Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, a method for data processing is disclosed that includes receiving a codeword that has at least a first circulant with a plurality of data bits and a first circulant parity bit, a second circulant with a plurality of data bits and a second circulant parity bit, and one or more codeword parity bits. The methods further include decoding the codeword using the one or more codeword parity bits to access the first circulant and the second circulant, performing a first circulant parity check on the first circulant, and performing a second circulant parity check on the second circulant.

Abstract: Various embodiments of the present invention provide systems and methods for data processing. For example, a data processing circuit is disclosed that includes a first data detection circuit that applies a phase dependent data detection algorithm to a data set such that a first output of the first data detection circuit varies depending upon a phase of the data set presented to the first data detection circuit. A first phase of the data set is presented to the first data detection circuit. The circuits further include a decoder circuit that applies a decoding algorithm to the first output to yield a decoded output, and a phase shift circuit that phase shifts the decoded output such that a second phase of the data set is provided as a phase shifted output.

Abstract: Various embodiments of the present invention provide systems and methods for generating a parity check matrix used in data processing. As an example, a method for generating a parity check matrix including selecting a non-affiliated variable node; identifying a check node of the lowest degree; connecting a first edge of the non-affiliated variable node to the identified check node; and connecting one or more additional edges of the non-affiliated variable node to check nodes in accordance with a quasi-cyclic constraint associated with a circulant is disclosed.

Abstract: Techniques are provided that generate bit reliabilities for a detected sequence. A detector generates the detected sequence. According to one embodiment, a post-processor finds a first set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the first bit value, finds a second set of combinations of one or more error events in the detected sequence satisfying a complete set or a subset of error correction constraints corresponding to the second bit value, selects a first most likely combination of one or more events of the first set and a second most likely combination of one or more events of the second set, and generates a bit reliability based on the first and the second most likely values.

Abstract: A detector generates a detected sequence, and a post processor generates probability values that indicate the likelihood of a plurality of error events in the detected sequence. The post processor partitions the values into first and second subsets. The post processor selects a first most likely value from the first subset of the values and a second most likely value from the second subset of the values. The post processor generates a bit reliability based on the first and the second most likely values.

Abstract: Techniques are provided for iteratively decoding data recorded on a data storage device. An iterative decoder decodes the data using multiple decoding iterations to correct errors. In multiple iterations of the iterative decoder, a post processing block generates soft information, and a decoder applies a minimum sum decoding algorithm to a low density parity check (LDPC) code to generate extrinsic information based on the soft information and updated soft information.