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Error Source Models

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

Abstract

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
$$\Pr \left( {b_{l}^{t},{{s}_{t}}|a_{l}^{t},{{s}_{0}}} \right) = \sum\limits_{{{}_{{{{S}_{1}}}}t - 1}} {\prod\limits_{{i = 1}}^{t} {\Pr \left( {{{b}_{i}},{{s}_{i}}|{{a}_{i}}{{s}_{{i - 1}}}} \right)} }$$
(1.1.1)

Keywords

Markov Chain Transition Probability Matrix Interval Distribution Travel Wave Tube Markov Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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