A system is provided to receive, by a controller, a first request to read a first page of data stored in a storage device which comprises a plurality of non-volatile memory units. The system accumulates, by a calculation module, a syndrome associated with the first page of data to obtain a syndrome weight. In response to determining that the syndrome weight is less than a predetermined threshold, the system writes, by the controller, the first page of data to a destination page of the storage device. In response to determining that the syndrome weight is greater than the predetermined threshold and that a current number of retries is less than a predetermined number: the system executes a retry process between the calculation module and a data flip engine of the controller to update the syndrome weight; and the system increments the current number of retries.

A method and device for energy-efficient decoders. The decoder device can include a plurality of decoder modules configured to process an input data signal having a plurality of forward error correction (FEC) codewords. This plurality of decoder modules can include at least a first decoder followed by a second decoder. The first decoder can be low-power to first eliminate most of the errors of the codewords and the second decoder can be high-performance to correct the remaining errors. Alternatively, the first decoder can be high-performance to correct the codewords until the low-power decoder can correct the remaining errors. A classifier module can be included to determine portions of the codewords to be directed to any one of the plurality of decoder modules. These implementations can be extended to use additional decoders with different decoding algorithms and optimized to maximize decoder performance given a maximum power constraint.

An operation method of a receiving node may include performing a decoding operation for calculating first and second output transform values corresponding to first and second unit output nodes in each of a plurality of operation units constituting the polar decoder, based on first and second input transform values corresponding to first and second unit input nodes, and the decoding operation may include setting initial values of first and second variables for calculating the first output transform value; performing an iterative loop operation for updating the first and second variables; and calculating the first output transform value based on values of the first and second variables updated until a time when the iterative loop operation is terminated, wherein the iterative loop operation is terminated without performing iterations in which the first and second variables are determined not to be updated among a plurality of iterations.

A processing device in a memory system reads a sense word from a memory device and executes a plurality of parity check equations on corresponding subsets of the sense word to determine a plurality of parity check equation results. The processing device determines a syndrome for the sense word using the plurality of parity check equation results, determines whether the syndrome for the sense word satisfies a codeword criterion, and responsive to the syndrome for the sense word not satisfying the codeword criterion, performs an iterative low density parity check (LDPC) correction process, wherein at least one criterion of the iterative LDPC correction process is adjusted after a threshold number of iterations is performed.

Devices, systems, and methods for detecting and mitigating oscillations in a bit-flipping decoder associated with a non-volatile memory are described. An example method includes receiving a noisy codeword based on a transmitted codeword generated from a low-density parity-check code, performing a first plurality of decoding iterations on the noisy codeword, which comprises performing a message passing algorithm in a first order, computing, based on a completion of the first plurality of decoding iterations, a plurality of checksum values and a plurality of bit flip counts corresponding to the first plurality of decoding iterations, determining that the plurality of checksum values and the plurality of bit flip counts are periodic with a period less than a predetermined threshold, and performing a subsequent decoding iteration on the noisy codeword, the subsequent decoding iteration comprising performing the message passing algorithm in a second order different from the first order.

A method employed in a low-density parity-check code decoder includes: receiving a specific data portion of a first codeword; calculating a flipping function value of the specific data portion of the first codeword according to the specific data portion by using checking equations of a parity check matrix to calculate checking values of the specific data portion; and determining whether to flip the specific data portion of the first codeword by comparing the flipping function value with a flipping threshold which has been calculated based on a plurality of flipping function values of a plurality of previous data portions earlier than the specific data portion.

A decoder that is a decoding apparatus includes an error-correction decoder that executes error correction decoding processing of iteratively performing decoding processing with a window size and the number of decoding iterations indicated by decoding parameters, on received data converted into a spatially coupled low-density parity-check code, and a decoding parameter control unit that updates the decoding parameters on the basis of a decoding result obtained by the iteratively executed decoding processing.

A hardware efficient implementation of a threshold modified attenuated min-sum algorithm (TAMSA”) and a threshold modified offset min-sum algorithm (“TOMSA”) that improve the performance of a low density parity-check (“LDPC”) decoder by reducing the bit error rate (“BER”) compared to the conventional attenuated min-sum algorithm (“AMSA”), offset min-sum algorithm (“OMSA”), and the min-sum algorithm (“MSA”). Embodiments of the present invention preferably use circuit optimization techniques, including a parallel computing structure and lookup tables, and a field-programmable gate array (“FPGA”) or application specific integrated circuit (“ASIC”) implementation.

A method of optimizing an iterative process defines a set of trainable parameters and a differentiable gating function to be applied to each parameter in the set of trainable parameters. A trainable model of the iterative process is built, wherein the iterative process is modified by using the value of the differentiable gating function applied to the parameters to compute a weighted sum of internal variables of the iterative process before and after each iteration. A machine learning-based optimization of the trainable model of the iterative process determines a subset of iterations of the iterative process to perform. The subset of iterations is determined such that an accuracy and a number of active iterations of the iterative process are jointly optimized. The method processes only the subset of the iterations to perform the iterative process. The method is applied to optimize the layered belief propagation algorithm for LDPC decoding.

In some embodiments, a bandwidth constrained equalized transport (BCET) communication system comprises a transmitter that transmits a signal, a communication channel that transports the signal, and a receiver that receives the signal. The transmitter can comprise a pulse-shaping filter that intentionally introduces memory into the signal, and an error control code encoder that is a low-density parity-check (LDPC) error control code encoder. The error control encoder comprises code that is optimized based on the intentionally introduced memory into the signal, a code rate, a signal-to-noise ratio, and an equalizer structure in the receiver. In some embodiments, the communication system is bandwidth constrained, and the transmitted signal comprises an information rate that is higher than for an equivalent system without intentional introduction of the memory at the transmitter.