An integrated circuit for outputting a function value, comprising a pattern matching circuit, configured to compare an input value and multiple transformed versions of the input value with a specified bit pattern, wherein the transformed versions of the input value or the specified bit pattern are created by repeated application of a transformation to the input value or the specified bit pattern, wherein the function is invariant under the transformation or wherein an inverse transformation exists for the transformation, by means of which a change in the function values that is caused by the transformation of the input values can be reversed, a selection circuit configured to select a function value depending on the matching result of the pattern matching circuit and the input value, and an output circuit configured to output a function value for the input value based on the selected function value.

A memory system includes a nonvolatile memory and a memory controller that encodes first XOR data generated by performing an exclusive OR operation on pieces of user data, wherein a value of each bit of the XOR data is generated by performing an exclusive OR operation on values of bits that are at one of a plurality of bit positions of a piece of user data, generates codewords by encoding the plurality of pieces of user data and the generated XOR data, respectively, and stores the codewords in the nonvolatile memory. The memory controller also performs a read operation by reading the codewords from the nonvolatile memory and decoding them. When the decoding of two or more of the codewords fails, the memory controller generates second XOR data, and corrects the value of one of the bits corresponding to a codeword whose decoding failed, based on the second XOR data.

A system comprises a forward error correction decoder comprising syndrome computation circuitry, key-equation solver circuitry, and search and evaluator circuitry. The syndrome computation circuitry may comprise a plurality of syndrome compute units connected in parallel. The syndrome computation circuitry may be dynamically configurable to vary a quantity of the syndrome compute units used for processing of a codeword based on conditions of a channel over which the codeword was received. The syndrome computation circuitry may be operable to use a first quantity of the syndrome compute units for processing of a first codeword received over the channel when the channel is characterized by a first bit error rate and a second quantity of the syndrome compute units for processing of a second codeword received over the channel when the channel is characterized by a second bit error rate.

A memory system includes a nonvolatile memory and a memory controller that encodes first XOR data generated by performing an exclusive OR operation on pieces of user data, wherein a value of each bit of the XOR data is generated by performing an exclusive OR operation on values of bits that are at one of a plurality of bit positions of a piece of user data, generates codewords by encoding the plurality of pieces of user data and the generated XOR data, respectively, and stores the codewords in the nonvolatile memory. The memory controller also performs a read operation by reading the codewords from the nonvolatile memory and decoding them. When the decoding of two or more of the codewords fails, the memory controller generates second XOR data, and corrects the value of one of the bits corresponding to a codeword whose decoding failed, based on the second XOR data.

An error correction code (ECC) decoder includes a syndrome calculation block and a path controller. The syndrome calculation block is configured to perform a syndrome calculation for generating a syndrome from a codeword. The path controller is configured to output data transmitted through first to third paths. The first path is a path for transmitting the codeword to the path controller when no error is detected. The second path includes a single-error decoding logic circuit, and the single-error decoding logic circuit corrects a single error of the codeword to transmit the corrected codeword to the path controller through the second path. The third path includes a multi-error decoding logic circuit, and the multi-error decoding logic circuit corrects at least two errors of the codeword to transmit the corrected codeword to the path controller.

A Reed Solomon decoder may include a syndrome calculation (SC) circuit, a key equation solver (KES) circuit, and a Chien search and error evaluation (CSEE) circuit. The SC circuit calculates a syndrome from a codeword. The KES circuit includes a plurality of sub-KES circuit and calculates an error location polynomial and an error evaluation polynomial from the syndrome. The CSEE circuit calculates an error location and an error value from the error location polynomial and the error evaluation polynomial. Each of the plurality of sub-KES circuits, the SC circuit and the CSEE circuit respectively constitute pipeline stages. The Read Solomon decoder may also include a FIFO queue that queues the codeword among a plurality of codewords sequentially received, and an error correction circuit that produces error corrected data using an output from the FIFO queue, the error location, and the error value.

An encoding method, an encoder, and a decoder for dynamic power consumption control are provided. The encoder includes a control unit, an initial encoding unit, and L incremental encoding units. The control unit is configured to enable only the initial encoding unit in an RS (N.sub.0, K) operating mode to perform encoding or enable only the initial encoding unit and first j incremental encoding units in the L incremental encoding units in an RS (N.sub.j, K) operating mode to perform encoding. The initial encoding unit is configured to perform RS FEC encoding on m(x) to obtain a quotient D.sub.0(x) and a remainder R.sub.0(x) of x.sup.N.sub.0.sup.Km(x) relative to g.sub.0(x). An (h+1).sup.th incremental encoding unit is configured to obtain, according to a quotient D.sub.h(x) and a remainder R.sub.h(x), a quotient D.sub.h+1(x) and a remainder R.sub.h+1(x) of x.sup.N.sub.h+1.sup.Km(x) relative to g.sub.h+1(x).

A method for operating a semiconductor memory device may include applying a program pulse for programming data of a first page included in the semiconductor memory device. The method may include determining whether the number of times of applying the program pulse has exceeded a first critical value. The method may include performing an error bit check on a second page coupled to the same word line as the first page, based on the determined result of whether the first critical value has been exceeded.

Digital data archival methods and systems are described, providing controlled and verifiable information destruction. In one embodiment, the method comprises storing digitally encoded information, wherein the information is encoded as a sequence of numbers or symbols using parameters defining an associated error correction ability of an error correcting algorithm based on a lifetime of the digitally encoded information. Errors are periodically added to the sequence of numbers or symbols, such that the digitally encoded information is recoverable from the sequence of numbers or symbols during the defined lifetime, and after a total of number of added errors exceeds the associated error correction ability, the digitally encoded information cannot be retrieved.

A Reed Solomon decoder may include a syndrome calculation (SC) circuit configured to calculate a codeword from a syndrome ; a key equation solver (KES) circuit configured to calculate an error location polynomial and an error evaluation polynomial from the syndrome; and a Chien search and error evaluation (CSEE) circuit configured to calculate an error location and an error value from the error location polynomial and the error evaluation polynomial, wherein the KES circuit comprises a plurality of sub-KES circuit and each of the plurality of sub-KES circuit, the SC circuit and the CSEE circuit constitutes pipeline stages respectively.