A method for storing input data in a flash memory. The method comprising generating a codeword by encoding the input data with an error correcting code and generating a shaped codeword by applying a shaping function to at least a part of the codeword. The shaping function comprising logically inverting every n-th occurrence of a bit associated with a high-charge storage state in the part of the codeword. The method further comprising writing the shaped codeword to the flash memory, generating an estimated shaped codeword by reading the flash memory, generating soft decision information for the estimated shaped codeword, and retrieving the input data by decoding the soft decision information using an error correcting code soft decoder.

A method for storing input data in a flash memory. The method comprising generating a codeword by encoding the input data with an error correcting code and generating a shaped codeword by applying a shaping function to at least a part of the codeword. The shaping function comprising logically inverting every n-th occurrence of a bit associated with a high-charge storage state in the part of the codeword. The method further comprising writing the shaped codeword to the flash memory, generating an estimated shaped codeword by reading the flash memory, generating soft decision information for the estimated shaped codeword, and retrieving the input data by decoding the soft decision information using an error correcting code soft decoder.

According to one embodiment, a decoding device comprises a converter configured to convert read data to first likelihood information by using a first conversion table, a decoder which decodes the first likelihood information, a controller which outputs a decoding result of the decoder when the decoder succeeds decoding, and a creator module which creates a second conversion table based on the decoding result when the decoder fails decoding. When the second conversion table is created, at least a part of the decoding result is converted to second likelihood information by using the second conversion table the second likelihood information is decoded.

According to one embodiment, a decoding device comprises a converter configured to convert read data to first likelihood information by using a first conversion table, a decoder which decodes the first likelihood information, a controller which outputs a decoding result of the decoder when the decoder succeeds decoding, and a creator module which creates a second conversion table based on the decoding result when the decoder fails decoding. When the second conversion table is created, at least a part of the decoding result is converted to second likelihood information by using the second conversion table the second likelihood information is decoded.

A hardware complexity reduction method for successive cancellation list decoders (SCL) is provided. In path pruning stages of an SCL decoding, L paths with smallest path metrics out of 2L candidate paths are chosen as surviving candidate paths as in a conventional SCL algorithm. Moreover, path indexes of L surviving candidate paths are provided in a sorted manner according to indexes at an output of a sorter module. After a path pruning, instead of L-to-1 multiplexers, (L/2+1)-to-1 multiplexers are deployed to perform copying operations of any required elements stored in dedicated registers of the L surviving candidate paths.

A hardware complexity reduction method for successive cancellation list decoders (SCL) is provided. In path pruning stages of an SCL decoding, L paths with smallest path metrics out of 2L candidate paths are chosen as surviving candidate paths as in a conventional SCL algorithm. Moreover, path indexes of L surviving candidate paths are provided in a sorted manner according to indexes at an output of a sorter module. After a path pruning, instead of L-to-1 multiplexers, (L/2+1)-to-1 multiplexers are deployed to perform copying operations of any required elements stored in dedicated registers of the L surviving candidate paths.

An error check code (ECC) decoder includes a buffer, a data converter and a decoding circuit. The buffer stores a plurality of read pages read from a plurality of multi-level cells connected to a same wordline. The data converter adjusts reliability parameters of read bits of the plurality of read pages based on state-bit mapping information and the plurality of read pages to generate a plurality of ECC input data respectively corresponding to the plurality of read pages. The state-bit mapping information indicate mapping relationships between states and bits stored in the plurality of multi-level cells. The decoding circuit performs an ECC decoding operation with respect to the plurality of read pages based on the plurality of ECC input data. An error correction probability is increased by adjusting the reliability parameters of read bits based on the state-bit mapping information.

An error check code (ECC) decoder includes a buffer, a data converter and a decoding circuit. The buffer stores a plurality of read pages read from a plurality of multi-level cells connected to a same wordline. The data converter adjusts reliability parameters of read bits of the plurality of read pages based on state-bit mapping information and the plurality of read pages to generate a plurality of ECC input data respectively corresponding to the plurality of read pages. The state-bit mapping information indicate mapping relationships between states and bits stored in the plurality of multi-level cells. The decoding circuit performs an ECC decoding operation with respect to the plurality of read pages based on the plurality of ECC input data. An error correction probability is increased by adjusting the reliability parameters of read bits based on the state-bit mapping information.

A communication apparatus for forward error correction and detection using polar codes comprising a polar encoder that encodes an input vector to output a codeword using a generator matrix of polar code wherein the input vector is a cyclic redundancy check (CRC) codeword of an information block; a memory that stores a frozen set including frozen bit indices and a non-frozen set including non-frozen bit indices sorted in order of error probabilities; and a controller that is configured to take as input the CRC codeword where CRC bits appended to the end of information block and interleave the CRC codeword using at least one of a first interleaver and second interleaver before feeding the CRC codeword to polar encoder such that the first interleaver places at least one CRC bit earlier than its original position in the CRC codeword and a second interleaver selects at least one bit from the CRC codeword whose corresponding index in a parity check matrix of the CRC code has the highest column weight and puts it in the non-frozen bit index with highest error probability.

A communication apparatus for forward error correction and detection using polar codes comprising a polar encoder that encodes an input vector to output a codeword using a generator matrix of polar code wherein the input vector is a cyclic redundancy check (CRC) codeword of an information block; a memory that stores a frozen set including frozen bit indices and a non-frozen set including non-frozen bit indices sorted in order of error probabilities; and a controller that is configured to take as input the CRC codeword where CRC bits appended to the end of information block and interleave the CRC codeword using at least one of a first interleaver and second interleaver before feeding the CRC codeword to polar encoder such that the first interleaver places at least one CRC bit earlier than its original position in the CRC codeword and a second interleaver selects at least one bit from the CRC codeword whose corresponding index in a parity check matrix of the CRC code has the highest column weight and puts it in the non-frozen bit index with highest error probability.