The present invention is directed to data communication. More specifically, an embodiment of the present invention provides an error correction system. Input data signals are processed by a feedforward equalization module and a decision feedback back equalization module. Decisions generated by the decision feedback equalization module are processed by an error detection module, which determines error events associated with the decisions. The error detection module implements a reduced state trellis path. There are other embodiments as well.

A double factor correction Turbo decoding method based on a simulated annealing algorithm is provided, including: S1: setting an initial bit error rate P.sub.e0 and an initial solution of correction factors; S2: randomly selecting a new solution of the correction factors from a proximinal subset of a current solution, and calculating a new bit error rate P.sub.enew; S3: determining whether the new bit error rate is smaller than a bit error rate of a previous decoding, and if so, receiving the new solution of the correction factors, otherwise calculating a reception probability based on a difference between the new bit error rate and the bit error rate of the previous decoding; S4: decreasing the initial bit error rate P.sub.e0 to determine whether a termination condition is satisfied, performing S5 if the termination condition is satisfied, otherwise performing S2; and S5: outputting a current solution of the correction factors as an optimal solution.

A double factor correction Turbo decoding method based on a simulated annealing algorithm is provided, including: S1: setting an initial bit error rate P.sub.e0 and an initial solution of correction factors; S2: randomly selecting a new solution of the correction factors from a proximal subset of a current solution, and calculating a new bit error rate P.sub.enew; S3: determining whether the new bit error rate is smaller than a bit error rate of a previous decoding, and if so, receiving the new solution of the correction factors, otherwise calculating a reception probability based on a difference between the new bit error rate and the bit error rate of the previous decoding; S4: decreasing the initial bit error rate P.sub.e0 to determine whether a termination condition is satisfied, performing S5 if the termination condition is satisfied, otherwise performing S2; and S5: outputting a current solution of the correction factors as an optimal solution.

Advanced ultra-low power error correcting codes are generated using soft quantization and lattice interpolation based on clock and Syndrome Weight. Reinforcement learning may be used to generate threshold values for flipping bits for low density parity check Ultra-Low Power error correction codes. The threshold values can be generated offline and downloaded to a storage device or generated while the storage device is in use.

The present invention is directed to data communication. More specifically, an embodiment of the present invention provides an error correction system. Input data signals are processed by a feedforward equalization module and a decision feedback back equalization module. Decisions generated by the decision feedback equalization module are processed by an error detection module, which determines error events associated with the decisions. The error detection module implements a reduced state trellis path. There are other embodiments as well.

The present invention is directed to data communication. More specifically, an embodiment of the present invention provides an error correction system. Input data signals are processed by a feedforward equalization module and a decision feedback back equalization module. Decisions generated by the decision feedback equalization module are processed by an error detection module, which determines error events associated with the decisions. The error detection module implements a reduced state trellis path. There are other embodiments as well.

A communications apparatus to receive a composite signal including a desired signal and interferer signals, where the desired signal may include desired symbols and the interferer signals may include interferer symbols. The system may include N frameworks, each framework may include a detector to partition the desired symbols and the interferer symbols based on an interference severity into a dominant group and a non-dominant group, and to generate A Posteriori Probabilities (APP) of the desired symbols and the interferer symbols. The detector of each of the N frameworks generates the APP based on a feedback of a priori probabilities from each of the N frameworks.

A communications apparatus to receive a composite signal including a desired signal and interferer signals, where the desired signal may include desired symbols and the interferer signals may include interferer symbols. The system may include N frameworks, each framework may include a detector to partition the desired symbols and the interferer symbols based on an interference severity into a dominant group and a non-dominant group, and to generate A Posteriori Probabilities (APP) of the desired symbols and the interferer symbols. The detector of each of the N frameworks generates the APP based on a feedback of a priori probabilities from each of the N frameworks.

A method includes: generating a trellis; generating one or more predicted symbols using a first non-linear model; computing and saving two or more branch metrics using a priori log-likelihood ratio (LLR) information, a channel observation, and the one or more predicted symbols; if alpha forward recursion has not yet completed, generating alpha forward recursion state metrics using a second non-linear model; if beta backward recursion has not yet completed, generating beta backward recursion state metrics using a third non-linear model; if sigma forward recursion has not yet completed, generating sigma forward recursion state metrics using the branch metrics, the alpha state metrics, and the beta backward recursion state metrics; generating extrinsic information comprising a difference of a posteriori LLR information and the a priori LLR information; computing and feeding back the a priori LLR information; and calculating the a posteriori LLR information.

The present invention is directed to data communication. More specifically, an embodiment of the present invention provides an error correction system. Input data signals are processed by a feedforward equalization module and a decision feedback back equalization module. Decisions generated by the decision feedback equalization module are processed by an error detection module, which determines error events associated with the decisions. The error detection module implements a reduced state trellis path. There are other embodiments as well.