Example systems, read channel circuits, data storage devices, and methods to use inter-symbol interference message passing (ISI-MP) data in a read channel are described. The read channel circuit includes a soft output detector, such as a soft output Viterbi algorithm (SOVA) detector, configured to determine both the first most likely and second most likely sets of symbols and output inter-symbol interference data based on the adjacent symbols and corresponding ISI in each set of symbols. The inter-symbol interference data may be used by an ISI-MP circuit configured to model ISI-MP and provide feedback to an iterative decoder during local iterations.

A soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellises of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, there is provided a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.

A data storage device is disclosed comprising a storage medium. First data is encoded into a first codeword, and second data is encoded into a second codeword, wherein a first code rate of the first codeword is less than a second code rate of the second codeword. The first codeword and the second codeword are interleaved to generate an interleaved codeword that is written to the storage medium.

The invention relates to a soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellises of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, the present invention provides a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.

The present application discloses a forward and backward smooth decoding method and device suitable for an OvXDM system, and a system. Importance weights of particles in a particle set corresponding to a symbol are calculated by using a forward process and a backward process, and screening is performed with reference to forward importance weights of particles and backward importance weights of particles, to output a final decoding sequence.

The present application discloses a forward and backward smooth decoding method and device suitable for an OvXDM system, and a system. Importance weights of particles in a particle set corresponding to a symbol are calculated by using a forward process and a backward process, and screening is performed with reference to forward importance weights of particles and backward importance weights of particles, to output a final decoding sequence.

The invention relates to a soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellises of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, the present invention provides a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.

A soft input decoding method and a decoder for generalized concatenated (GC) codes. The GC codes are constructed from inner nested block codes, such as binary Bose-Chaudhuri-Hocquenghem, BCH, codes and outer codes, such as Reed-Solomon, RS, codes. In order to enable soft input decoding for the inner block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code. In one aspect, the present invention applies instead a representation of the block codes based on the trellizes of supercodes in order to reduce the memory requirements for the representation of the inner codes. This enables an efficient hardware implementation. In another aspect, there is provided a soft input decoding method and device employing a sequential stack decoding algorithm in combination with list-of-two decoding which is particularly well suited for applications that require very low residual error rates.