Methods and transceivers transmit communication frames that comprise a sequence of N symbols, ensuing payload header symbols, and ensuing payload message symbols. The sequence of N symbols encodes information according to signal-to-noise ratio associated with the communication frame.

An apparatus for polar coding includes an encoder circuit that implements a transformation C=u.sub.1.sup.N-sB.sub.N-s{tilde over (M)}.sub.n, wherein u.sub.1.sup.N-s, B.sub.N-s, {tilde over (M)}.sub.n, and C are defined over a Galois field GF(2.sup.k), k>1, wherein N=2.sup.n, s<N, u.sub.1.sup.N-s=(u.sub.1, . . . , u.sub.N-s) is an input vector of N−s symbols over GF(2.sup.k), B.sub.N-s is a permutation matrix, {tilde over (M)}.sub.n=((N−s) rows of M.sub.n=), the matrix M.sub.1 is a pre-defined matrix of size q×q, 2<q and N=q.sup.n, and C is a codeword vector of N−s symbols, and wherein a decoding complexity of C is proportional to a number of symbols in C; and a transmitter circuit that transmits codeword C over a transmission channel.

Methods and transceivers transmit communication frames that comprise a sequence of N symbols, ensuing payload header symbols, and ensuing payload message symbols. The sequence of N symbols encodes information according to signal-to-noise ratio associated with the communication frame.

Methods and transceivers transmit communication frames that comprise a sequence of N symbols, ensuing payload header symbols, and ensuing payload message symbols. The sequence of N symbols encodes information according to signal-to-noise ratio associated with the communication frame.

A method for performing polar coding is disclosed in the application. A data block is segmented into a plurality of first blocks. Difference in bit length between any two first blocks is not more than one bit. For each first block, one or more consecutive padding bits is added to obtain a second block of a bit length K if the bit length of the first block is less than K, so as to obtain a plurality of second blocks corresponding to the first blocks. N-K consecutive bits are added to each of the second blocks to obtain a plurality of third blocks. Polar encoding is performed on the third blocks.

A data protection technique combines error correcting code and redundant array of independent disk functionality for a non-volatile memory (NVM) array of a data storage system. The technique includes receiving, by a controller, data for storage in the NVM. In response to receiving the data for storage in the NVM array, the controller forms first component codewords based on encodings with a first level code of respective first portions of the data. In response to receiving the data for storage in the NVM array, the controller forms a second component codeword based on an encoding with a second level code of a second portion of the data and the first component codes. The controller stores a respective portion of each of the first and second component codeswords on packages of the NVM array. The storing achieves maximum equal spreading of each of the component codewords across all of the packages.

A data protection technique combines error correcting code and redundant array of independent disk functionality for a non-volatile memory (NVM) array of a data storage system. The technique includes receiving, by a controller, data for storage in the NVM. In response to receiving the data for storage in the NVM array, the controller forms first component codewords based on encodings with a first level code of respective first portions of the data. In response to receiving the data for storage in the NVM array, the controller forms a second component codeword based on an encoding with a second level code of a second portion of the data and the first component codes. The controller stores a respective portion of each of the first and second component codeswords on packages of the NVM array. The storing achieves maximum equal spreading of each of the component codewords across all of the packages.

Method and apparatus for managing data in a memory, such as a flash memory. In accordance with some embodiments, a solid-state non-volatile memory (NVM) has a total user data storage capacity and an overprovisioning (OP) level. A control circuit writes parity data sets to the NVM each having a plurality of code words and an outer code. The code words include inner codes at an inner code rate to detect and correct read errors in a user data payload. The outer code includes parity data at an outer code rate to detect and correct read errors in the code words. A code adjustment circuit increases the inner code rate to compensate for a measured parameter associated with the NVM, and decreases the outer code rate to maintain the data capacity and OP levels above selected thresholds.

A data storage system stores a set of codewords in memory. The set of codewords are encoded in accordance with a joint nesting matrix specifying multiple layers of integrated interleaved codes, including first, second and third layers of integrated interleaved codes, and the set of codewords stored in the memory include first, second and third layers of parity information corresponding to the first, second and third layers of integrated interleaved codes. When decoding a first codeword and a first subgroup containing the first codeword fail, the system decodes a group of codewords that include two more subgroups of codewords, including the first subgroup of codewords, using the third layer parity information for the group of codewords. The second and third layers of integrated interleaved codes are configured to enable decoding of two codewords, in a subgroup of codewords, having errors beyond the correction capability of the first layer codes.

A data storage system stores a set of codewords in memory. The set of codewords are encoded in accordance with a joint nesting matrix specifying multiple layers of integrated interleaved codes, including first, second and third layers of integrated interleaved codes, and the set of codewords stored in the memory include first, second and third layers of parity information corresponding to the first, second and third layers of integrated interleaved codes. When decoding a first codeword and a first subgroup containing the first codeword fail, the system decodes a group of codewords that include two more subgroups of codewords, including the first subgroup of codewords, using the third layer parity information for the group of codewords. The second and third layers of integrated interleaved codes are configured to enable decoding of two codewords, in a subgroup of codewords, having errors beyond the correction capability of the first layer codes.