Exemplary embodiments for providing multi-bit error correction based on a BCH code are provided. In one such embodiment, the following operations are repeatedly performed, including shifting each bit of the BCH code rightward by 1 bit while filling the bit vacated due to the rightward shifting in the BCH code with 0, calculating syndrome values corresponding to the shifting of the BCH code, and determining a first error number in the BCH code under the shifting based on the syndrome values corresponding to the shifting of the BCH code. In the case where the first error number is not equal to 0, modified syndrome values are calculated corresponding to the shifting of the BCH code. The modified syndrome values are those corresponding to the case that the current rightmost bit of the BCH code under the shifting is changed to the inverse value. Additional operations are performed as described herein.

Disclosed is a GEL codeword structure encoding method. The method includes: first transforming an H.sub.C of a code B into an H.sup.B; obtaining a parity bit of the code B by performing an operation on the H.sup.B and an information bit of the code B; using the parity bit to perform RS coding on a code A, to obtain a parity bit of the code A; then obtaining a check code of a GEL code by performing an operation on the parity bits of the code B and the code A; and finally adding a single bit parity check bit, where the code A is defined in a finite field GF (2.sup.l1), the code B is defined in a finite field GF (2.sup.l2), and 1.sub.1 and 1.sub.2 are positive integers. A success rate of decoding the code A in the first row can be improved using this method.

Decoder circuitry for an input channel having a data rate, where a codeword on the input channel includes a plurality of symbols, includes options to provide a first output channel having that data rate, and a plurality of second output channels having slower data rates. The decoder circuitry includes syndrome calculation circuitry, polynomial calculation circuitry, and search-and-correct circuitry. The syndrome calculation circuitry includes finite-field multipliers for multiplying each symbol by a power of a root of the field. Each multiplier other than a first multiplier multiplies a symbol by a higher power of the root than an adjacent multiplier. First-level adders add outputs of a number of groups of multipliers. A second-level adder adds outputs of the first-level adders to be accumulated as syndromes of the first output channel. Another plurality of accumulators accumulates outputs of the first-level adders, which after scaling, are syndromes of the second output channels.

A construction method for a (n,n(n1),n1) permutation group code based on coset partition is provided. The presented (n,n(n1),n1) permutation group code has an error-correcting capability of d1 and features a strong anti-interference capability for channel interferences comprising multi-frequency interferences and signal fading. As n is a prime, for a permutation code family with a minimum distance of n1 and a code set size of n(n1), the invention provides a method of calculating n1 orbit leader permutation codewords by O.sub.n={o.sub.1}.sub.=1.sup.n1(mod n) and enumerating residual codewords of the code set by P.sub.n=C.sub.nO.sub.n={(l.sub.1).sup.n1O.sub.n}={(r.sub.n).sup.n1O.sub.n)}. Besides, a generator of the code set thereof is provided. The (n,n(n1),n1) permutation group code of the invention is an algebraic-structured code, n1 codewords of the orbit leader array can be obtained simply by adder and (mod n) calculator rather than multiplication of positive integers. Composition operations of the cyclic subgroup C.sub.n acting on all permutations o.sub. of the orbit leader permutation array O.sub.n are replaced by well-defined cyclic shift composite operation functions (l.sub.1).sup.n1 and (r.sub.n).sup.n1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.

Provided are an apparatus, memory device, and method to determine error location polynomial coefficients to provide to bit correction logic instances to decode bits of a codeword. A memory controller for a memory includes coefficient generating logic to receive as input a plurality of syndrome values to generate a plurality of coefficients for an error locator polynomial. A plurality of instances of bit correction logic, one instance for each bit of bits to correct in a codeword for a block in the memory array to decode. Each instance of bit correction logic is to receive as input the coefficients for the error locator polynomial and elements for the bit to correct from a decoder alphabet to determine whether to correct the bit and output as a decoded bit the bit or a corrected bit to include in a decoded codeword.

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).

The present discloses provides a decoding method, decoding apparatus and decoder for correcting burst errors. In particular, the decoding method for correcting burst errors comprises: computing an initial syndrome of a received data frame, wherein the data frame is encoded according to cyclic codes for correcting burst errors; determining error correctability of burst error contained in the data frame based on the computed initial syndrome; and processing the burst error in the data frame and outputting the processed data frame based on the determined error correctability. With the decoding method, decoding apparatus, and decoder of the present invention, error correctability of burst errors contained in a data frame can be determined before the data is send out, while having smaller decoding latency through determining the error correctability and error pattern of the burst errors contained in the data frame using initial syndrome of the data frame.

A method for decoding a (n, k, d) cyclic code is disclosed. The method includes: receiving a word corresponding to the cyclic code; constructing a look-up table, wherein the look-up table includes k syndrome vectors and k error patterns; computing a syndrome vector of the received word by a hardware processor; comparing the weight of the syndrome vector of the received word with an error-correcting capacity; decoding the received word by adding the received word and the syndrome vector if the weight of the syndrome vector of the received word is not more than the error-correcting capacity; decoding the received word by inverting bits in the message section in sequence and re-compute a syndrome vector of the inverted received word if the weight of the syndrome vector of the received word is more than the error-correcting capacity.

A method for decoding a cyclic code is disclosed. The method includes: determining a plurality of syndromes for the cyclic code; determining, by a hardware processor, a first coefficient and a second coefficient based on the plurality of syndromes; determining, by the hardware processor, a third coefficient based on the second coefficient; and generating an error-locator polynomial based on the first coefficient, the second coefficient, and the third coefficient.

A memory system includes a memory module that supports error detection and correction (EDC) in a manner that relieves a memory controller or processor of some or all of the computational burden associated with EDC. Individual EDC components perform EDC functions on subsets of the data, and share data between themselves using relatively short, fast interconnections.