Research Articleshttps://hdl.handle.net/10539/213432019-03-20T12:08:21Z2019-03-20T12:08:21ZAnalysis of Bounded Distance Decoding for Reed Solomon Codes.Babalola, O.P.Versfeld, D.J.J.https://hdl.handle.net/10539/254702018-08-24T06:07:55Z2018-09-01T00:00:00ZAnalysis of Bounded Distance Decoding for Reed Solomon Codes.
Babalola, O.P.; Versfeld, D.J.J.
Bounded distance decoding of Reed-Solomon codes involves finding a unique codeword if there is at least one codeword within the given distance. A corrupted message having errors that is less than or equal to half the minimum distance corresponds to a unique codeword and therefore, the probability of decoding error is one for a minimum distance decoder. However, increasing the decoding radius to be slightly higher than half of the minimum distance may result in multiple codewords within the Hamming sphere. In this study, we computed the probability of having unique codewords for (7, k) RS codes when the decoding radius is increased from the error correcting capability t to t+1. Simulation results show a significant effect of the code rates on the probability of having unique codewords. It also shows that the probability of having unique codeword for low rate codes is close to one.
2018-09-01T00:00:00ZThermal excitation of gadolinium-based contrast agents using spin resonance.Dinger, S.C.Fridjhon, P.Rubin, D.M.https://hdl.handle.net/10539/213202016-10-31T14:27:02Z2016-06-01T00:00:00ZThermal excitation of gadolinium-based contrast agents using spin resonance.
Dinger, S.C.; Fridjhon, P.; Rubin, D.M.
Theoretical and experimental investigations into the thermal excitation of liquid paramagnetic contrast agents using the spin resonance relaxation mechanism are presented. The electronic spin-lattice relaxation time ole of gadolinium-based contrast agents, which is estimated at 0.1 ns, is ten orders of magnitude faster than the relaxation time of protons in water. The shorter relaxation time is found to significantly increase the rate of thermal energy deposition. To the authors knowledge this is the first study of gadolinium based contrast agents in a liquid state used as thermal agents. Analysis shows that when ô1e and other experimental parameters are optimally selected, a maximum theoretical heating rate of 29.4 °C.s.1 could be achieved which would suffice for clinical thermal ablation of neoplasms. The experimental results show a statistically significant thermal response for two out of the four contrast agents tested. The results are compared to the simulated estimates via analysis of a detailed model of the system. While these experimentally determined temperature rises are small and thus of no clinical utility, their presence supports the theoretical analysis and strongly suggests that the chemical structure of the selected compounds plays an important role in this mechanism of heat deposition. There exists an opportunity for the development of alternative gadolinium-based compounds with an order of magnitude longer τ1e in a diluted form to be used as an efficient hyperthermia agent for clinical use.
2016-06-01T00:00:00Z