Systems and methods are disclosed for decoding data. A first block of data may be obtained from a storage medium or received from a computing device. The first block of data includes a first codeword generated based on an error correction code. A first set of likelihood values is obtained from a neural network. The first set of likelihood values indicates probabilities that the first codeword will be decoded into one of a plurality of decoded values. A second set of likelihood values is obtained from a decoder based on the first block of data. The second set of likelihood values indicates probabilities that the first codeword will be decoded into one of the plurality of decoded values. The first codeword is decoded to obtain a decoded value based on the first set of likelihood values and the second set of likelihood values.

An encoding circuit includes: a polar encoding unit capable of encoding a polar code of N bits; a frozen bit adding unit that generates a first sequence by adding frozen bits to an input signal; and a bit arrangement changing unit that: generates a second sequence of N bits by arranging the first sequence in the second sequence according to an arrangement rule dependent on a ratio of N.sub.t bits, being a code length of a polar code to be encoded and being N bits or less, and N bits, and setting bit values at bit positions other than positions where the first sequence is arranged in the second sequence to zero when N.sub.t bits are less than N bits; and inputs the second sequence to the polar encoding unit. A code word of N.sub.t bits is generated by thinning processing based on a result of encoding the second sequence.

Apparatuses and methods relating generally to a decoder. In an apparatus, a control circuit receives first-third sign signals, a partial sum signal, a function select signal, and a carry signal as an input vector to provide an output sign and a vector select. A select generation circuit receives the first and second sign signals and the partial sum signal to provide an add/subtract select signal. A subtractor subtracts from a first absolute value signal a second absolute value signal to provide the third sign signal and a difference signal. Responsive to the add/subtract select signal, an adder/subtractor either adds or subtracts the first absolute value signal to or from the second absolute value signal to provide the carry signal and a sum/difference signal. A multiplexer selects from the first and second absolute value signals, the difference signal, and the sum/difference signal a selected value signal responsive to the vector select.

There is described a method for communicating data, the method comprising: receiving an incomplete data stream, wherein the incomplete data stream comprises a plurality of sequences of data points having respective values and a plurality of sequences of missing data points; receiving a missing data model; determining values for each of the plurality of sequences of missing data points, comprising: selecting a sequence of missing data points that has not previously been processed, wherein the sequence of missing data points to be processed is selected as a smallest sequence of missing data points of the plurality of sequences of missing data points that have not previously been processed; processing the incomplete data stream to determine values for the selected sequence of missing data points based upon the missing data model; updating the incomplete data stream to include the determined values for the selected sequence of missing data points; and wherein values for subsequent sequences of missing data points are generated based upon the updated data stream; and outputting a corrected data stream comprising the determined values for each of the plurality of sequences of missing data points.

An encoder signal processing device detects position data at every predetermined time interval from an original signal which is an analog amount generated in an encoder according to movement of a measurement target. The encoder signal processing device includes: an approximate curve calculation unit that calculates an approximate curve of a detection error included in the original signal on the basis of the detection error of the position data at at least three or more points; an approximate error computation unit that computes an approximate value of the detection error of the position data at an arbitrary time point on the basis of the approximate curve of the detection error; and a position data correction unit that corrects the detection error of the position data at the arbitrary time point on the basis of the approximate value of the detection error of the position data.

Provided is a quantum error correction code generating method using a graph state. According to the exemplary embodiment of the present invention, a quantum error correction code generating method using a graph state: includes: generating a graph state representing an adjacency relationship between a plurality of qubits including at least one entangled qubit (ebit); generating a first stabilizer generator which corresponds to the graph state and is configured by a plurality of stabilizers for detecting errors of the plurality of qubits; and generating at least one logical Z operator used for a phase flip operation of a codeword, at least one logical X operator used for a bit flip operation of a codeword, and a second stabilizer generator which is a sub set of the first stabilizer generator, based on the first stabilizer generator and the at least one entangled qubit.

A systematic polar encoder with data checks includes a data mapper receiving input data containing information to be polar coded for transmission and generating modified data, and a nonsystematic polar encoder implementing a transform matrix encoding the modified data to produce a codeword x such that, for some sub-sequence of coordinates S, x.sub.S=d. For nonsystematic encoding, a transform input u includes first and second parts for words independent of the data, the second part for an inverse puncture word, a third part carrying the modified data, and a non-null part carrying a check word derived from the modified data. A transform output includes a punctured part for a puncture word, a part carrying the data, and a part serving as redundant symbols, with the codeword x related to the transform output by x=z.sub.Q where Q is the complement of the punctured part P.

Decoding logic is provided that is operational upon a data buffer to represent a plurality of variable nodes and a plurality of check nodes. For a respective one of the variable nodes, a vector component is selected from a confidence vector associated with the variable node. Using a respective one of the check nodes, a check node return value is calculated based on one or more other vector components from one or more other vectors and one or more vector indices corresponding to the one or more other vector components. The confidence vector is then updated based on the check node return value and an index for the check node return value, and a current state of a memory cell associated with the respective one of the variable nodes is determined based on a location of a primary one of multiple vector components within the updated confidence vector.

Systems and methods for error correction in structured light are disclosed. In one aspect, a method includes receiving, via a receiver sensor, a structured light image of at least a portion of a composite code mask encoding a plurality of codewords, the image including an invalid codeword. The method further includes detecting the invalid codeword. The method further includes generating a plurality of candidate codewords based on the invalid codeword. The method further includes selecting one of the plurality of candidate codewords to replace the invalid codeword. The method further includes generating a depth map for an image of the scene based on the selected candidate codeword. The method further includes generating a digital representation of a scene based on the depth map. The method further includes outputting the digital representation of the scene to an output device.

An encoder signal processing device detects position data at every predetermined time interval from an original signal which is an analog amount generated in an encoder according to movement of a measurement target. The encoder signal processing device includes: an approximate curve calculation unit that calculates an approximate curve of a detection error included in the original signal on the basis of the detection error of the position data at at least three or more points; an approximate error computation unit that computes an approximate value of the detection error of the position data at an arbitrary time point on the basis of the approximate curve of the detection error; and a position data correction unit that corrects the detection error of the position data at the arbitrary time point on the basis of the approximate value of the detection error of the position data.