Relaxation Dynamics of Decoding Processes of Sourlas Code
Tomoko Ozeki, Masato Okada · Progress of Theoretical Physics Supplement · 2005
We have investigated the relaxation dynamics of decoding processes of Sourlas code through a dynamical replica approach proposed by Coolen and Sherrington (1994). Dynamical replica approach describes the dynamics in terms of some macrovariables. In equilibrium, the performance measure, or the overlap between the original and the decoded messages, depends on the decoding temperature and takes a maximum value at the Nishimori temperature. We are also interested in the dynamical behavior of the overlap during the decoding processes and its dependency on the decoding temperature. At the finite temperature, the estimate of each bit is given by the average of each bit over the Boltzmann distribution and in the dynamics it must be averaged over the solution of the master equations. Instead of directly calculating the time-dependent average, we have used a real replica approach to avoid the difficulty to solve the master equation.