In various embodiments, a method of correcting and/or detecting an error in a memory device is provided. The method may include, in a first operations mode, applying a first code to detect and/or correct an error, and

in a second operations mode after an inactive mode and before entering the first operations mode, applying a second code for correcting and/or detecting an error, wherein the first code and the second code have different code words.

An arrangement for decoding a data word using a Reed-Muller code, has: (1) N input terminals, (2) a first level of E>>D summing modules, each summing module being linked with F different input terminals and each input terminal being linked with E summing modules, (3) a first level of E decision modules, each of the D inputs of each decision module being linked respectively with an output from D different summing modules, (4) a second level of H summing modules, (5) a second level of G decision modules, (6) a third level of G summing modules, and (7) G output terminals. N signifies the code length and D signifies the minimum spacing of the code, E is equal to D-2, F is equal to N/D, G is the number of symbols of the data word that need to be corrected and is a natural number between 1 and E<<D.

An apparatus for decoding a TPC codeword is disclosed. The apparatus includes a memory and a processor coupled to the memory. The processor is configured to receive a first set of soft information corresponding to the TPC codeword. The TPC codeword includes at least one codeword corresponding to each of first, second, and third dimensions. The processor is further configured to iteratively perform a first soft decoding procedure on the at least one codeword corresponding to the first dimension to generate a first candidate codeword and upon determining that the first candidate codeword is not a correct codeword, and perform a second decoding procedure on the at least one codeword corresponding to the third dimension to generate a second candidate codeword. The second decoding procedure generates a second set of soft information to be used at a later iteration of the first decoding procedure.

A data processing system having a neural network architecture for receiving a binary network input and, in dependence on the binary network input, propagating signals via a plurality of processing nodes, in accordance with respective binary weights, to form a network output, the data processing system being configured to train a node by implementing an error correcting function to identify a set of binary weights which minimize, for a given input to the node, any error between an output of the node when formed in accordance with current binary weights of the node and a preferred output from the node and to update the binary weights of the node to be the identified weights. This training is performed without storing and/or using any higher arithmetic precision weights or other components.

A data processing method and apparatus. The data process method includes: determining, by a transmitting node, a code block length N.sub.0 for encoding an information bit sequence to be transmitted according to a data characteristic for representing the information bit sequence to be transmitted and a preset parameter corresponding to the data characteristic; performing, by the transmitting node, polar encoding on the information bit sequence to be transmitted according to the code block length N.sub.0; and transmitting, by the transmitting node, a code block obtained through the polar encoding to a receiving node.

Techniques are described for joint encoding and decoding of information symbols. In one embodiment, a method for joint encoding includes, in part, obtaining a sequence of information symbols, generating a plurality of cyclic codewords each corresponding to a portion of the sequence of information symbols, jointly encoding the plurality of cyclic codewords to generate at least one combined codeword, and providing the combined codeword to a device. The at least one combined codeword may be generated through Galois Fourier Transform (GFT). In one embodiment, a method for joint decoding includes, in part, obtaining a sequence of encoded symbols, wherein the sequence of encoded symbols is generated through GFT, jointly decoding the sequence of encoded symbols using an iterative soft decision decoding algorithm to generate a decoded sequence, transforming the decoded sequence to generate a plurality of cyclic codewords, and decoding the plurality of cyclic codewords to generate a plurality of decoded information symbols.

Described is a method and device for processing a signal received at an uplink control information (UCI) receiver in a wireless communication system. The method comprises processing a signal received on an uplink (UL) at said UCI receiver to transform said received signal into a likelihood calculation of possible transmitted codewords (θ.sub.1 . . . θi . . . θ.sub.N). The likelihood calculation of possible transmitted codewords (θ.sub.1 . . . θi . . . θ.sub.N) may comprise a multi-dimensional discrete Fourier transform (DFT) (θ.sub.1 . . . θi . . . θ.sub.N) of said received signal. The multi-dimensional may be formed as a Hadamard Transform. The method includes determining a maximum magnitude θ.sub.max value from said likelihood calculation of possible transmitted codewords (θ.sub.1 . . . θi . . . θ.sub.N) and then comparing said θ.sub.max value to a selected, calculated or predetermined scaled threshold c.Math.τ where τ is a threshold and c is a scaling factor for the threshold τ. The comparison is such that, where θ.sub.max>c.Math.τ, it is determined that the signal received on the UL at said UCI receiver comprises a linear block encoded signal. In some cases, the scaling factor c may be omitted.

Various aspects of the present disclosure generally relate to wireless communication. In some aspects, a wireless communication device may generate a Reed Muller generating matrix for an information bit vector that includes a plurality of information bits. The wireless communication device may remove, from the Reed Muller generating matrix, a row vector consisting of all 1-values to form a modified Reed Muller generating matrix. The wireless communication device may encode the information bit vector using the modified Reed Muller generating matrix to form a codeword. The wireless communication device may transmit the codeword without transmitting a pilot signal or demodulation reference signal for the codeword. Numerous other aspects are provided.

A transmitter (200) generates (602) an encoded vector (404) by encoding (406) a data vector (402), the encoded vector representing payload information and parity information. The encoding is mathematically equivalent to calculating three or more forward error correction (FEC) codewords from the data vector and then calculating the encoded vector from the codewords, at least one codeword being calculated from at least one recursion of a mathematical operation, and at least one codeword comprising more than 6 terms. The transmitter transmits (604) a signal representing the encoded vector over a communication channel. A receiver (300) determines (702) a vector estimate (502) from the signal and recovers (716) the data vector from the vector estimate by sequentially decoding (706, 710, 714) the codewords, wherein at least one codeword that is decoded earlier in the decoding enhances an estimate of at least one codeword that is decoded later in the decoding.

Various embodiments are directed to Reed-Muller decoding systems and methods based on recursive projections and aggregations of cosets decoding, exploiting the self-similarity of RM codes, and extended with list-decoding procedures and with outer-code concatenations. Various embodiments are configured for decoding RM codes (and variants thereof) over binary input memoryless channels, such as by, for each received word of RM encoded data, projecting the received word onto each of a plurality of cosets of different subspaces to form thereby a respective plurality of projected words; recursively decoding each of the respective plurality of projected words to form a respective plurality of decoded projected words; and aggregating each of the respective decoded projected words to obtain thereby a decoding of the corresponding received word of RM encoded data.