Examples include techniques to improve error correction using an exclusive OR (XOR) rebuild scheme that includes two uncorrectable codewords. Examples include generation of soft XOR codewords using bits of correctable codewords to rebuild a codeword read from a memory that has uncorrectable errors and adjust bit reliability information to generate a new codeword having correctable errors. Examples also include techniques to prevent mis-correction due to read reference voltage shifts using non-linear transformations.

A transmission apparatus includes an encoder that codes a data sequence with a parity check matrix, wherein the data sequence includes a final information bit sequence and virtual information bits, and outputs the final information bit sequence and a parity sequence, as LDPC codes, and a transmitter that transmits the LDPC codes as a transmission data. A column length of the parity check matrix is longer than a total length of the final information bit sequence and the parity sequence, by a length of the virtual information bits that are set to 0 and are not transmitted. The total length of the final information bit sequence and the parity sequence has a sequence length corresponding to a length from a first column to a determined column of the parity check matrix. The encoder generates the LDPC codes by using the first column to the determined column among one or more column(s) of the parity check matrix.

Certain aspects of the present disclosure generally relate to techniques for encoding and decoding bits of information using cyclic redundancy check (CRC) concatenated polar encoding and decoding. The CRC concatenated polar encoding techniques may avoid transmission of dummy bits. A method generally includes obtaining the bits of information to be transmitted. The method includes performing CRC outer encoding of the bits of information using an even-weighted generator polynomial to produce CRC encoded bits. The method includes performing polar inner encoding of the CRC encoded bits to generate a codeword. The method includes discarding a first code bit at a beginning of the codeword. The shortened codeword is transmitted over a wireless medium. In another method, bit-level scrambling is performed on the CRC encoded bits before the polar encoding to avoid generating a dummy bit. In another method, only odd-weighted generator polynomials are selected to avoid generating the dummy bit.

Devices, systems, and methods that reduce the latency of detecting that a codeword is uncorrectable are disclosed and described. Such devices, systems, and methods allow the determination that a codeword is uncorrectable prior to determining error locations in the codeword, thus eliminating the need for such an error location search.

An apparatus is described. The apparatus includes a memory chip. The memory chip has an error correction code (ECC) encoder logic circuit and an ECC decoder logic circuit. The ECC decoder logic circuit is to place an additional one or more errors that result from incorrect error correction applied to a read code word into a same block of multiple blocks of the read code word's raw data bit portion where original errors in the read code word existed before the read code word was decoded by the ECC decoder logic circuit.

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.n-1(mod n) and enumerating residual codewords of the code set by P.sub.n=C.sub.nO.sub.n={(l.sub.1).sup.n-1O.sub.n}={(r.sub.n).sup.n-1O.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.n-1 and (r.sub.n).sup.n-1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.

The present invention is directed to data communication systems and methods thereof. According to various embodiments, the present invention provides a communication with a reconfigurable forward-error-correction (FEC) module. The FEC module processes data received from two or more communication lanes, and depending on the mode of operation, the FEC module can combine data from the two or more communication lanes and perform error correction on the combined data, or the FEC module can processes data from the two communications lanes separately and perform error correction independently for the each of the data communication lanes. There are other embodiments as well.

The present invention is directed to data communication systems and methods thereof. According to various embodiments, the present invention provides a communication with a reconfigurable forward-error-correction (FEC) module. The FEC module processes data received from two or more communication lanes, and depending on the mode of operation, the FEC module can combine data from the two or more communication lanes and perform error correction on the combined data, or the FEC module can processes data from the two communications lanes separately and perform error correction independently for the each of the data communication lanes. There are other embodiments as well.

A method and a decoder for receiving a message encoded in Turbo Codes and modulated for transmission as an analog signal includes: (a) demodulating the analog signal to recover the Turbo Codes; and (b) decoding the Turbo Codes to recover the message using an iterative Turbo Code decoder, wherein the decoding includes performing an error detection after a predetermined number of iterations of the Turbo Code decoder to determine whether or not an error has occurred during the transmission. The predetermined number of iterations may be, for example, two. Depending on the result of the error detection, the decoding may stop, a request for retransmission of the message may be sent, or further iterations of decoding in the Turbo Code decoder may be carried out.

The present disclosure relates to a method and an apparatus for coding data to be transmitted in a communication system, and more particularly, to a method and an apparatus for generating a sequence for a polar code for use in a communication system and a method and an apparatus for transmitting data using the same. The method according to the embodiment of the present disclosure is a method for transmitting data using a polar code including: generating a single polar code sequence for transmitting the data; coding the data using the generated single polar code sequence; and transmitting the polar-coded data.