A modified Gradient Descent Bit Flipping (GDBF) algorithm is proposed for decoding Low Density Parity Check (LDPC) codes on the binary-input additive white Gaussian noise channel. The new algorithm, called Noisy GDBF (NGDBF), introduces a random perturbation into each symbol metric at each iteration. The noise perturbation allows the algorithm to escape from undesirable local maxima, resulting in improved performance. A combination of heuristic improvements to the algorithm are proposed and evaluated. When the proposed heuristics are applied, NGDBF performs better than any previously reported GDBF variant, and comes within 0.5 dB of the belief propagation algorithm for several tested codes. Unlike other previous GDBF algorithms that provide an escape from local maxima, the proposed algorithm uses only local, fully parallelizable operations and does not require computing a global objective function or a sort over symbol metrics, making it highly efficient in comparison. The proposed NGDBF algorithm requires channel state information which must be obtained from a signal to noise ratio (SNR) estimator. Architectural details are presented for implementing the NGDBF algorithm. Complexity analysis and optimizations are also discussed.Comment: 16 pages, 22 figures, 2 table

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This Chapter presents a solution for fault-tolerance in Multi-Valued Logic (MVL) circuits comprised of Carbon Nano-Tube Field Effect Transistors (CNTFET). This chapter reviews basic primitives of MVL and describes ternary implementations of CNTFET circuits. Finally, this chapter describes a method for error correction called Restorative Feedback (RFB). The RFB method is a variant of Triple-Modular Redundancy (TMR) that utilizes the fault masking capabilities of the Muller C element to provide added protection against noisy transient faults. Fault tolerant properties of Muller C element is discussed and error correction capability of RFB method is demonstrated in detail.