit senses analog signals associated with the memory array and converts the analog signals into distributions of digital values. An error-correcting code (ECC) unit receives the distributions of digital values from the analog to digital sense unit. A configurable non-volatile look-up table generates ECC parameters including error probability data and provides the ECC parameters to the ECC unit for error correction. The error probability data has error probability values that are associated with the distributions of digital values. The ECC unit executes an ECC algorithm to provide error correction using the error probability data.

Abstract: Methods, apparatuses, systems, and architectures for providing fast, independent, and reliable retrieval of system data (e.g., metadata) from a storage system, which enables minimal degradation in the reliability of user data. Methods generally include encoding the system data at least twice, at least once independently and at least once jointly along with user data. Methods can also include decoding the system data first, and upon a decoding failure, jointly decoding the system data and the user data.

Abstract: The apparatus for appending CRC to the data or signaling to be transmitted in the communication systems is proposed in present invention. If the length of the CRC-bit sequence is 16, one of the CRC generation polynomials listed in present invention can be adopted. If the length of the CRC bit sequence is 18, one of the CRC generation polynomials listed in present invention can be adopted. If the length of the CRC bit sequence is 20, one of the CRC generation polynomials listed in present invention can be adopted. With the optimized CRC generation polynomials proposed in present invention, mistakes in signaling detection can be effectively reduced so that system spectrum utility can be improved.

Abstract: Methods, apparatus, systems, and data structures may operate to combine block management data with a portion of data, to generate error correction data for the combined portion, and to store the data, the block management data, the error correction data for the combined portion, and error correction data for the data in a memory. Methods, apparatus, systems, and data structures may operate to generate or store error correction data for each of a plurality of sectors of a page except for a particular sector in the page and combine block management data with the particular sector to generate a modified sector. Additionally, various methods, apparatus, systems, and data structures may operate to generate or store error correction data for the modified sector and combine the plurality of sectors, the error correction data for each of the plurality of sectors other than the particular page, and the block management data and the error correction data for the modified sector.

Abstract: An embodiment of the invention provides a method of correcting 2 bits and detecting three bit using an extended bidirectional Hamming code. A data word with length K=2m-1 is received. A code word with length N=2m-1+2m+1 is generated from the data word in accordance with the extended bidirectional Hamming code defined by the following parity check matrix: H = [ 1 1 … 1 1 ? … ? N - 1 1 ? - 1 … ? - N + 1 ] . The number of parity bit is given by (2m+1).

Abstract: This invention relates to methods and devices for verifying the identity of a person based on a sequence of feature components extracted from a biometric sample. Thereafter, the feature components are quantized and assigned a data bit sequence in such a way that adjacent quantization intervals have a Hamming distance of 1. The data bit sequences are concatenated into a bit string, and said bit string is combined with a helper data set by using an exclusive disjunction (XOR) operation into a codeword. Finally, the codeword is decoded into a secret V and a secret S is matched with the secret V.

Abstract: A channel has a first and a second end. The first end of the channel is coupled to a transmitter. The channel is capable of transmitting symbols selected from a symbol set from the first end to the second end. The channel exhibits incomplete error introduction properties. A code comprises a set of code words. The elements of the set of code words are one or more code symbols long. The code symbols are members of the symbol set. The minimum modified Hamming separation between the elements of the set of code words in light of the error introduction properties of the channel is greater than the minimum Hamming distance between the elements of the set of code words. A memory device, a method of using the channel, and a method of generating the code are also described.

Abstract: According to one embodiment, an encoder/decoder apparatus includes an encoder module, a decoder module, and a transposing module. The encoder module is configured to generate a Hamming code from the input data, in accordance with a check matrix having a specific regularity. The decoder module is configured to detect an error position in the output data composed of the Hamming code, in accordance with the check matrix. The transposing module is configured to perform a transposing process of transposing some of the columns of the check matrix, while maintaining the regularity of the check matrix, and to change the error position in accordance with the transposing process, during the decoding process.

Abstract: A device for detecting and correcting errors in a data stream. For example, a device for detecting and correcting errors in a data stream including identifiers for a track address or identifiers for encoded words in a wireless transmission. The devices employ a class of error correction codes to, for instance, encode track addresses on a surface of a data storage medium. The encoding modifies natural track addresses so that the difference between bit sequences in adjacent track addresses is constant while simultaneously enabling both error detection and error correction, thereby enabling more accurate head positioning in a data storage device, in one embodiment.

Abstract: Method and system embodiments of the present invention are directed to encoding information in ways that are compatible with constraints associated with electrical-resistance-based memories and useful in other, similarly constrained applications, and to decoding the encoded information. One embodiment of the present invention encodes k information bits and writes the encoded k information bits to an electronic memory, the method comprising systematically encoding the k information bits to produce a vector codeword, with additional parity bits so that the codeword is resilient to bit-transition errors that may occur during storage of the codeword in, and retrieval of the codeword from, the electronic memory, ensuring that the codeword does not violate a weight constraint, and writing the codeword to the electronic memory.

Abstract: A memory device having a plurality of nonvolatile memory cells for storing stored data where the stored data includes user stored data and nuisance stored data. A memory controller includes a transmitter for transmitting write data for storage as the stored data in the memory. The transmitter includes a selector for selection of user write data for storage as the user stored data in the memory and for selection of nuisance write data for storage as the nuisance stored data in the memory. The memory controller includes a receiver for receiving the stored data from the memory as read data where the read data includes the user stored data and the nuisance stored data. The receiver includes a Hamming weight detector for detecting the Hamming weights of read data received from the memory for distinguishing user stored data from nuisance stored data.

Abstract: Erasure-encoded data is stored across a plurality of storage devices in a data storage system. The erasure-encoded data includes k data elements to store on k data storage devices and m parity elements to store on m parity storage devices, wherein for a given minimum Hamming distance d of the data storage system and m?(d?1), data elements are assigned only to corresponding unique combinations of parity elements of size (d?1).

Abstract: The error tolerance of an array of m storage units is increased by using a technique referred to as “dodging.” A plurality of k stripes are stored across the array of storage units in which each stripe has n+r elements that correspond to a symmetric code having a minimum Hamming distance d=r+1. Each respective element of a stripe is stored on a different storage unit. An element is selected when a difference between a minimum distance of the donor stripe and a minimum distance of a recipient stripe is greater or equal to 2. The selected element is also stored on a storage unit having no elements of the recipient stripe. A lost element of the recipient stripe is then rebuilt on the selected element.

Abstract: A semiconductor memory device includes a plurality of detecting code generators configured to generate a plurality of detecting codes to detect errors in a plurality of data items, respectively, a plurality of first correcting code generators configured to generate a plurality of first correcting codes to correct errors in a plurality of first data blocks, respectively, each of the first data blocks containing one of the data items and a corresponding detecting code, a second correcting code generators configured to generate a second correcting code to correct errors in a second data block, the second data block containing the first data blocks, and a semiconductor memory configured to nonvolatilely store the second data block, the first correcting codes, and the second correcting code.

Abstract: An error correction coding is provided that generates P bits of check data from K M-bit words of payload data. The P bits of check data include an address field A, a bit error indicating field E and an auxiliary field P?(E+A). The address field encodes a set of error addresses which has a cardinality equal to the bit size K of the payload data and providing a one-to-one mapping between values of the address field and the locations of a single bit error within the payload data. The bit error indicating field indicates if a bit error is present. The auxiliary field is a minimum size bit vector such that together with the address field and the bit area indicating field it provides a checksum for a systematic code for the payload data with a minimum Hamming distance serving to provide either single error correction capability or single error correction and double error detection capability.

Abstract: To provide a receiving device and a receiving method which achieve iterative decoding regarding concatenated codes containing a convolutional code while suppressing increase in circuit scale, a decoder and an error correcting part iteratively perform decoding and error correction corresponding to a convolutional code on soft-decision inputs corresponding to the received signal sequence. Depending on whether a decoding result matches error corrected decoded data obtained in previous processing or not, penalties are calculated corresponding to branches transiting with the respective decoded results, and a branch metric is calculated by reflecting the calculated penalties as to decrease likelihood ratio of each of the branches to which the penalties are to be added. The obtained branch metric is input to a decoder, thereby reflecting the penalty corresponding to the decoding result.

Abstract: A control system includes an error calculation module that receives a data bit pattern having a predetermined quantity of data bits and that calculates a binary vector based on a predetermined binary matrix and the data bit pattern. The error calculation module further determines the data bit pattern contains a corrupted data bit when the binary vector is not a predetermined value. The control system further includes a bit position module that receives the binary vector, that locates the corrupted data bit based on the binary vector and that corrects the data bit pattern. The bit position module receives the data bit pattern when the binary number is the predetermined value. The data bits are pre-assigned a base-10 value that corresponds to a data bit position.

Abstract: A cipher processing device includes: a MAC loss detecting/estimating section which estimates the radio bearer of the lost protocol data unit and a data amount of the lost protocol data unit out of protocol data units produced by division according to the logical channel information included in a packet combining data unit received by a base station of a mobile communication system; an RLC loss detecting/estimating section which detects occurrence of loss in the protocol data units when the protocol data units are put together into a service data unit, and estimates a lost amount of the protocol data units when the protocol data units are put together into the service data unit according to the estimated data amount; and a correction section which corrects a frame number of the service data unit based on the estimated data amount estimated by the detecting/estimating section.

Abstract: Linear Feedback Shift Registers (LFSRs) based 2p state with p>2 or p?2 scramblers, descramblers, sequence generators and sequence detectors in binary implementation are provided. An LFSR may apply devices implementing a binary XOR or EQUIVALENT function, a binary shift register and binary inverters and binary state generator, wherein at least an output of one shift register element in a first LFSR is connected to a device implementing a reversible binary logic function is a second LFSR. They may also apply 2p state inverters using binary combinational logic are applied. Memory based binary 2p state inverters are also applied. Non-LFSR based n-state scramblers and descramblers in binary logic are also provided. A method for simple correlation calculation is provided. Communication systems and data storage systems applying the provided LFSR devices are also disclosed.

Abstract: The present invention is directed to an archival data storage system. The archival data storage system includes write once and read many (WORM) capability, data redundancy, error correction, and access control. The combination of these capabilities enable the archival storage system to be secure, error proof, and reliable. Additionally, to provide fast data access time, solid state storage devices are used in place of conventional tape drive. Solid state storage devices such as, for example, flash memory devices are fast, versatile and reliable.

Abstract: Systems and methods for processing and decoding TCM/BCM-coded signal vectors. A multi-dimensional signal vector is received by, for example, a TCM or BCM decoder. The TCM/BCM decoder identifies the closest signal points in the signal constellation set, or “nearest neighbors,” for each dimension of the received signal vector. The TCM/BCM decoder then forms a test set that includes a plurality of multi-dimensional test vectors, where each dimension of each test vector is based on an identified nearest neighbor. In particular, each test point in the test set is based on a different combination of the nearest neighbors. The TCM/BCM decoder can compute branch metrics based on only the test points in the test set, and can make detection decisions using the computed branch metrics.

Abstract: Embodiments of the present disclosure provide methods, systems, and apparatuses related to multilevel encoding with error correction. In some embodiments, a plurality of bits may be encoded into a plurality of multilevel memory cells by level-shifting a subset of the plurality of multilevel memory cells for a bit of the plurality of bits. Other embodiments may be described and claimed.

Abstract: In a method of reading data from a non-volatile memory device, read data is generated based on a word line voltage. The read data includes data read from a plurality of sectors included in the non-volatile memory device. Bad sector data is transferred data based on read data and bad sector information. The bad sector data corresponds to data read from at least one bad sector included in the plurality of sectors. The bad sector information is updated by checking error bits of the bad sector data. The word line voltage is generated based on the updated bad sector information.

Abstract: A technique for reducing parity bit-widths for check bit and syndrome generation through the use of additional check bits to increase the number of minimum weighted codes in the Hamming Code H-Matrix. The technique of the present invention may be implemented while adding no additional correction/detection capability, in order to reduce the number of data bits that are used for each check bit/syndrome generation and to reduce the width of the parity generating circuitry.

Abstract: In one embodiment, the present invention includes a method for generating a hybrid error correction code for a data block. The hybrid code, which may be a residual arithmetic-Hamming code, includes a first residue code based on the data block and a first parity code based on the data block and a Hamming matrix. Then the generated code along with the data block can be communicated through at least a portion of a datapath of a processor. Other embodiments are described and claimed.

Abstract: A method and apparatus providing improved set membership determination and group membership identification of candidate data elements using a single Bloom filter programmed to provide a plurality of non-zero f-bit binary vectors, where each of the f-bit binary vectors is associated with a respective group. The Bloom filter is programmed using one or more (but not all) of a plurality of hash filter sets.

Abstract: Signal transmitting and decoding methods considering repeatedly transmitted information in transmitting informations in various types are disclosed. Both a first type information varying with a long period and a second type information varying with a short period are simultaneously transmitted by a same period. A receiving side receiving these informations is able to perform fast decoding by unmasking the corresponding information prior to decoding of a next received signal after obtaining the first type information in a manner of considering a fact that the first type information is repeatedly transmitted for a prescribed period of time.

Abstract: A technique for selecting an erasure code from a plurality of erasure codes for use in a fault tolerant system comprises generating a preferred set of erasure codes based on characteristics of the codes' corresponding Tanner graphs. The fault tolerances of the preferred codes are compared based at least on the Tanner graphs. A more fault tolerant code is selected based on the comparison.

Abstract: The present invention provides a method for enhancing reliability of information transmission by (a) establishing a matrix based on the length of bits of valid information in frame time slots; and creating a new matrix by presetting Error Correction Coding (ECC) for rows and columns of said matrix; (b) adopting the 1st Interleaving method to re-allocate bits which have been processed twice by using said ECC in said new matrix, to both ends of said frame time slots; and (c) adopting the 2nd Interleaving method to re-allocate the remaining bits in said new matrix to the middle of said frame time slots. After processed like this, the anti-interfering ability of the bits at both ends of TDMA frame time slot can be significantly enhanced, and the bit-error rate is decreased most, and all redundancy bits of Hamming codes can be arrayed at both ends of TDMA frame time slot.