Disclosed are methods, systems, devices, apparatus, media, and other implementations, including a method that includes obtaining input visual data comprising a sequence of symbols, selected from a symbol set, with each of the symbols associated with a glyph representation. The method also includes obtaining a code message comprising code message symbols, and modifying at least one of the symbols of the input visual data to a different glyph representation associated with a respective at least one of the code message symbols to generate, at a first time instance, a resultant coded visual data.

The present disclosure relates to methods and systems for decoding a Bose-Chaudhuri-Hocquenghem (BCH) encoded codeword. The methods-may include receiving a codeword over a data channel; determining a plurality of syndrome values for the codeword during a first time interval; determining a set of initial elements during the first time interval; generating an error locator polynomial based on the plurality of syndrome values, the error locator polynomial representing one or more errors in the codeword; evaluating, based on the set of initial elements, the error locator polynomial to identify one or more error locations corresponding to the one or more errors in the codeword; and correcting the codeword based on the one or more error locations.

A method and an apparatus for transmitting broadcast signals thereof are disclosed. The apparatus for transmitting broadcast signals, the apparatus comprises an encoder to encode service data corresponding to a number of physical paths, a time interleaver to time interleave the encoded service data in each physical path, a frame builder to build at least one signal frame including the time interleaved service data, a modulator to modulate data in the built at least one signal frame by an OFDM (Orthogonal Frequency Division Multiplex) scheme and a transmitter to transmitting the broadcast signals having the modulated data.

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 computer-implemented method includes encoding an array of (p1)k symbols of data into a p(k+r) array. The method includes p is a prime number, r1, and kpr. The method also includes each column in the p(k+r) array has an even parity and each line of slope j for 0jr1 in the p(k+r) array has an even parity. The method includes the lines of slope j taken with a toroidal topology modulo p. A computer program product for encoding an array of (p1)k symbols of data into a p(k+r) array includes a computer readable storage medium having program instructions executable by a computer. The program instructions cause the computer to perform the foregoing method.

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 an apparatus for transmitting broadcast signals thereof are disclosed. The apparatus for transmitting broadcast signals, the apparatus comprises an encoder to encode service data corresponding to a number of physical paths, a time interleaver to time interleave the encoded service data in each physical path, a frame builder to build at least one signal frame including the time interleaved service data, a modulator to modulate data in the built at least one signal frame by an OFDM (Orthogonal Frequency Division Multiplex) scheme and a transmitter to transmitting the broadcast signals having the modulated data.

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 disclosure relates to methods and systems for decoding a Bose-Chaudhuri-Hocquenghem (BCH) encoded codeword. The methods may include receiving a codeword over a data channel; determining a plurality of syndrome values for the codeword during a first time interval; determining a set of initial elements during the first time interval; generating an error locator polynomial based on the plurality of syndrome values, the error locator polynomial representing one or more errors in the codeword; evaluating, based on the set of initial elements, the error locator polynomial to identify one or more error locations corresponding to the one or more errors in the codeword; and correcting the codeword based on the one or more error locations.

A system for error correction code (ECC) management of write-once memory (WOM) codes includes, for example, a controller for selecting between one of a WOM (Write-Once Memory) mode and an ECC (error correction code) mode. A codec is arranged to operate in the selected mode. The codec while operating in the ECC mode is arranged to identify a bit position of at least one bit error in response to ECC parity bits of a first received data word. The codec while operating in the WOM mode is arranged to receive a WOM-encoded word from an addressed location in a WOM device, to receive a second received data word to be encoded and written to the addressed location, and to generate WOM-encoded word for writing to the addressed location in the WOM device. The WOM-encoded word for writing to the addressed location is optionally ECC encoded.