Abstract: A method includes accessing information, and at least one of encoding or decoding the information using a parity check matrix based on a coding rate. A portion of a data part in the parity check matrix has been generated based on part or all of another matrix. Apparatus, computer programs, and computer program products are also described. The apparatus may be a wireless mobile device or a wireless network access node. A communication system may include one or more of the wireless mobile devices and one or more of the access nodes, each using a version of the method.

Abstract: Systems and methods providing for storing fragments for one or more source objects at storage nodes of multiple cluster instances comprising a cluster set are disclosed. Repair of the stored data is operated within cluster instances autonomously or semi-autonomously of other cluster instances of the cluster set according to embodiments. Embodiments may provide a storage process operable to generate fragments for a first source object to be stored in a storage system using a first encoding, wherein a different plurality of fragments of the generated fragments are stored at different cluster instances of a cluster set. A repair process may be enacted at each cluster instance of the cluster set, wherein a repair process enacted at a cluster instance is used to maintain the recoverability of the fragments of the first source object stored at that cluster instance using a second encoding.

Abstract: Embodiments include device, storage media, and methods for decoding a codeword of encoded data. In embodiments, a processor may be coupled with a decoder and configured to multiply the codeword and a parity-check matrix of the encoded data to produce a syndrome. If the syndrome is non-zero then the processor may identify a bit error in the codeword based at least in part on a comparison of the syndrome to one or more columns of the parity-check matrix. Other embodiments may be described and claimed.

Abstract: The Universal Packet Loss Recovery System (UPLRS) is capable of recovering end-to-end network packet losses to obtain reliable end-to-end network delivery of multimedia streaming content over IP networks where packet losses appear above the transport layer. The UPLRS incorporates the use of Packet Forward Error Correction Coding (FEC) with packet interleaving processing prior to transport. Packet FEC is an error correction coding method at the packet level to improve link transmission reliability. At the source end of the packet-switching network, the Packet FEC scheme encodes a stream of transport multimedia content packets by including redundant packets in the stream to allow for the recovery of lost packets by the Packet FEC decoder at the user end of the packet-switching network. Since lost packets appear only above the transport layer in the IP network protocol stack, Packet FEC can be viewed as a transport layer or an application layer coding method.

Abstract: A method including generating a matrix. The matrix includes first and second portions. The first portion includes data bits. The second portion includes parity bits and has a triple diagonal structure. The triple diagonal structure includes a first central diagonal, a second central diagonal, and a last row diagonal. Bits of the first central diagonal, the second central diagonal, and the last row diagonal are equal to 1 and a remainder of bits in the triple diagonal structure are equal to 0. The method further includes: determining parity bits based on the matrix; if the matrix is generated to codify data for transmission from a first device to a second device, transmitting the parity bits from the first device to the second device; and if the matrix is generated based on a vector of bits received from the second device, generating a block of data based on the parity bits.

Abstract: An apparatus and method for transmitting and receiving data in a wireless communication is provided. The method includes Low Density Parity Check (LDPC)-encoding LDPC information bits to generate a codeword, determining a number (Npunc) of bits to be punctured in parity bits of the codeword, determining a number (Npunc—group) of parity bit groups in which all bits are punctured, and puncturing the all bits within 0th to (Npunc—group?1)th parity bit groups indicated by a puncturing pattern, wherein the puncturing pattern is defined as an order of the parity bit groups defined as 29, 45, 43, 27, 32, 35, 40, 38, 0, 19, 8, 16, 41, 4, 26, 36, 30, 2, 13, 42, 46, 24, 37, 1, 33, 11, 44, 28, 20, 9, 34, 3, 17, 6, 21, 14, 23, 7, 22, 47, 5, 10, 12, 15, 18, 25, 31 and 39.

Abstract: Some embodiments of the invention are directed to systems and methods for an optimized and efficient encoding scheme that can accommodate higher block lengths of data. Some embodiments generally relate to: (1) coding structures for a new class of LDPC matrices based on algebraic relations, and (2) encoding method that achieves the R=1?k/n exact bound on code rate. In addition, in some embodiments, the coding structures efficiently create matrices with excellent error-correcting properties and are devoid of short cycles (leading to robust performance). The implementations of the coding structures are scalable over a range of code rates and block lengths.

Abstract: A method is provided for transmitting a Low Density Parity Check (LDPC) code by a signal transmission apparatus in a multimedia system. The method includes generating the LDPC code based on a resulting parity check matrix, which is generated by performing a scaling down operation on a base parity check matrix; and transmitting the LDPC code. The scaling down operation is performed based on a scaling factor for determining a size of each permutation matrix in the resulting parity check matrix and a size of each zero matrix included in the resulting parity check matrix, and the scaling factor is determined based on a number of column blocks included in the base parity check matrix and a size of each permutation matrix included in the base parity check matrix.

Abstract: A method begins by a dispersed storage (DS) processing module mapping a set of data partitions to a set of storage regions. For each data partition, the method continues with the DS processing module segmenting the data partition into a plurality of data segments and designating a first data segment. The method continues with the DS processing module generating data storage mapping information. The method continues with the DS processing module encoding the data storage mapping information to produce at least one set of encoded mapping information slices and for each data partition, encoding the plurality of data segments to produce a plurality of sets of encoded data slices. The method continues with the DS processing module outputting the at least one set of encoded mapping information slices and, for each data partition, the plurality of sets of encoded data slices to the DSN for storage therein.

Abstract: The present invention discloses a data error-detection system and the method thereof. The system includes an initializing module, an encoding module, a decoding module and a restoring module. The initializing module arranges the transmitting data in a 3D matrix to produce information data. The encoding module encodes the information data to produce checking data, and outputs encoding data which includes information data and checking data. The decoding module receives encoding data and detects information data according to the checking data to correct the information data and then produces 3D matrix receiving data. The restoring module produces receiving data according to the 3D matrix receiving data. Herewith, the effect of error-detection and correction of the data can be achieved.

Abstract: A processor includes a first memory module for storing a first set of storage values each representing a respective input, and a second memory module for storing a second set of storage values in analog form. An analog module is coupled to the first and the second memory modules. The analog module is configured to, in each operation cycle of at least one iteration, update at least some of the second set of storage values based on the first and the second sets of storage values. An output module is for generating a set of outputs from at least some of the second set of storage values.

Abstract: A method for decoding data is disclosed. The method includes partitioning a low-density parity check (LDPC) matrix into a plurality of groups, each comprising one or more check node layers. The method further includes selecting one of the groups based at least in part on a cost function, the cost function based at least in part on information associated with a variable node, or information associated with a check node, or both. The method further includes performing LDPC layered decoding on the selected group.

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: A method begins by a dispersed storage (DS) processing module receiving a zero information gain (ZIG) encoded data slice and a subset of encoded data slices of a set of encoded data slices. The method continues with the DS processing module generating a set of ZIG encoded data slices using a ZIG function and corresponding ones of the subset of encoded data slices, wherein the set of ZIG encoded data slices represents additional components of recovery information of a first encoded data slice. The method continues with the DS processing module recreating the first encoded data slice from the ZIG encoded data slice and the set of ZIG encoded data slices. The method continues with the DS processing module decoding the subset of encoded data slices and the first encoded data slice using a dispersed storage error coding function to reproduce data.

Abstract: The present inventions are related to systems and methods for data processing. As one example, a data processing system is discussed that includes a data decoder circuit and a matrix select control circuit. The data decoder circuit is operable to apply a data decode algorithm to a decoder input using a selected parity check matrix to yield a decoder output. The matrix select control circuit operable to select one of a first parity check matrix and a second parity check matrix as the selected parity check matrix.

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: Cyclic redundancy check (CRC) values are efficiently calculated using an improved linear feedback shift register (LFSR) circuit. CRC value generation is separated into two sub-calculations, which are then combined to form a final CRC value. A programmable XOR engine performs logic functions via a table lookup rather than via a random logic circuit. LCRC and ECRC calculations are performed using a single shared LFSR circuit. Multiple links share the same CRC value generator. One advantage of the present invention is that CRC values are generated using smaller and fewer LFSR circuits relative to conventional circuit designs. As a result, a CRC value generator utilizing the disclosed techniques consumes less surface area of an integrated circuit and consumes less power, resulting in cooler operation.

Abstract: Various embodiments of the present inventions provide a symbol flipping LDPC decoding system. For example, a symbol flipping data processing system is disclosed that includes a low density parity check decoder operable to decode codewords and to identify unsatisfied parity checks, a symbol flipping controller operable to change values of at least one symbol in the codewords based on the unsatisfied parity checks to assist the low density parity check decoder to decode the codewords, a scheduler operable to control a decoding and symbol flipping mode in the low density parity check decoder and the symbol flipping controller, and a hard decision queue operable to store hard decisions for converged codewords from the low density parity check decoder.

Abstract: A receiver for use in a wireless communications network capable of decoding encoded transmissions. The receiver comprises receive path circuitry for receiving and downconverting an incoming radio frequency (RF) signal to produce an encoded received signal; and a low-density parity check (LDPC) decoder associated with the receive path circuitry for decoding the encoded received signal. The LDPC decoder further comprises a memory for storing a parity check H matrix comprising R rows and C columns, where each element of the parity check H matrix comprises one of a shift value or a ?1 value; and a plurality of processing elements for performing LDPC layered decoding, wherein at least one processing element is operable to process in the same cycle a first row and a second row of the parity check H matrix.

Abstract: A graphics memory device includes a memory array configured to store data for a display device comprising b*y rows by a*x columns of pixels, where b>a. The memory array is arranged in a*y rows by b*x columns of memory locations. Each memory location is adapted to store n-bit image data for one of the pixels of the display device. A memory location remapping circuit is adapted to map image data stored in the b*x columns of memory locations in the memory device to the a*x columns of the display device.

Abstract: In one embodiment a variable barrel shifter includes a shifter operable to apply a cyclic shift to each of a number of portions of a data word, a pivot circuit operable to swap sections of the data word around at least one pivot point in the data word, a first multiplexer operable to select between an input of the variable barrel shifter or an output of the pivot circuit as an input to the shifter, a second multiplexer operable to select between the input of the variable barrel shifter or an output of the shifter as an input to the pivot circuit, and a third multiplexer operable to select between the output of the shifter or the output of the pivot circuit as an output to the variable barrel shifter.

Abstract: Methods and apparatuses are provided for achieving maximum diversity gain through channel coding based on a Low-Density Parity-Check (LDPC) code in a multiple antenna communication system. A method includes determining a parity-check matrix; generating a codeword using the parity-check matrix; puncturing a part of an information word; dividing a parity into a plurality of partial parities based on a number of transmit antennas; transmitting an unpunctured part of the information word and a partial parity over a first antenna; and transmitting at least one other partial parity over at least one other transmit antenna.

Abstract: A method of identifying a parallel recovery plan for a data storage system comprises identifying base recovery plans for symbols of an erasure code implemented across a plurality of storage devices in a data storage system, generating a list of first recovery plans for a first symbol by manipulating the base recovery plans, and combining selected first recovery plans from the list to generate a set of parallel recovery plans to reconstruct a failed storage device.

Abstract: Various embodiments of the present invention provide systems and methods for stochastic stream decoding of binary LDPC codes. For example, a data decoder circuit is discussed that includes a number of variable nodes and check nodes, with serial connections between the variable nodes and the check nodes. The variable nodes are each operable to perform a real-valued computation of a variable node to check node message for each neighboring check node. The check nodes are operable to perform a real-valued computation of a check node to variable node message for each neighboring variable node. The messages are passed iteratively between the variable nodes and the check nodes.

Abstract: A method includes calculating a first syndrome of a codeword read from a memory location under a first set of conditions and calculating a second syndrome of the codeword read from the memory location under a second set of conditions. The method also includes analyzing the first and second syndromes and applying one of the first and second syndromes to the codeword to find the codeword having a minimum number of errors.

Abstract: LDPC (Low Density Parity Check) codes with corresponding parity check matrices selectively constructed with CSI (Cyclic Shifted Identity) and null sub-matrices. An LDPC matrix corresponding to an LDPC code is employed within a communication device to encode and/or decode coded signals for use in any of a number of communication systems. The LDPC matrix is composed of a number of sub-matrices and may be partitioned into a left hand side matrix and a right hand side matrix. The right hand side matrix may include two sub-matrix diagonals therein that are composed entirely of CSI (Cyclic Shifted Identity) sub-matrices; one of these two sub-matrix diagonals is located on the center sub-matrix diagonal and the other is located just to the left thereof. All other sub-matrices of the right hand side matrix may be null sub-matrices (i.e., all elements therein are values of zero “0”).

Abstract: In an aspect, in general, a forward error correction algorithm (FEC) utilizes an FEC block structure in a manner that extends the effective error correction such that it can approach an “infinite” length to obtain benefits typical of very large FEC block size without the commensurate computation cost.

Abstract: In one embodiment, a de-interleaver receives soft-output values corresponding to bits of an LDPC-encoded codeword. The de-interleaver has scratch pad memory that provides sets of the soft-output values to a local de-interleaver. The number of values in each set equals the number of columns in a block column of the LDPC H-matrix. Each set has at least two subsets of soft-output values corresponding to at least two different block columns of the LDPC H-matrix, where the individual soft-output values of the at least two subsets are interleaved with one another. Local de-interleaving is performed on each set such that the soft-output values of each subset are grouped together. Global de-interleaving is then performed on the subsets such that the subsets corresponding to the same block columns of the H-matrix are arranged together. In another embodiment, an interleaver performs global then local interleaving to perform the inverse of the de-interleaver processing.

Abstract: In row calculation, a value which is obtained by subtracting an offset according to a minimum of the absolute values of column LLRs from the minimum of the absolute values of the column LLRs is set as a row LLR corresponding to a column of the column LLRs.

Abstract: One embodiment of the present invention relates to an error tolerant memory circuit having a low hardware overhead that can tolerate both single volatile soft errors and permanent errors. In one embodiment, the method and apparatus comprise a memory circuit having a plurality of memory element pairs, respectively having two memory storage elements configured to store a data unit. One or more parity generation circuits are configured to calculate a first parity bit from data written to the plurality of memory element pairs (e.g., the two memory storage elements) and a second parity bit from data read from one of the two memory storage elements in the plurality of memory element pairs. Based upon the calculated first and second parity bits, the memory circuit chooses to selectively output data from memory storage elements not known to contain an error.

Abstract: Techniques to support low density parity check (LDPC) encoding and decoding are described. An apparatus includes at least one processor and a memory coupled to the at least one processor. The at least one processor is configured to encode or decode a packet based on a base parity check matrix and a set of lifting values. In a particular embodiment, the set of lifting values is limited to lifting values that are each a different power of two. The memory is configured to store parameters associated with the base parity check matrix.

Abstract: A Software Defined Radio (SDR) subsystem capable of supporting a multiple communication standards and platforms for modulation, demodulation and trans-modulation of an input signal is provided. The SDR subsystem includes a Signal Conditioning Cluster (SCC) unit that includes a signal conditioning CPU adapted for sample based signal processing, a Signal Processing Cluster (SPC) unit that includes a signal processing CPU adapted for block based signal processing, and a Channel Codec Cluster (CCC) unit that performs a channel encoding or a channel decoding operation.

Abstract: A layered decoder that uses a non-standard schedule, where a non-standard schedule is a schedule where the frequency of one or more layers in the schedule is greater than one. When the layered decoder converges on a near codeword using an initial schedule, the layered decoder identifies the layer Lmaxb of the near codeword, which layer contains the greatest number of unsatisfied check nodes, and selects a subsequent non-standard schedule from a schedule set. The non-standard schedules in the schedule set are sorted by key layer, where the key layer is a layer that appears in the non-standard schedule with the greatest frequency. The layer decoder selects a non-standard schedule from the schedule set where the key layer of selected non-standard schedule is equal to the identified Lmaxb value.

Abstract: A method and system for decoding low density parity check (“LDPC”) codes. An LDPC decoder includes a control unit that controls decoder processing, the control unit causing the decoder to process the blocks of a low density parity check (“LDPC”) matrix out of order. A decoder embodiment may process the layers of the LDPC matrix out of order and/or perform partial state processing on out of order blocks of the LDPC matrix and/or generate R messages out of order.

Abstract: Error correction and detection in a redundant memory system including a a computer implemented method that includes receiving data including error correction code (ECC) bits, the receiving from a plurality of channels, each channel comprising a plurality of memory devices at memory device locations. The method also includes computing syndromes of the data; receiving a channel identifier of one of the channels; and removing a contribution of data received on the channel from the computed syndromes, the removing resulting in channel adjusted syndromes. The channel adjusted syndromes are decoded resulting in channel adjusted memory device locations of failing memory devices, the channel adjusted memory device locations corresponding to memory device locations.

Abstract: A decoder-implemented method for layered decoding that, when the decoder converges on a near codeword using an initial schedule, (i) selects a subsequent schedule from a schedule set based on the layer Lmaxb of the near codeword, which layer contains the greatest number of unsatisfied check nodes and (ii) re-performs decoding using the subsequent schedule. When used in an offline schedule-testing system, the layered-decoding method (i) identifies which schedules, out of a population of schedules, correctly decode a decoder input codeword and (ii) associates the identified schedules with the Lmaxb value of the near codeword.

Abstract: Methods and systems for DVB-C2 are disclosed and may include receiving data encoded utilizing variable encoding, variable modulation and outer codes via a physical layer matched to a desired quality of service. An error probability may be determined for said received data and retransmission of portions of said data with error probability above an error threshold may be requested. The variable modulation may include single carrier modulation, orthogonal frequency division modulation, synchronous code division multiple access, and/or from 256 QAM to 2048 QAM or greater. The variable encoding may include forward error correction code, which may include low density parity check code.

Abstract: Techniques to support low density parity check (LDPC) encoding and decoding are described. In an aspect, LDPC encoding and decoding of packets of varying sizes may be supported with a set of base parity check matrices of different dimensions and a set of lifting values of different powers of two. A base parity check matrix G of dimension mB×nB may be used to encode a packet of kB=nB?mB information bits to obtain a codeword of nB code bits. This base parity check matrix may be “lifted” by a lifting value of L to obtain a lifted parity check matrix H of dimension L·mB×L·nB. The lifted parity check matrix may be used to encode a packet of up to L·kB information bits to obtain a codeword of L·nB code bits. A wide range of packet sizes may be supported with the set of base parity check matrices and the set of lifting values.

Abstract: A transmitting device and method enables improved reception quality on the receiving side when LDPC-CC (Low-Density Parity-Check Convolutional Codes) encoding is used. The transmitting device includes an LDPC-CC encoding section, a sorting section for sorting the encoded data acquired by the LDPC-CC encoding section into a first encoded data set corresponding to the column number of the column containing “1” in a part of an LDPC-CC check matrix H from which a protograph is excluded and a second encoded data set corresponding to the column numbers of the columns other than that, and a frame constructing section (control section) for constructing a transmission frame where the first and second encoded data sets are arranged in positions different in time or frequency in the transmission frame.

Abstract: A method and system for decoding low density parity check (“LDPC”) codes. An LDPC decoder includes a control unit that controls decoder processing, the control unit causing the decoder to process the blocks of a low density parity check (“LDPC”) matrix out of order. A decoder embodiment may process the layers of the LDPC matrix out of order and/or perform partial state processing on out of order blocks of the LDPC matrix and/or generate R messages out of order.

Abstract: LDPC codes robust to non-stationary narrowband ingress noise. Particularly designed LDPC codes are adapted to address deleterious noise-effects incurred within LDPC coded signals that propagate via a communication channel (such as from a transmitting communication device to a receiving communication device). Such LDPC matrices employed for encoding and/or decoding such LDPC coded signals are composed of sub-matrices (e.g., all-zero values sub-matrices and/or CSI (Cyclic Shifted Identity) sub-matrices). The sub-matrices are generally uniform in size and square in shape. Based on certain operational conditions, such as communication channel noise, various operations within a communication device are adaptively modified (e.g., signaling, modulation, demodulation, symbol mapping, metric generation, decoding, etc.).

Abstract: A parity-check-code decoder includes: a verifying device that multiplies (N) bit nodes by a matrix provided with (N) columns so as to obtain a plurality of check nodes; a reliability generator that generates a reliability index for each of the bit nodes in accordance with a channel; a reliability-updating device that uses the bit nodes and the check nodes to exchange message iteratively, and following each iteration, updates (N) exchange results corresponding to the (N) columns; and a recording controller that includes a separator, a quantizing determiner and a quantizer. The separator divides the matrix into at least one column group based on the characterizing signals. The quantizing determiner determines a shift signal for each column group based on the characterizing signals. The quantizer quantizes the characterizing signals according to the shift signals for subsequent output.

Abstract: Certain aspects of the present disclosure relate to a method for designing structured multi-rate low-density parity-check (LDPC) codes. These LDPC codes can be also adapted to support efficient encoding.

Abstract: LDPC (Low Density Parity Check) codes with corresponding parity check matrices selectively constructed with CSI (Cyclic Shifted Identity) and null sub-matrices. An LDPC matrix corresponding to an LDPC code is employed within a communication device to encode and/or decode coded signals for use in any of a number of communication systems. The LDPC matrix is composed of a number of sub-matrices and may be partitioned into a left hand side matrix and a right hand side matrix. The right hand side matrix may include two sub-matrix diagonals therein that are composed entirely of CSI (Cyclic Shifted Identity) sub-matrices; one of these two sub-matrix diagonals is located on the center sub-matrix diagonal and the other is located just to the left thereof. All other sub-matrices of the right hand side matrix may be null sub-matrices (i.e., all elements therein are values of zero “0”).

Abstract: A system and method are provided for creating codewords using common partial parity products. The method initially accepts an algorithm for creating p indexed parity bit positions, where the parity bit for each position is calculated from mathematical operations performed on bits from n indexed user word positions. A first group of parity bit positions is found, where the parity bit for each position in the first group is calculated using at least a first number of common mathematical operations. A second group of parity bit positions is found, where the parity bit for each position in the second group is calculated using at least a second number of common mathematical operations. The common mathematical operations are subtracted from the first and second group of parity bit position calculations, so that unique mathematical operations can be found, associated with each parity bit position calculation in the first and second group.

Abstract: A system that provides error detection and correction for a memory that has a specific failed memory component accesses a block of data from the memory. Each block of data includes an array of bits logically organized into rows and columns, including a column including row-checkbits, a column including inner checkbits and data bits, and columns containing data bits. Each column is stored in a different memory component and the checkbits are generated from the data bits. Next, the system attempts to correct a column of the block by using the checkbits and the data bits to produce a corrected column. The system then regenerates row-parity bits and the inner checkbits for the block of data, wherein the block includes the corrected column, and compares the regenerated row-parity bits and inner checkbits with existing row-parity bits and inner checkbits.

Abstract: Overlapping sub-matrix based LDPC (Low Density Parity Check) decoder. Novel decoding approach is presented, by which, updated bit edge messages corresponding to a sub-matrix of an LDPC matrix are immediately employed for updating of the check edge messages corresponding to that sub-matrix without requiring storing the bit edge messages; also updated check edge messages corresponding to a sub-matrix of the LDPC matrix are immediately employed for updating of the bit edge messages corresponding to that sub-matrix without requiring storing the check edge messages. Using this approach, twice as many decoding iterations can be performed in a given time period when compared to a system that performs updating of all check edge messages for the entire LDPC matrix, then updating of all bit edge messages for the entire LDPC matrix, and so on. When performing this overlapping approach in conjunction with min-sum processing, significant memory savings can also be achieved.

Abstract: A method is disclosed that allows the easy generation of low-density parity-check codes that can realize superior error-correcting characteristics. A processor of a transmission line encoder constructs parity check matrix H from partial matrix H1 of m rows and k columns on the left side and partial matrix H2 of m rows and m columns on the right side. The processor generates partial matrix H2 as a unit matrix. The processor generates partial matrix H1 to satisfy the conditions that, when any two rows contained in partial matrix H1 are selected, the two rows have periods that are relatively prime, or when the periods are identical, the two rows have different phases. The processor then joins partial matrix H1 and partial matrix H2 to generate parity check matrix H.

Abstract: A serial concatenated coder includes an outer coder and an inner coder. The outer coder irregularly repeats bits in a data block according to a degree profile and scrambles the repeated bits. The scrambled and repeated bits are input to an inner coder, which has a rate substantially close to one.

Abstract: Methods, apparatus, and systems are provided to encode a low-density parity-check codeword for transmission in a communications channel. In an embodiment, the encoding may include partially computing parity-check bits in response to receiving a block of message bits before obtaining all the message bits for the low-density parity-check codeword, including updating previously partially computed parity-check bits that depend on the received block.