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 improved layered decoding method for a low density parity check (LDPC) code and a device therefor are disclosed. Disclosed is the layered decoding method for an LDPC code, capable of determining whether decoding is successful by performing a syndrome check on each check node at every variable node update. In addition, the syndrome check can be performed by using reduced variable nodes, thereby reducing decoding power consumption and decoding time consumption.

Described is a decoder suitable for use with any communication or storage system. The described decoder has a modular decoder hardware architecture capable of implementing a noise guessing process and due to its dependency only on noise, the decoder design is independent of any encoder, thus making it a universal decoder. Hence, the decoder architecture described herein is agnostic to any coding scheme.

A computer-implemented method includes encoding an array of (p−1)×k symbols of data into a p×(k+r) array. The method includes p is a prime number, r≥1, and k≤p−r. The method also includes each column in the p×(k+r) array has an even parity and each line of slope j for 0≤j≤r−1 in the p×(k+r) array has an even parity. The method includes the lines of slope j taken with a toroidal topology modulo p. A computer program product for encoding an array of (p−1)×k symbols of data into a p×(k+r) array includes a computer readable storage medium having program instructions executable by a computer. The program instructions cause the computer to perform the foregoing method.

An inter-die double data rate (DDR) data transfer scheme is provided. In particular, the data transfer scheme utilizes an error correction code (ECC) encoding scheme that exploits the DDR property that a single microbump defect can only yield four possible error scenarios. A specialized single error correcting, double error detecting, and double adjacent error correcting (SEC-DED-DAEC) encoding scheme that imposes at least four parity check matrix constraints may be used. Configured and operated in this way, a fewer number of parity check bits are required to detect data bit errors associated with a single defective microbump.

Methods, systems, and devices for operating memory cell(s) using a direct-input column redundancy scheme are described. A device that has read data from data planes may replace data from one of the planes with redundancy data from a data plane storing redundancy data. The device may then provide the redundancy data to an error correction circuit coupled with the data plane that stored the redundancy data. An output of the error correction circuit may be used to generate syndrome bits, which may be decoded by a syndrome decoder. The syndrome decoder may indicate whether a bit of the data should be corrected by selectively reacting to inputs based on the type of data to be corrected. For example, the syndrome decoder may react to a first set of inputs if the data bit to be corrected is a regular data bit, and react to a second set of inputs if the data bit to be corrected is a redundant data bit.

A polar decoder kernal is described. The polar decoder kernal is configured to: receive one or more soft bits from a soft kernal encoded block having a block size of N and output one or more recovered kernal information bits from a recovered kernal information block having a block size of N. The polar decoder kernal comprises a decomposition of a polar code graph into an arbitrary number of columns depending on the kernal block size N.

A data error correction circuit includes: a data error correction circuit, configured to receive first data and a first check code corresponding to the first data, perform error correction on the first data according to the first check code to generate second data, and output the second data; and a check code generation circuit, configured to receive the first data and the first check code, generate a second check code according to the first data and the first check code, and output the second check code.

A method of encoding input data. The method includes receiving a plurality of data bits of a bit stream. The method further includes forming words using the plurality of data bits to create a plurality of data packets including a first data packet. The method further includes encoding the words of the first data packet into coded words, partitioning the coded words into a plurality of blocks of M words each and integrating the coded words in each block in an interleaved order to generate a coded data packet for transmission through a communication channel.

An FEC codec module is provided. Code elements, i.e., code words of forward error correction code, are added to the data code stream of each transmission link through the codec module, so that accurate error determination and automatic error correction may be realized at the receiving end. The interleaving process is performed on multi-link data to prevent the occurrence of continuous burst errors in the data link in a transmission process, and the error correction capability of FEC is utilized to improve the data transmission efficiency and anti-interference ability of the system.