Abstract: A transmission device that performs multiple-input multiple-output (MIMO) transmission of transmit data using a plurality of fundamental bands. The transmission device includes an error correction coding unit, a mapping unit, and a MIMO coding unit. The error correction coding unit, for each data block of predefined length, performs error correction coding and thereby generates an error correction coded frame. The mapping unit maps each predefined number of bits in the error correction coded frame to a corresponding symbol and thereby generates an error correction coded block. The MIMO coding unit performs MIMO coding with respect to the error correction coded block. Components of data included in the error correction coded block are allocated to at least two of the fundamental bands and transmitted.

Abstract: Wireless communication devices are adapted to employ Golay-based matrices for encoding a wireless transmissions. According to at least one example, a wireless communication device can identify an information vector to be transmitted as a wireless communication. A Golay-based generator matrix may be selected based on a length of the information vector, where the selected Golay-based generator matrix is generated by shortening a Golay generator matrix by removing a plurality of columns of systematic bits and a plurality of rows to obtain the shortened generator matrix, and extending the shortened generator matrix to obtain an extended generator matrix by adding columns to at least the systematic bits and appending rows to obtain a desired matrix size. A respective bit value may be determined for bits in each added column and for at least some of the bits in each appended row. Other aspects, embodiments, and features are also included.

Abstract: In some examples, a memory device may be configured to provide quad bit error correction circuits. For example, the memory device may be equipped with a two layer error correction circuit. In some cases, the first layer may utilized one or more Hamming coders and the second layer may utilize one or Golay coders. In some examples, the Golay coders may be grouped into sets of Golay coders.

Abstract: Encoding or decoding can operate a processing system to apply one or more recursive relations to a known parameter associated with a length m and a Hamming weight l to produce a computed parameter associated with length m?1. An encoding process can thus assign values to bits of a code based on comparison of the data value being encoded and the computed parameter. A decoding process can use the computed parameters in a calculation of a decoded data value.

Abstract: A method is provided for improving synchronization and information transmission in a communication system, including: generating a signal with a centrally symmetric part s(k) exploitable for synchronization; and sending the signal over a communication channel. The signal is based on a uniquely identifiable sequence c(l) from a set of sequences exploitable for information transmission. The centrally symmetric part s(k) is centrally symmetric in the shape of absolute value thereof. The centrally symmetric part s(k) is of arbitrary length N.

Abstract: An apparatus for detecting and timing a transmitting device is disclosed. The device includes a receiving system receiving a signal containing at least a preamble code of a known length and at least one pulse within a receive window after the preamble code, a circuit receiving the at least one pulse comprising a zero-crossing circuit for indicting a zero-voltage crossing of the at least one pulse and a trigger device for latching the indication of zero-voltage crossing, and a ripple circuit counter, receiving the latched indication of said zero-voltage crossing and associating a time to the receipt of the latched indication. A system for detecting and locating a transmitting device is further disclosed. The system includes a plurality of sensor apparatus each determining a reception time of a signal and a processor for determining a location based on groups of the reception times.

Abstract: A Golay-code generator configured for generating Golay complementary code pairs comprises a sequence of delay elements configured for providing a predetermined set of fixed delays to at least a first input signal and a sequence of adaptable seed vector insertion elements configured for multiplying at least a second input signal by a variable seed vector, wherein each of a plurality of seed vectors corresponds to at least one predetermined piconet. The Golay-code generator may further comprise multiplexers configured for switching inputs and outputs of at least two delay elements in the sequence of delay elements to produce a plurality of compatible delay vectors. The Golay-code generator may further comprise a code-truncation module configured to shorten the Golay complementary code pairs for producing a plurality of daughter codes.

Abstract: In one embodiment, a Chien search circuit includes a plurality of evaluation circuits, each configured to sequentially evaluate possible roots ?i in a respective subset of possible roots of an error location polynomial (?(x)). Each evaluation circuit includes a respective sub-circuit for each of a plurality of coefficients ?i (0?i?T) of the error location polynomial ?(x) having T+1 coefficients. Each sub-circuit is configured to calculate one term of the error location polynomial for each possible root ?i in the respective subset of possible roots. Each evaluation circuit is configured to evaluate the error location polynomial for each possible root in the respective subset of possible roots, as a sum of the terms calculated by the plurality of sub-circuits.

Abstract: A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal's transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

Abstract: A method for communicating comprises generating at least one generalized Golay code from a concatenation of constituent Golay codes, and spreading at least a portion of a data stream with the at least one generalized Golay code. Generalized Golay codes comprise pseudo-complementary sequences having code lengths that differ from Golay complementary sequences and are characterized by low autocorrelation sidelobes relative to the autocorrelation peak.

Abstract: A communication method comprises generating a Golay code having a zero-DC level when differentially encoded and continuously rotated. A preamble of a data stream is spread with the Golay code, and the data stream is modulated with continuous phase modulation (CPM), such as constant envelope 2-CPM, before being transmitted. A method for acquiring a received signal having a spread sync field modulated with 2-CPM comprises performing chip-level differential detection of the received signal, correlating the received signal with a Golay sequence; and accumulating the correlator outputs.

Abstract: A method for performing channel estimation in a millimeter wave wireless communication system. The method includes receiving complementary sequences at a receiver of the millimeter wave wireless communication system. The received complementary sequences are generated at a first sampling rate; producing special complementary sequences from the received complementary sequences; cross-correlating the special complementary sequences with an input signal related to the received complementary sequences. The cross-correlation is performed at a second sampling rate and the second sampling rate is higher than the first sampling rate; and analyzing the result of the cross-correlation to estimate at least characteristics of a channel between the receiver and a transmitter of the millimeter wave wireless communication system.

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: Described herein are an apparatus, system, and method for encoder assisted decoding of linear systematic block codes. The apparatus comprises a first logic unit to receive a codeword from a memory, the codeword having a data portion and a corresponding parity portion; an encoder to encode the data portion of the received codeword and to generate a corresponding parity of the data portion of the received codeword; a second logic unit to generate a first parity portion from the corresponding parity portion of the codeword received by the first logic unit and the corresponding parity portion generated by the encoder; and a correction unit to correct the data portion of the codeword via the generated first parity portion.

Abstract: An apparatus is configured to perform both Fourier transform processing and Golay code processing. Each of a plurality of processing elements comprises a delay element configured for providing a predetermined delay to at least a first input signal, at least one seed vector insertion element configured for multiplying at least a second input signal by at least one seed-vector value for producing at least one scaled input signal value, and at least one multiplexer configurable by at least one control signal for selecting an operating mode of the apparatus. At least one twiddle-factor multiplier is coupled between stages of the processing elements and employed for Fourier transform processing. The apparatus may be configured to perform both multi-mode and multi-band operation.

Abstract: A method for communicating comprises generating at least one spreading code from a preferred Golay generator and/or a preferred generalized Golay generator. The preferred generalized Golay generator may comprise a plurality of preferred Golay generators. The outputs of the preferred Golay generator are logic 0 and 1. Each stage of the preferred Golay generator may comprise a single basic storage unit, such as a Flip-Flop. Generalized Golay codes comprise pseudo-complementary sequences having code lengths that differ from Golay complementary sequences and are characterized by low autocorrelation sidelobes relative to the autocorrelation peak.

Abstract: Efficient secure password protocols are constructed that remain secure against offline dictionary attacks even when a large, but bounded, part of the storage of a server responsible for password verification is retrieved by an adversary through a remote or local connection. A registration algorithm and a verification algorithm accomplish the goal of defeating a dictionary attack. A password protocol where a server, on input of a login and a password, carefully selects several locations from the password files, properly combines their content according to some special function, and stores the result of this function as a tag that can be associated with this password and used in a verification phase to verify access by users.

Abstract: A Golay-code generator configured for generating Golay complementary code pairs comprises a sequence of delay elements configured for providing a predetermined set of fixed delays to at least a first input signal and a sequence of adaptable seed vector insertion elements configured for multiplying at least a second input signal by a variable seed vector, wherein each of a plurality of seed vectors corresponds to at least one predetermined piconet. The Golay-code generator may further comprise multiplexers configured for switching inputs and outputs of at least two delay elements in the sequence of delay elements to produce a plurality of compatible delay vectors. The Golay-code generator may further comprise a code-truncation module configured to shorten the Golay complementary code pairs for producing a plurality of daughter codes.

Abstract: The present invention relates to a signal modulation device, a transmission method, and a code generation method. The signal modulation device includes a code storage unit including a plurality of n-bit members and storing a code with a number n or n?1 of different bits between two neighboring members, and a mapper for mapping data on symbols according to the code.

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: A single frame format is employed by a millimeter wave communication system for single-carrier and OFDM signaling. A Golay-coded sequence in the start frame delimiter (SFD) field identifies the data transmission as single carrier or OFDM. Complementary Golay codes are employed in a channel estimation field to allow a perfect estimate of the multipath channel to be made. Marker codes generated from Golay codes are inserted periodically between slots for tracking and/or for reacquiring timing, frequency, and multipath channel estimates. The length of the marker codes may be adapted relative to the multipath delay spread.

Abstract: A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal's the transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

Abstract: The invention provides a method for decoding an error correction code. First, an error syndrome of the error correction code is calculated. A plurality of coefficients of an error locator polynomial of the error correction code is then sequentially determined according to the error syndrome. When a new coefficient of the error locator polynomial is determined, it is also determined whether the new determined coefficient is equal to zero. When the new determined coefficient is equal to zero, a speculated error locator polynomial is built according to a plurality of low-order-term coefficients of the error locator polynomial, wherein the orders of the low-order-term coefficients are lower than that of the new determined coefficient. A Chien search is then performed to determine a plurality of roots of the speculated error locator polynomial. The error correction code is then corrected according to the roots of the speculated error locator polynomial.

Abstract: A Euclid processing module for obtaining an error locator polynomial of a binary BCH code in an error correction decoding circuit, in which error corrections of words are performed, includes registers, a shifter, a zero insertion unit, selectors and a sequencer. Coefficients of polynomials Ri (z) and Bi (z) stored in the registers are subjected to Galois field calculations by the processing module. Results of the calculations and the data of the registers are shifted by the shifter. Some of the coefficients are erased by the zero insertion unit and stored in registers by controlling the selectors with the sequencer. A necessary polynomial ? (z) is calculated by repeated processing of the processing module. The Euclid processing module decreases a logic scale and simplifies controlling logic in a state of small latency and high operating frequency.

Abstract: A matched filter is configured for matching an input signal to a plurality of programmable-length complementary Golay-code pairs. The matched filter includes a sequence of delay elements configured for delaying the input signal with respect to at least one delay vector. A sequence of programmable seed vector insertion elements is configured for multiplying the input signal and delayed versions of the input signal by a set of seed-vector values. At least one of the seed-vector values may be set to zero to facilitate processing Golay codes having different lengths.

Abstract: Certain aspects of the present disclosure relate to a method for generating a frame structure suitable for use in both single carrier (SC) and Orthogonal Frequency Division Multiplexing (OFDM) transmission modes, while ensuring accurate channel estimation at a receiver.

Abstract: A wireless communications network uses a beamforming process to increase signal quality as well as transmission capabilities and reduction of interference. An improved Golay sequence is also used in the wireless communications network. In one aspect, the processes can be used to communicate regardless of whether the system is on an OFDM mode or a single carrier mode.

Abstract: A method for generating block codes from Golay code and a method and apparatus for encoding data are provided. The method can effectively generate codes having various lengths, various dimensions, and superior hamming weight distribution, and encodes data such as control information having various lengths into codes having strong resistance to channel errors, resulting in an increase of error correction performance.

Abstract: A method of de-mapping non-binary Galois field symbols from physical layer code-words in a data communication system, in which at least one physical layer code-word includes portions mapped from more than one non-binary Galois field symbol is provided. The method includes calculating at least a provisional likelihood estimate for values of a first non-binary Galois field symbol having at least portions within a first physical layer code-word, the calculating including selecting a first number of values of a second non-binary Galois field symbol having at least portions within the first physical layer code-word, the first number forming a subset of the possible values of the second non-binary Galois field symbol.

Abstract: A Golay-code generator configured for generating Golay complementary code pairs comprises a sequence of delay elements configured for providing a predetermined set of fixed delays to at least a first input signal and a sequence of adaptable seed vector insertion elements configured for multiplying at least a second input signal by a variable seed vector, wherein each of a plurality of seed vectors corresponds to at least one predetermined piconet. The Golay-code generator may further comprise multiplexers configured for switching inputs and outputs of at least two delay elements in the sequence of delay elements to produce a plurality of compatible delay vectors. The Golay-code generator may further comprise a code-truncation module configured to shorten the Golay complementary code pairs for producing a plurality of daughter codes.

Abstract: An error detection and correction system in accordance with an embodiment comprises: an encoding unit; a syndrome calculating unit; a syndrome element calculating unit; an error search unit; and an error correction unit, read and write of a memory cell array being assumed to be performed concurrently for m bits, and error detection and correction being assumed to be performed in data units of M bits (where M is an integer multiple of m), and an encoding unit and a syndrome calculating unit sharing a time-division decoder for performing data bit selection according to respective tables of check bit generation and syndrome generation, the time-division decoder being operative to repeat multiple cycles of m bit concurrent data input.

Abstract: The optical line terminal has a PON transceiver including an error correction code decoder. The error correction decoder includes: a shortening compensation parameter table; and a syndrome calculator for calculating a syndrome by referring to the shortening compensation parameter table, or an error search part for calculating an error position or an error value by referring to the shortening compensation parameter table. Also the optical network terminal has a PON transceiver including an error correction code decoder. The error code decoder includes: a shortening compensation parameter table; and a syndrome calculator for calculating a syndrome by referring to the shortening compensation parameter table, or an error search part for calculating an error position or an error value by referring to the shortening compensation parameter table.

Abstract: A public safety communications network uses asymmetric channels for receiving requests for data from a mobile client over a narrowband land mobile radio system (LMRS) channel and delivering wideband data over a digital television (DTV) network channel to a DTV datacast receiver with the mobile client. An emergency operations center connected to the LMRS receives and processes the data requests and forwards the requested data. DTV network stations have a data multiplex insertion system for inserting the requested data into a DTV signal. The DTV network may be a public television network. An addressing system identifies unique mobile client addresses and unique mobile client group addresses and selects a DTV transmitter for delivering response messages in accordance with the addresses. A forward error correction (FEC) regulation system is used in transmitting requested data with FEC strength regulated as a function of historical bit-error-rate or receive power for a geographical location.

Abstract: A first device receives first data that includes a plurality of input vectors, which includes a primary input vector and a set of secondary input vectors and detects uncorrectable errors in the first data based on a quality metric indication. Based on detecting the uncorrectable errors in the first data, the first device substitutes a predetermined codeword for the primary input vector encoded using a non-perfect code, and substitutes a predetermined input vector for the primary input vector. The first device modulates a set of encoded secondary input vectors using the predetermined input vector to generate a modulated set of encoded secondary input vectors and transmits as second data the predetermined codeword and the modulated set of encoded secondary input vectors to a target device, wherein the substituting step creates a first number of errors that is detected by the target device as uncorrectable errors in the transmitted second data.

Abstract: Certain aspects of the present disclosure relate to a method for employing a special format for transmitting data blocks which allows parallel equalizations at a receiver. By applying parallel equalization operations, a clock at the receiver can operate at a fraction of the input signal's data rate, which is more practical in the case of very high data rates while power dissipation is also reduced.

Abstract: A method for generating block codes from Golay code and a method and apparatus for encoding data are provided. The method can effectively generate codes having various lengths, various dimensions, and superior hamming weight distribution, and encodes data such as control information having various lengths into codes having strong resistance to channel errors, resulting in an increase of error correction performance.

Abstract: A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal's the transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

Abstract: A wireless communications network uses a beamforming process to increase signal quality as well as transmission capabilities and reduction of interference. An improved Golay sequence is also used in the wireless communications network. In one aspect, the processes can be used to communicate regardless of whether the system is on an OFDM mode or a single carrier mode.

Abstract: A method and a device are proposed for the synchronization of a radio transmitter and a radio receiver, notably for UMTS, while utilizing a Golay correlator, which synchronization should be performed reliably without imposing severe requirements as regards the frequency stability of the local oscillator. To this end, absolute value squaring B1, B2 is performed in the Golay correlator already prior to the last delay stages (D7, D8).

Abstract: A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal's the transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

Abstract: A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal's the transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

Abstract: In one or more of the disclosed embodiments, memory cells in a memory device are refreshed upon an indication of a fatigue condition. In one such embodiment, controller monitors behavior parameters of the cells and determines if any of the parameters are outside of a normal range set for each one, thus indicating a fatigue condition. If any cell indicates a fatigue condition, the data from the block of cells indicating the fatigue is moved to another block. In one embodiment, an error detection and correction process is performed on the data prior to being written into another memory block.

Abstract: Systems, methods, and devices are disclosed, including a device that includes a plurality of data locations, a quantizing circuit coupled to the plurality of data locations, and an error detection module coupled to the quantizing circuit. In some embodiments, the error detection module includes an encoder configured to encode incoming data with redundant data derived from the incoming data and a decoder configured to detect errors in stored data based on the redundant data.

Abstract: A first device receives first data that includes a plurality of input vectors, which includes a primary input vector and a set of secondary input vectors and detects uncorrectable errors in the first data based on a quality metric indication. Based on detecting the uncorrectable errors in the first data, the first device substitutes a predetermined codeword for the primary input vector encoded using a non-perfect code, and substitutes a predetermined input vector for the primary input vector. The first device modulates a set of encoded secondary input vectors using the predetermined input vector to generate a modulated set of encoded secondary input vectors and transmits as second data the predetermined codeword and the modulated set of encoded secondary input vectors to a target device, wherein the substituting step creates a first number of errors that is detected by the target device as uncorrectable errors in the transmitted second data.

Abstract: There is described a method for enabling the operation of automation components of a technical system via a mobile control and monitoring device. In a first step, the control and monitoring device receives a first identification from a first transponder device, with the first transponder device being attached to the technical system, with the first transponder device having been activated by the automation components and with the first identification having been transmitted via a wireless communication connection from the automation components to the mobile control and monitoring device. In a further step the communication connection between the control and monitoring device and the automation components is deactivated. The mobile control and monitoring device sends a carrier signal and following that receives the carrier signal modulated by the first transponder device.

Abstract: Improved memory devices, circuitry, and data methods are described that facilitate the detection and correction of data in memory systems or devices in combination with a stored record of known flaws, errors, or questionable data bits of a read memory row or block to allow for more efficient processing and correction of these errors. An embodiment of the present invention utilizes an erasure pointer that can store the location of N bad or questionable bits in the memory segment that is currently being read, where for each bit stored by the erasure pointer the embodiment also contains 2N ECC generators to allow the read data to be quickly checked with the know bad bits in each possible state. This allows the read data to then be easily corrected on the fly before it is transferred by selecting the bad bit state indicated by the ECC generator detecting an uncorrupted read.

Abstract: Stopping or reducing oscillations in Low Density Parity Check (LDPC) codes. A novel solution is presented that completely eliminates and/or substantially reduces the oscillations that are oftentimes encountered with the various iterative decoding approaches that are employed to decode LDPC coded signals. This novel approach may be implemented in any one of the following three ways. One way involves combining the Sum-Product (SP) soft decision decoding approach with the Bit-Flip (BF) hard decision decoding approach in an intelligent manner that may adaptively select the number of iterations performed during the SP soft decoding process. The other two ways involve modification of the manner in which the SP soft decoding approach and the BF hard decision decoding approach are implemented. One modification involves changing the initialization of the SP soft decoding process, and another modification involves the updating procedure employed during the SP soft decoding approach process.

Abstract: A data dictionary uses a reverse error correction procedure to identify near matches, tolerating mismatches at Hamming's distance 2 utilizing pairwise combinations of indices of a central index decoding sphere and all adjacent decoding spheres (each index identified as a vector defining the center of the decoding sphere) to form sets of hash indices for storing a dictionary entry. Using a Golay code procedure, this arrangement resolves the cases of dictionary entries at distances three and two from the center of a particular central index decoding sphere. In the former case, five adjacent decoding spheres are identified with the dictionary entry stored in the fifteen pairwise combinations formed by the central index and these five adjacent spheres. In the latter case, the twenty-one adjacent decoding spheres are identified, and the data entry is stored in the twenty-one concatenated arrangements formed by the central index and the twenty-one adjacent decoding spheres.

Abstract: A method of turbo decoding using soft input-soft output information. A vector of data is sampled from a channel of data. The vector of data is then processed to output a final code word of bits. A final reliability vector of reliability values associated with the final code word is generated, such that each bit of the final code word of bits has a corresponding reliability value in the final reliability vector. Corresponding reliability values for one or more bit positions of the final code word are determined by a difference of distance metrics, and corresponding reliability values for one or more bit positions of the final code word are determined utilizing a numerical approximation.

Abstract: A hashing system produces hash values by manipulating n-bit sequences in accordance with a selected distance d error correction code (“ECC”) over an associated Galois Field. The current system produces a hash value for a given n-bit sequence by treating the sequence as either a corrupted n-bit ECC codeword or as “n” information bits of an (n+r)-bit ECC codeword. The hashing system may decode the n bits as a corrupted codeword of an (n, k, d) perfect ECC to produce an n-bit error-free codeword, and then use as the hash value the information bits of the error-free codeword. Alternatively, the hashing system may treat the n-bit sequence as a corrupted code word of a cyclic distance d ECC, and map the codeword to an (n?k)-bit “error pattern” that the system then uses as the hash value. The hashing system may instead treat the n-bit sequence as n “information” bits and encode the bits in accordance with an (n+r, n, d) ECC, to produce an r-bit hash value that consists of the associated redundancy bits.