A transmitter for transmitting an encoded codeword over a communication channel is described. The transmitter 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 an encoded codeword, a modulator to modulate the encoded codeword, and a front end to transmit the modulated and encoded codeword over the communication channel, wherein the polar code is specified by a set of regular parameters and a set of irregular parameters.

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.

Systems and methods for decoding block and concatenated codes are provided. These include advanced iterative decoding techniques based on belief propagation algorithms, with particular advantages when applied to codes having higher density parity check matrices such as iterative soft-input soft-output and list decoding of convolutional codes, Reed-Solomon codes and BCH codes. Improvements are also provided for performing channel state information estimation including the use of optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics. Particular improvements are also provided for decoding HD radio signals, satellite radio signals, digital audio broadcasting (DAB) signals, digital audio broadcasting plus (DAB+) signals, digital video broadcasting-handheld (DVB-H) signals, digital video broadcasting-terrestrial (DVB-T) signals, world space system signals, terrestrial-digital multimedia broadcasting (T-DMB) signals, and China mobile multimedia broadcasting (CMMB) signals. These and other improvements enhance the decoding of different digital signals.

A decoding method for a rewritable non-volatile memory module is provided according to an exemplary embodiment of the disclosure. The decoding method includes: reading first data from memory cells of the rewritable non-volatile memory module, wherein the first data includes a first bit stored in a first memory cell; obtaining a storage state of at least one second memory cell which is different from the first memory cell; obtaining first reliability information corresponding to the first bit according to the storage state of the second memory cell, wherein the first reliability information is different from default reliability information corresponding to the first bit; and decoding the first data according to the first reliability information. Therefore, a decoding efficiency can be improved.

Systems and methods for decoding block and concatenated codes are provided. These include advanced iterative decoding techniques based on belief propagation algorithms, with particular advantages when applied to codes having higher density parity check matrices such as iterative soft-input soft-output and list decoding of convolutional codes, Reed-Solomon codes and BCH codes. Improvements are also provided for performing channel state information estimation including the use of optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics. Particular improvements are also provided for decoding HD radio signals, satellite radio signals, digital audio broadcasting (DAB) signals, digital audio broadcasting plus (DAB+) signals, digital video broadcasting-handheld (DVB-H) signals, digital video broadcasting-terrestrial (DVB-T) signals, world space system signals, terrestrial-digital multimedia broadcasting (T-DMB) signals, and China mobile multimedia broadcasting (CMMB) signals. These and other improvements enhance the decoding of different digital signals.

A node (110, 115) receives (804) transmissions associated with a given set of information bits, wherein each of the transmissions use a different polar code and share one or more information bits of the given set of information bits. The node determines (808), at each of a plurality of polar decoders (505, 605) of the node, soft information for each information bit included in an associated one of the transmissions, wherein each of the plurality of polar decoders is associated with a different transmission of the transmissions. The node provides (812), from each polar decoder of the plurality to one or more other polar decoders of the plurality, the determined soft information for any information bits shared by their respective associated transmissions, and uses (816) the provided soft information in an iterative decoding process to decode one or more of the received transmissions.

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 iterative decoder is controlled to iteratively decode a block by performing one or more decoding iterations for the block. The iterative decoder uses a parity-check matrix and can be configured to process that parity-check matrix for parallel, sequential or a combination of parallel and sequential (hybrid) parity constraint updates.

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.