In some aspects, methods and apparatus for wireless communications are configured to generate a packet for wireless communication where the packet includes a mark symbol in a preamble of the packet where the mark symbol includes a signature or stamp field in the mark to provide protocol information that indicates the protocol of the packet, such as an 802.11 EHT packet. In some other aspects, a cyclic redundancy check field in the mark symbol may be manipulated in various ways to indicate the protocol of the packet in lieu of providing the signature or stamp field.

Systems and methods are provided for fast cyclic redundancy check code generation. For example, a method includes representing the sequence of bits as a polynomial over a Galois field base 2; partitioning the polynomial into a plurality of partial polynomials, wherein the polynomial equals the sum of the partial polynomials; concurrently generating a respective partial CRC code for each of the partial polynomials; weighting each partial CRC code according to a position of the respective partial polynomial in the polynomial; and summing the weighted partial CRC codes.

An error correction and fault, tolerance method and system for an array of disks is presented. The array comprises k+5 disks, where k disks store user data and 5 disks store computed parity. The present invention further comprises a method and a system for reconstituting the original content of each of the k+5 disks, when up to disks have been lost, wherein the number of disks at unknown locations is E and the number of disks wherein the location of the disks is known is Z. All combinations of faulty disks wherein Z+2×E≤4 are reconstituted. Some combinations of faulty disks wherein Z+2×E≤5 are either reconstituted, or errors are limited to a small list.

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 processing element includes an input zero detector to detect whether the input from the neighbor processing element contains a zero. When the input from the neighbor processing element contains the zero, a zero disable circuit controls the input from the neighbor processing element and respective data of the memory to both appear as unchanged to the arithmetic logic unit for the operation. A controller of an array of processing elements adds a row of error-checking values to a matrix of coefficients, each error-checking value of the row of error-checking values being a negative sum of a respective column of the matrix of coefficients. The controller controls a processing element to perform an operation with the matrix of coefficients and an input vector to accumulate a result vector. Owing to the error-checking values, when a sum of elements of the result vector is non-zero, an error is detected.

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.

Systems and methods are provided for fast cyclic redundancy check code generation. For example, a method includes representing the sequence of bits as a polynomial over a Galois field base 2; partitioning the polynomial into a plurality of partial polynomials, wherein the polynomial equals the sum of the partial polynomials; concurrently generating a respective partial CRC code for each of the partial polynomials; weighting each partial CRC code according to a position of the respective partial polynomial in the polynomial; and summing the weighted partial CRC codes.

A method for correcting an error of a received signal is provided. The method includes: determining a target degree based upon a length of the received signal; obtaining plural primitive polynomials each having a degree equal to the target degree; selecting one of the primitive polynomials as a target polynomial; defining plural syndromes according to the received signal; generating a group of product values based on the syndromes; obtaining plural coefficient polynomials based on the product values; obtaining monomial trace coefficients based on the coefficient polynomials; generating an error correction value based on the monomial trace coefficients; and correcting the error based on the error correction 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 dual-mode Reed-Solomon decoder is configured to perform error correction for two different encoding schemes. The decoder includes a syndrome calculator block, a key equation solver block, a polynomial evaluation block, and an error correction block. The syndrome calculator block receives encoded input data and calculates syndromes, with the number of calculated syndromes based on the selected decoding mode. The key equation solver block calculates an error locator polynomial and an error evaluator polynomial for the encoded input data, with the degree of the polynomials based on the selected decoding mode. The polynomial evaluation block identifies error locations and magnitudes in the encoded data, with an array of constants input to the block based on the selected decoding mode. The error correction block decodes the encoded input data based on the identified error locations and error magnitudes.