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Unformatted text preview: r1,N ) (m) (38) for Sj ∈ Sj . So the bit probabilities, required to determine the symbol-bysymbol MAP bit estimates, are P (xj /r1,N ) =
(l) Sj (l) λj (l,m) , l = 0, 1 ; j = 1, 2 , · · · N . (39) These “gamma” terms are likelihoods (i.e. data PDFs, conditioned on the states and therefore codeword values, with data plugged in). For Gaussian noise, they are exponential functions of the data and the information bits represented by the two states being transitioned. Note that, since these state transition probabilities are conditioned on the states, they are not eﬀected by prior distributions on the information bits the states represent. In an alternative derivation of the BCJR algorithm, presented in Lin and Costello [?] Section 12.6, the “alpha”, “beta” and “gamma” functions are deﬁned slightly diﬀerently, such that priors on the information bits are incorporated into the gammas. In particular, therein γ l (rj , m′ , m) ≡ P (Sj
(m) 1 , rj /Sj −1 ) = P (Sj (m′ ) (m) /Sj −1 ) P (rj /Sj
(m) (m′ ) (m′ ) (m) , Sj...
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This document was uploaded on 10/12/2009.
- Spring '09