Abstract: A method evaluates and optimizes an error-correcting code to be transmitted through a noisy channel and to be decoded by an iterative message-passing decoder. The error-correcting code is represented by a parity check matrix which is modeled as a bipartite graph having variable nodes and check nodes. A set of message passing rules is provided for the decoder. The decoder is analyzed to obtain a set of density evolution rules including operators and operands which are then transformed to projective operators and projected operands to generate a set of projective message passing rules. The projective message passing rules are applied iteratively to the error-correcting code modeled by the bipartite graph until a termination condition is reached. Error rates of selected bits of the error-correcting code are then determined by evaluating the corresponding operands. The error rates can be passed to an optimizer to optimize the error-correcting code.

Abstract: The present invention provides systems and methods for statistically analyzing collected data and providing training for the collection of the data. In one embodiment, the system and method are configured to collect data about a plurality of objects and determine a measure of agreement between the collected data and a benchmark. Based on the measure of agreement reliability and a variance of the collected data are determined relative to the benchmark. In training a plurality of raters are instructed to rate at least one of a plurality of objects such that each rater collects data that rates at least one of the objects. A measure of agreement of the data collected by a rater is determined relative to the benchmark, and reliability and variance of the data collected are determined, which are used to evaluate the rater.

Abstract: The present invention provides systems and methods for statistically analyzing collected data and providing training for the collection of the data. In one embodiment, the system and method are configured to collect data about a plurality of objects and determine a measure of agreement between the collected data and a benchmark. Based on the measure of agreement reliability and a variance of the collected data are determined relative to the benchmark. In training a plurality of raters are instructed to rate at least one of a plurality of objects such that each rater collects data that rates at least one of the objects. A measure of agreement of the data collected by a rater is determined relative to the benchmark, and reliability and variance of the data collected are determined, which are used to evaluate the rater.

Abstract: A method evaluates and optimizes an error-correcting code to be transmitted through a noisy channel and to be decoded by an iterative message-passing decoder. The error-correcting code is represented by a parity check matrix which is modeled as a bipartite graph having variable nodes and check nodes. A set of message passing rules is provided for the decoder. The decoder is analyzed to obtain a set of density evolution rules including operators and operands which are then transformed to projective operators and projected operands to generate a set of projective message passing rules. The projective message passing rules are applied iteratively to the error-correcting code modeled by the bipartite graph until a termination condition is reached. Error rates of selected bits of the error-correcting code are then determined by evaluating the corresponding operands. The error rates can be passed to an optimizer to optimize the error-correcting code.