Error Source Models

  • William Turin
Part of the Information Technology: Transmission, Processing and Storage book series (PSTE)


A discrete finite state channel (FSC) model was introduced by Shannon.38According to this model, the channel can be in any state from the state space \(S = \left\{ {{{\alpha }_{1}},{{\alpha }_{2}},...,{{a}_{u}}} \right\}\). Usually, states are enumerated by integers:S={1,2,...,u}. If the channel is in state \( {{S}_{{t - 1}}} \in S\) and the input to the channel is at∈A,the channel outputs symbol bt∈B and transfers to state st∈S with probability \( \Pr \left( {{{b}_{t}},{{s}_{t}}|{{a}_{t}},{{s}_{{t - 1}}}} \right)\). The probability of the final states 0 and receiving a sequence \(b_{1}^{t} = \left( {{{b}_{1}},{{b}_{2}},...,{{b}_{t}}} \right)\) conditional on the initial state s t and transmitted sequence \( a_{1}^{t} = \left( {{{a}_{1}},{{a}_{2}},...,{{a}_{t}}} \right)\) has the form
$$\Pr \left( {b_{l}^{t},{{s}_{t}}|a_{l}^{t},{{s}_{0}}} \right) = \sum\limits_{{{}_{{{{S}_{1}}}}t - 1}} {\prod\limits_{{i = 1}}^{t} {\Pr \left( {{{b}_{i}},{{s}_{i}}|{{a}_{i}}{{s}_{{i - 1}}}} \right)} }$$


Markov Chain Transition Probability Matrix Interval Distribution Travel Wave Tube Markov Function 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • William Turin
    • 1
  1. 1.AT&T Labs—ResearchFlorham ParkNew JerseyUSA

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