Apparatuses and methods related to correcting errors can include using FD decoders and AD decoders. Correcting errors can include receiving input data from the memory array, performing a plurality of operations associated with an error detection on the input data, and providing, based on processing the input data, output data, a validation flag, and a plurality of parity bits to a second decoder hosted by a controller coupled to the memory device.

A polar decoder kernal is described. The polar decoder kernal includes a processing unit having: at least one input configured to receive at least one input Logarithmic Likelihood Ratio, LLR; a logic circuit configured to manipulate the at least one input LLR; and at least one output configured to output the manipulated at least one LLR. The logic circuit of the processing unit includes only a single two-input adder to manipulate the at least one input LLR, and the input LLR and manipulated LLR are in a format of a fixed-point number representation that comprises a two's complement binary number and an additional sign bit.

In encoding systems and methods, data or information is encoded using one or more encoding methodologies to generate encoded data or information corresponding to the data or information. Similarly, in decoding systems and methods, encoded data or information is decoded using one or more decoding methodologies to generate the data or information corresponding to the encoded data or information. The encoding/decoding systems and methods can include polar encoding/decoding systems and methods operable for encoding data or information to generate polar codes and for decoding polar codes to generate the corresponding data or information. The information or data can be control information and application data for communication over networks. The networks can include wireless and wireline networks, and network segments, links or channels, including mixed wireline and wireless networks.

An electronic device configured to perform polar coding is described. The electronic device includes a bit pattern generator (3403) configured to successively perform a bit pattern generation process over a series (t=┌n/w┐) of clock cycles; and a counter (c, 4203), operably coupled to the bit pattern generator (3403) and configured to count a number of successive bit pattern generation sub-processes over the series (t=┌n/w┐) of clock cycles. The bit pattern generator (3403) is configured to: provide a successive sub-set of (w) bits from a bit pattern vector (b.sub.k,n) in each successive t=┌n/w┐ clock cycle; where the bit pattern vector comprises n bits, of which ‘k’ bits adopt a first binary value and n−k bits adopt a complementary binary value.

A transmitter generates determiners from data vectors representing payload information, each determiner representing parity information dependent on the payload information. The transmitter encodes the determiners to generate a nub vector representing compressed parity information dependent on the parity information, wherein the encoding is mathematically equivalent to calculating three or more forward error correction (FEC) codewords from the determiners and then calculating the nub vector from the codewords, at least one of the codewords being calculated from at least one recursion of a mathematical operation, and at least one of the codewords comprising more than 6 terms. The transmitter transmits signals representing the data vectors and the nub vector to a receiver, where recovery of the data vectors at the receiver involves sequential decoding of the FEC codewords, wherein at least one codeword decoded earlier in the decoding enhances an estimate of at least one codeword decoded later in the decoding.

A novel method for providing encoding of polar codes without the use of generator matrix is proposed.

An electronic device configured to perform polar coding is described. The electronic device includes a bit pattern generator (3403) configured to successively perform a bit pattern generation process over a series (t=┌n/w.box-tangle-solidup.) of clock cycles; and a counter (c, 4203), operably coupled to the bit pattern generator (3403) and configured to count a number of successive bit pattern generation sub-processes over the series (t=┌n/w.box-tangle-solidup.) of clock cycles. The bit pattern generator (3403) is configured to: provide a successive sub-set of (w) bits from a bit pattern vector (b.sub.k,n) in each successive t=┌n/w.box-tangle-solidup. clock cycle; where the bit pattern vector comprises n bits, of which ‘k’ bits adopt a first binary value and n−k bits adopt a complementary binary value.

Parity logic is widely used in forward error correction codes and error detection codes. When used for error correction and error detection applications, the role of parity bits is to increase code distance by introducing memory between encoded bits and input bits at cost of overhead bits. Present disclosure provide systems and methods for implementing invertible parity functions using parity logic wherein ‘k’ input bits are received and encoded using a first invertible parity function. The ‘k’ input bits can be iteratively encoded to obtain nonlinearity and higher dependency between set of encoded parity bits and the ‘k’ input bits or other data bits. Further the decoding is performed on the set of encoded bits to retrieve original ‘k’ input bits using a second invertible parity function.

A polar decoder kernal is described. The polar decoder kernal includes a processing unit having: at least one input configured to receive at least one input Logarithmic Likelihood Ratio, LLR; a logic circuit configured to manipulate the at least one input LLR; and at least one output configured to output the manipulated at least one LLR. The logic circuit of the processing unit includes only a single two-input adder to manipulate the at least one input LLR, and the input LLR and manipulated LLR are in a format of a fixed-point number representation that comprises a two's complement binary number and an additional sign bit.

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.