A receiver includes a polar decoder for decoding an encoded codeword transmitted over a communication channel The receiver includes a front end to receive over a communication channel a codeword including a sequence of bits modified with noise of the communication channel and a soft decoder operated by a processor to produce a soft output of the decoding. The codeword is encoded by at least one polar encoder with a polar code. The processor is configured to estimate possible values of the bits of the received codeword using a successive cancelation list (SCL) decoding to produce a set of candidate codewords, determine a distance between each candidate codeword and a soft input to the soft decoder, and determine a likelihood of a value of a bit in the sequence of bits using a difference of distances of the candidate codewords closest to the received codeword and having opposite values at the position of the bit.

A transmitter for transmitting an encoded codeword over a communication channel includes a source to accept source data, an irregular polar encoder operated by a processor to encode the source data with at least one polar code to produce the encoded codeword, a modulator to modulate the encoded codeword, and a front end to transmit the modulated and encoded codeword over the communication channel. The polar code is specified by a set of regular parameters including one or combination of parameters defining a number of data bits in the codeword, a parameter defining a data index set specifying locations of frozen bits in the encoded codeword, and a parameter defining a number of parity bits in the encoded codeword. The polar code is further specified by a set of irregular parameters including one or combination of parameters defining an irregularity of values of at least one regular parameter of the polar code, a parameter defining an irregularity of permutation of the encoded bits, a parameter defining an irregularity of polarization kernels in the polar code, and a parameter defining an irregularity in selection of de-activated exclusive-or operations on different stages of the polar encoding, and wherein the irregular polar encoder encodes the codeword using the regular and the irregular parameters of the polar code.

An optical transmission technique includes receiving data for transmission over the optical communication network, applying a three-dimensional (3D) error correction code to the data using three component codes, resulting in error correction coded signal, modulating the error correction coded signal using a quadrature amplitude modulation (QAM) scheme and processing and transmitting the modulated signal over the optical communication medium.

A method including mapping an address space of the buffer configured to store a plurality of data values into a first two-dimensional array of values. For each row in the first two-dimensional array, calculating, by a processor comprising an encoder, a row parity value. For each row, a plurality of data values in the row and the row parity value form a row codeword. For each column in the first two-dimensional array, a column parity value is calculated by the processor comprising an encoder, wherein for each column, a plurality of data values in the column and the column parity value form a column codeword. The exclusive-OR (XOR) of the plurality of data values is calculated. A parity value based on the XOR of the plurality of data values is calculated by the processor comprising an encoder.

Techniques are described for decoding a codeword, including, obtaining a first message comprising a plurality of information bits and a plurality of parity bits, wherein the message corresponds to a turbo product code (TPC) comprising two or more constituent codes, wherein each constituent code corresponds to a class of error correcting codes capable of correcting a pre-determined number of errors, performing an iterative TPC decoding using at least one of a first decoder corresponding to a first constituent code and a second decoder corresponding to a second constituent code on the first message to generate a second message, determining if the decoding was successful. Upon determining that the TPC decoding was not successful, determining one or more error locations in the second message based on a third constituent code using a third decoder. The third decoder determines the one or more error locations in a predetermined number of clock cycles.

A method for fast decoding, the method may include (a) performing a hard read of a group of flash memory cells to provide hard read data; wherein the group of flash memory cells store a codeword that comprises component codes of multiple dimensions; (b) hard decoding the hard read data to provide a hard decoding result; wherein the hard decoding result comprises first suggested values of component codes of at least one dimension of the multiple dimensions; (c) performing at least one additional read attempt of the group of flash memory cells to provide additional data; (d) performing a partial extensiveness soft decoding the additional data, in response to the first suggested values, to provide a soft decoding result; and (e) wherein the soft decoding result comprises second suggested values of component codes of one or more dimensions of the multiple dimensions.

An apparatus is provided. The apparatus comprises a first syndrome computation circuit configured to receive a codeword having a plurality of rows and a plurality of columns and further configured to compute a first syndrome for at least a portion of a first component codeword of the codeword. The apparatus further comprises a second syndrome computation circuit configured to receive the codeword and to compute a second syndrome for at least a portion of a second component codeword of the codeword. The apparatus further comprises a bit correction circuit configured to correct one or more erroneous bits in the codeword based, at least in part, on at least one of the first and second syndrome, wherein the first and second component codewords span two or more rows and two or more columns of the codeword.

A storage system and method for reducing XOR recovery time are provided. In one embodiment, a storage system is provides comprising a memory and a controller. The controller is configured to generate a first exclusive-or (XOR) parity for pages of data written to the memory; after the first XOR parity has been generated, determine that there is at least one page of invalid data in the pages of data written to the memory; and generate a second XOR parity for the pages of data that excludes the at least one page of invalid data, wherein the second XOR parity is generated by performing an XOR operation using the first XOR parity and the at least one page of invalid data as inputs. Other embodiments are possible, and each of the embodiments can be used alone or together in combination.

Various implementations described herein relate to systems and methods for decoding data stored in a non-volatile storage device, including determining error candidates and determining whether at least one first error candidate from the error candidates is found based on two of the component codes agreeing on a same error candidate. In addition, whether at least one second error candidate is found based on two of the component codes agreeing on a same error candidate is determined in response to implementing a suggested correction at one of the error candidates. Errors in the data are corrected based on at least one of whether the at least one first error candidate is found or whether the at least one second error candidate is found.

Forward Error Correction technique: parity vectors are computed such that each parity vector spans multiple FEC frames; in a given FEC frame, a first set of syndrome bits are due to the parity vectors, and a second set of syndrome bits satisfy FEC equations that involve bits of the given FEC frame including the first set of syndrome bits; and the parity vectors are staggered with respect to any sequence in which the FEC frames are processed. Values of decoded bits of a first frame are deduced from known bits of a first parity vector having an effective length of one frame. For parity vectors having an effective length greater than one frame, a Log Likelihood Ratio of each unknown bit associated with the first frame is updated based on known and unknown bits of each parity vector. First frame is decoded using deduced bit values and updated LLR values.