In this paper, the mean field (MF) and mixed mean field (MMF) algorithms for decoding low-density parity-check (LDPC) codes are considered. The MF principle is well established in statistical physics and artificial intelligence. Instead of using a single completely factorized approximated distribution as in the MF approach, the mixed MF algorithm forms a weighted average of several MF distributions as an approximation of the true posterior probability distribution. The MF decoding algorithm for linear block codes is derived and shown to be an approximation of the a posteriori probability (APP) decoding algorithm. The MF approach is then developed in the context of iterative decoding and presented as an approximation of the popular belief propagation decoding method. These results are extended to iterative decoding with the MMF algorithm. Simulation results show that the MF and MMF decoding algorithms yield a good performance-complexity tradeoff, especially when employed for decoding LDPC codes based on finite geometries.
This thesis presents progress on a path to Rubidium-85 Feshbach molecules that could be used for magnetometery and other experiments. An apparatus including a magneto-optical trap, magnetic trap, and dual laser dipole trap has been modified for studies of the 155 G Feshbach resonance and associated production of ultracold Rubidium-85 molecules. Modifications include changes in the optical pumping technique to spin-polarize Rubidium-85 atoms in the F=2, mF =-2 hyperfine state. In addition, we constructed a dual 6.8 GHz and 3.0 GHz source and a 3 GHz microwave amplifier to evaporatively cool Rubidium-87 and Rubidium-85 and allow for more control of the atomic spin. These modifications and techniques will aid in manipulating the atomic spins in future experiments. As an example, we perform microwave spectroscopy on Rubidium-85 atoms from which we infer a residual magnetic field in the MOT cell of 170 +/- 5 mG. We also found the |F=2, mF = 0> to |F=3, mF = 0> transition to have a Rabi Frequency of 8.9 +/- 0.5 kHz, the |F=2, mF = 0> to |F=3, mF = -1> transition to have a Rabi frequency of 10.1 +/- 0.5 kHz, and the |F=2, mF = 0> to |F=3, mF = +1> transition to have a Rabi frequency of 11.0 +/- 0.5 kHz.