Abstract: A method and device determines an optimization solution for an optimization problem. The method includes receiving the optimization problem having cost functions and variables in which each of the cost functions has a predetermined relationship with select ones of the variables. The variables comprise a sub-solution of a spline indicative of a curved path along an estimated trajectory. The method includes generating a first message for each of the cost functions for each corresponding variable based upon the relationship and a second message for each of the variables for each corresponding cost function based upon the relationship. The method includes generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs. The method includes forming a consensus between the first and second messages until the optimization solution is determined.

Abstract: A method and device determines an optimization solution for an optimization problem. The method includes receiving the optimization problem having cost functions and variables in which each of the cost functions has a predetermined relationship with select ones of the variables. The method includes generating a first message for each of the cost functions for each corresponding variable based upon the respective predetermined relationship and a second message for each of the variables for each corresponding cost function based upon the respective predetermined relationship. The method includes generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs. The method includes repeating steps (b), (c), and (d) until a consensus is formed between the first and second messages until the optimization solution is determined based upon the consensus.

Abstract: A method and device determines an optimization solution for an optimization problem. The method includes receiving the optimization problem having cost functions and variables in which each of the cost functions has a predetermined relationship with select ones of the variables. The variables comprise a sub-solution of a spline indicative of a curved path along an estimated trajectory. The method includes generating a first message for each of the cost functions for each corresponding variable based upon the relationship and a second message for each of the variables for each corresponding cost function based upon the relationship. The method includes generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs. The method includes forming a consensus between the first and second messages until the optimization solution is determined.

Abstract: There is provided a system and method for training and utilizing a boundary graph machine learning algorithm. The system including a processor configured to receive a plurality of entry nodes, each of the plurality of entry nodes including an entry node input and an entry node output, add each of the plurality of entry nodes to a graph using the entry node input and the entry node output, receiving a plurality of training nodes, each of the plurality of training nodes including a training node input and a training node output, add each of the plurality of training nodes to the graph when the training node input for each of the plurality of training nodes is similar to the training node output of a closest node and the training node output of each of the plurality of training nodes is different than the training node output of the closest node.

Abstract: There is provided a system and method for training and utilizing a boundary graph machine learning algorithm. The system including a processor configured to receive a plurality of entry nodes, each of the plurality of entry nodes including an entry node input and an entry node output, add each of the plurality of entry nodes to a graph using the entry node input and the entry node output, receiving a plurality of training nodes, each of the plurality of training nodes including a training node input and a training node output, add each of the plurality of training nodes to the graph when the training node input for each of the plurality of training nodes is similar to the training node output of a closest node and the training node output of each of the plurality of training nodes is different than the training node output of the closest node.

Abstract: A method and device determines an optimization solution for an optimization problem. The method includes receiving the optimization problem having cost functions and variables in which each of the cost functions has a predetermined relationship with select ones of the variables. The method includes generating a first message for each of the cost functions for each corresponding variable based upon the respective predetermined relationship and a second message for each of the variables for each corresponding cost function based upon the respective predetermined relationship. The method includes generating a disagreement variable for each corresponding pair of variables and cost functions measuring a disagreement value between the first and second beliefs. The method includes repeating steps (b), (c), and (d) until a consensus is formed between the first and second messages until the optimization solution is determined based upon the consensus.

Abstract: A system and a method for determining a quasi-cyclic (QC) low-density parity-check (LDPC) code, such that the QC LDPC code has no trapping sets are disclosed. A set of matrices representing a family of QC LDPC codes are acquired, wherein each QC LDPC code is a tail-biting spatially-coupled code of girth not less than eight, and wherein each column of each matrix in the set has a weight not less than four. Based on a trapping set pattern, a matrix from the set of matrices is selected such that the matrix represents the QC LDPC code with no trapping sets. The matrix can be stored into a memory.

Abstract: A method estimates parameters of 3-phase voltage signals to synchronize a power grid in a presence of a voltage unbalance by transforming the 3-phase voltage signals to ??-reference signals using a Clarke transformation matrix, and estimating sinusoidal signals and corresponding quadrature signals of the ??-reference signals using an extended Kalman filter, and determining a phase angle of a positive sequence based on a relationship of the phase angle to the estimated the sinusoidal signals.

Abstract: A system and a method determine a quasi-cyclic (QC) low-density parity-check (LDPC) code corresponding to a protograph and having a predetermined girth. At least several elements of the connectivity matrix representing the protograph are duplicated along at least one line of duplication to produce an inflated connectivity matrix, wherein values of at least several elements in the connectivity matrix form a pattern indicated by the predetermined girth. A hierarchical quasi-cyclic (HQC) LDPC code corresponding to the inflated connectivity matrix is determined and at least several elements of a matrix representing the HQC LDPC code are removed, such that the matrix is squashed along the line of duplication to produce the QC LDPC code.

Abstract: A system and a method for determining a quasi-cyclic (QC) low-density parity-check (LDPC) code, such that the QC LDPC code has no trapping sets are disclosed. A set of matrices representing a family of QC LDPC codes are acquired, wherein each QC LDPC code is a tail-biting spatially-coupled code of girth not less than eight, and wherein each column of each matrix in the set has a weight not less than four. Based on a trapping set pattern, a matrix from the set of matrices is selected such that the matrix represents the QC LDPC code with no trapping sets. The matrix can be stored into a memory.

Abstract: A code to be decoded by message-passing is represented by a factor graph. The factor graph includes variable nodes indexed by i and constraint nodes indexed by a connected by edges for transferring messages mi?a outgoing from the variable nodes to the constraint nodes and messages ma?i incoming from the constraint nodes to the variable nodes. The messages mi?a are initialized based on beliefs bi of a received codeword. The messages ma?i are generated by overshooting the messages mi?a at the constraint nodes. The beliefs bi are updated at the variable nodes using the messages ma?i. The codeword is outputted if found, otherwise, the messages mi?a are updated using a correction for the overshooting.

Abstract: A method converts an input image of noisy wrapped phases to an output image of absolute unwrapped phases. The noisy wrapped phases in the input image are represented as a set of re-wrapped phases and a set of phase shifts. The set of re-wrapped phases are partitioned into a first group and a second group. Integer differences between the phase shifts are optimized while holding the re-wrapped phases fixed. Then, the first group of re-wrapped phases are optimized, while holding the integer differences between the phase shifts, and the second group of re-wrapped phases fixed. The integer differences between the phase shifts are optimized again, while holding the re-wrapped phases fixed. Then, the second group of re-wrapped phases are optimized, while holding the integer differences between the phase shifts, and the first group of re-wrapped phases fixed. The optimizing steps are repeated until the re-wrapped phase converge.

Abstract: A method converts an input image of noisy wrapped phases to an output image of absolute unwrapped phases. The noisy wrapped phases in the input image are represented as a set of re-wrapped phases and a set of phase shifts. The set of re-wrapped phases are partitioned into a first group and a second group. Integer differences between the phase shifts are optimized while holding the re-wrapped phases fixed. Then, the first group of re-wrapped phases are optimized, while holding the integer differences between the phase shifts, and the second group of re-wrapped phases fixed. The integer differences between the phase shifts are optimized again, while holding the re-wrapped phases fixed. Then, the second group of re-wrapped phases are optimized, while holding the integer differences between the phase shifts, and the first group of re-wrapped phases fixed. The optimizing steps are repeated until the re-wrapped phase converge.

Abstract: A system and method for communicating information in a wireless cooperative relay network of nodes, the nodes including a source, a set of relays, and a destination. The source broadcasts a code word encoded as a data stream using a rateless code. The relays receive the data stream, decode the data stream to recover the code word, and reencode and transmit the recovered code word as the data stream with the rateless code. The destination receives and decodes the reencoded data streams to recover the code word.

Abstract: Biometric parameters acquired from human forces, voices, fingerprints, and irises are used for user authentication and access control. Because the biometric parameters are continuous and vary from one reading to the next, syndrome codes are applied to determine biometric syndrome vectors. The biometric syndrome vectors can be stored securely while tolerating an inherent variability of biometric data. The stored biometric syndrome vector is decoded during user authentication using biometric parameters acquired at that time. The syndrome codes can also be used to encrypt and decrypt data.

Abstract: A method generates a combined-replica group-shuffled iterative decoder, comprising. First. an error-correcting code and an iterative decoder for an error-correcting code is received by the method. Multiple group-shuffled sub-decoders for the error-correcting code are constructed, based on the iterative decoder. Then, the multiple group-shuffled sub-decoders are combined into a combined-replica group-shuffled iterative decoder.

Abstract: First biometric parameters are acquired from a user. Input data are encrypted according to the biometric parameters to produce ciphertext. The biometric parameters are encoded using a syndrome encoder to produce a syndrome code. The ciphertext and the syndrome code are associated with each other and stored in a computer readable media so that only the same user can subsequently decrypt the cipher text.

Abstract: A method encodes a sequence of blocks of input bits to be transmitted over a wireless channel. Each block of input bits is converted to a codeword, and each codeword is mapped to multiple sub-blocks of complex numbers. Each sub-block is multiplied by a disambiguating spreading transform to obtain a sub-block of transformed symbols, which can be modulated and transmitted to a receiver, where each received block is demodulated to a block of complex numbers, which are partitioned into sub-blocks. The sub-block of complex numbers are converted to a set of likelihood ratios that correspond to decoded codewords. The input bits can be decoded unambiguously even if only one of the blocks of symbols corresponding to the block of input bits is received correctly.

Abstract: A method represents a correlated set of images. The correlation can be spatial or temporal. A lossy operation is applied to each image in the correlated set to generate a coarse image. The coarse image is encoded losslessly to yield an encoded coarse image. Each image is also represented by syndrome bits. The combination of the encoded coarse images and the syndrome bits represent the correlated set of images.

Abstract: A method compresses a set of correlated signals by first converting each signal to a sequence of integers, which are further organized as a set of bit-planes. This can be done by signal transformation and quantization. An inverse accumulator is applied to each bit-plane to produce a bit-plane of shifted bits, which are permuted according to a predetermined permutation to produce bit-planes of permuted bits. Each bit-plane of permuted bits is partitioned into a set of blocks of bits. Syndrome bits are generated for each block of bits according to a rate-adaptive base code. Subsequently, the syndrome bits can be decompressed in a decoder to recover the original correlated signals. For each bit-plane of the corresponding signal, a bit probability estimate is generated. Then, the bit-plane is reconstructed using the syndrome bits and the bit probability estimate.