Abstract: A device includes a controller, and the controller includes a root detection circuit having multiple sets of multipliers. A method includes configuring the root detection circuit according to a degree of a polynomial. In response to detection of a root of multiple roots of the polynomial, a configuration of the root detection circuit is modified based on a polynomial degree reduction (PDR) scheme. Depending on the particular implementation, the device may be implemented in a data storage device, a communication system (e.g., a wireless communication device or a wired communication device), or another electronic device.

Abstract: A decoder includes syndrome storage and a first barrel shifter configured to bit-shift hard decision bit data to generate shifted data that is aligned with a set of syndromes from the syndrome storage. The decoder also includes a first syndrome update circuit coupled to the first barrel shifter and configured to process the set of syndromes based on the shifted data to generate an updated version of the set of syndromes. The decoder may also be configured to perform on-the-fly syndrome weight computation.

Abstract: In an illustrative example, a method includes receiving data that includes a set of data symbols. The method further includes generating a set of parity symbols based on the set of data symbols using an erasure correcting code. The set of parity symbols includes at least a first parity symbol that is generated based on a first proper subset of the set of data symbols. The first parity symbol enables recovery of a data symbol of the first proper subset independently of a second proper subset of the set of data symbols.

Abstract: A controller is configured to access information to generate data blocks. The controller includes a data block interleaver and a low-density parity check (LDPC) decoder. The data block interleaver is configured to interleave the data blocks to generate interleaved data blocks. The LDPC decoder is configured to decode the interleaved data blocks.

Abstract: Low complexity partial parallel architectures for performing a Fourier transform and an inverse Fourier transform over subfields of a finite field are described. For example, circuits to perform the Fourier transforms and the inverse Fourier transform as described herein may have architectures that have simplified multipliers and/or computational units as compared to traditional Fourier transform circuits and traditional inverse Fourier transform circuits that have partial parallel designs. In a particular embodiment, a method includes, in a data storage device including a controller and a non-volatile memory, the controller includes an inverse Fourier transform circuit having a first number of inputs coupled to multipliers, receiving elements of an input vector and providing the elements to the multipliers. The multipliers are configured to perform calculations associated with an inverse Fourier transform operation.

Abstract: High-speed multi-block-row layered decoding for low density parity check (LDPC) codes is disclosed. In a particular embodiment, a method, in a device that includes a decoder configured to perform an iterative decoding operation, includes processing, at the decoder, first and second block rows of a layer of a parity check matrix simultaneously to generate a first output and a second output. The method includes performing processing of the first output and the second output to generate a first result of a first computation and a second result of a second computation. A length of a “critical path” of the decoder is reduced as compared to a critical path length in which a common feedback message is computed.

Abstract: A decoder includes syndrome storage and a first barrel shifter configured to bit-shift hard decision bit data to generate shifted data that is aligned with a set of syndromes from the syndrome storage. The decoder also includes a first syndrome update circuit coupled to the first barrel shifter and configured to process the set of syndromes based on the shifted data to generate an updated version of the set of syndromes. The decoder may also be configured to perform on-the-fly syndrome weight computation.

Abstract: A decoder includes a syndrome value calculator configured to generate multiple syndrome values. The decoder further includes a check node to variable node message generator that is coupled to the syndrome value calculator. The check node to variable node message generator is configured to generate multiple check node to variable node messages in a single clock cycle based on the multiple syndrome values.

Abstract: A device includes a controller, and the controller includes a root detection circuit having multiple sets of multipliers. A method includes configuring the root detection circuit according to a degree of a polynomial. In response to detection of a root of multiple roots of the polynomial, a configuration of the root detection circuit is modified based on a polynomial degree reduction (PDR) scheme. Depending on the particular implementation, the device may be implemented in a data storage device, a communication system (e.g., a wireless communication device or a wired communication device), or another electronic device.

Abstract: A low-density parity-check (LDPC) encoder is configured to encode data for storage into a non-volatile memory of a data storage device. The LDPC encoder includes a message mapping circuit configured to receive an input message and to generate a mapped message based on the input message. The LDPC encoder also includes a matrix multiplier circuit configured to multiply the mapped message with columns of a Fourier transform of an LDPC generator matrix to generate at least a portion of a transform of an LDPC codeword. The LDPC encoder is configured to provide the transform of the LDPC codeword to an inverse Fourier transform circuit to generate the LDPC codeword.

Abstract: A quasi-cyclic low-density parity-check (QC-LDPC) encoder includes a Fourier transform circuit configured to receive an input message and to generate a transformed message based on the input message. The transformed message includes leading symbols with indices corresponding to leading elements of cyclotomic cosets of a finite field with respect to a subfield. The QC-LDPC encoder further includes a matrix multiplier circuit configured to multiply the leading symbols of the transformed message by leading symbols of a transformed LDPC generator matrix to generate leading symbols of transformed parity symbols associated with an LDPC codeword. The QC-LDPC encoder is configured to provide the leading symbols of the transformed parity symbols to an inverse Fourier transform circuit to generate parity information of the LDPC codeword.

Abstract: A quasi-cyclic low-density parity-check (QC-LDPC) encoder includes a Fourier transform circuit configured to receive an input message and to generate a transformed message based on the input message. The transformed message includes leading symbols with indices corresponding to leading elements of cyclotomic cosets of a finite field with respect to a subfield. The QC-LDPC encoder further includes a matrix multiplier circuit configured to multiply the leading symbols of the transformed message by leading symbols of a transformed LDPC generator matrix to generate leading symbols of transformed parity symbols associated with an LDPC codeword. The QC-LDPC encoder is configured to provide the leading symbols of the transformed parity symbols to an inverse Fourier transform circuit to generate parity information of the LDPC codeword.

Abstract: A low-density parity-check (LDPC) encoder is configured to encode data for storage into a non-volatile memory of a data storage device. The LDPC encoder includes a message mapping circuit configured to receive an input message and to generate a mapped message based on the input message. The LDPC encoder also includes a matrix multiplier circuit configured to multiply the mapped message with columns of a Fourier transform of an LDPC generator matrix to generate at least a portion of a transform of an LDPC codeword. The LDPC encoder is configured to provide the transform of the LDPC codeword to an inverse Fourier transform circuit to generate the LDPC codeword.

Abstract: A decoder includes a syndrome value calculator configured to generate multiple syndrome values. The decoder further includes a check node to variable node message generator that is coupled to the syndrome value calculator. The check node to variable node message generator is configured to generate multiple check node to variable node messages in a single clock cycle based on the multiple syndrome values.

Abstract: A controller is configured to access information to generate data blocks. The controller includes a data block interleaver and a low-density parity check (LDPC) decoder. The data block interleaver is configured to interleave the data blocks to generate interleaved data blocks. The LDPC decoder is configured to decode the interleaved data blocks.

Abstract: High-speed multi-block-row layered decoding for low density parity check (LDPC) codes is disclosed. In a particular embodiment, a method, in a device that includes a decoder configured to perform an iterative decoding operation, includes processing, at the decoder, first and second block rows of a layer of a parity check matrix simultaneously to generate a first output and a second output. The method includes performing processing of the first output and the second output to generate a first result of a first computation and a second result of a second computation. A length of a “critical path” of the decoder is reduced as compared to a critical path length in which a common feedback message is computed.

Abstract: Low complexity partial parallel architectures for performing a Fourier transform and an inverse Fourier transform over subfields of a finite field are described. For example, circuits to perform the Fourier transforms and the inverse Fourier transform as described herein may have architectures that have simplified multipliers and/or computational units as compared to traditional Fourier transform circuits and traditional inverse Fourier transform circuits that have partial parallel designs. In a particular embodiment, a method includes, in a data storage device including a controller and a non-volatile memory, the controller includes an inverse Fourier transform circuit having a first number of inputs coupled to multipliers, receiving elements of an input vector and providing the elements to the multipliers. The multipliers are configured to perform calculations associated with an inverse Fourier transform operation.

Abstract: A method of generating a parity check matrix for iterative decoding of a linear block code includes: determining a set of parity check vectors for the linear block code; ordering according to Hamming weight non-zero parity check vectors of the set; selecting a criterion for generating the parity check matrix; and building the parity check matrix by incrementally selecting according to the criterion a parity check vector for each consecutive row of the parity check matrix, wherein the parity check vector is selected from the ordered non-zero parity check vectors remaining in the set.

Abstract: A method of generating a parity check matrix for iterative decoding of a linear block code includes: determining a set of parity check vectors for the linear block code; ordering according to Hamming weight non-zero parity check vectors of the set; selecting a criterion for generating the parity check matrix; and building the parity check matrix by incrementally selecting according to the criterion a parity check vector for each consecutive row of the parity check matrix, wherein the parity check vector is selected from the ordered non-zero parity check vectors remaining in the set.

Abstract: A method and apparatus for memory allocation for turbo decoder input with a long turbo codeword, the method comprising computing a bit level log likelihood ratio (LLR) of a demodulated signal over a superframe to generate at least one systematic bit LLR and at least one parity bit LLR; storing the at least one systematic bit LLR and the at least one parity bit LLR over the superframe in a decoder memory; and reading the systematic bit LLR and the parity bit LLR over the superframe to decode at least one codeword from the decoder memory.