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The performance of Maximum a posteriori (MAP) estimation is studiedanalytically for binary symmetric multi-channel Hidden Markov processes. Wereduce the estimation problem to a 1D Ising spin model and define orderparameters that correspond to different characteristics of the MAP-estimatedsequence. The solution to the MAP estimation problem has different operationalregimes separated by first order phase transitions. The transition points for$L$-channel system with identical noise levels, are uniquely determined by $L$being odd or even, irrespective of the actual number of channels. Wedemonstrate that for lower noise intensities, the number of solutions isuniquely determined for odd $L$, whereas for even $L$ there are exponentiallymany solutions. We also develop a semi analytical approach to calculate theestimation error without resorting to brute force simulations. Finally, weexamine the tradeoff between a system with single low-noise channel and onewith multiple noisy channels.

Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models