Abstract: An error detection/correction system provides an electronic circuit detecting and correcting transmission errors using linear programming. Linear programming techniques are made practical for real-time error correction and decoding by dividing the linear programming problem into independent parallelizable problems so that separate independent portions of the electronic circuit may simultaneously address solutions related to individual bits and/or parity rules.

Abstract: An error detection/correction system provides an electronic circuit detecting and correcting transmission errors using linear programming. Linear programming techniques are made practical for real-time error correction and decoding by dividing the linear programming problem into independent parallelizable problems so that separate independent portions of the electronic circuit may simultaneously address solutions related to individual bits and/or parity rules. Linear programming is believed to avoid error floors inherent in conventional belief propagation error detection and correction techniques providing a decoding system suitable for high reliability applications.

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 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: 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.