# The eq 33 denominator normalizes j over l and m

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: has been shown, [?], that λj (l,m) (m) 15 = αj (l,m) m βj . (32) This suggests the following algorithm: ∗ Forward pass: For each j = 1, 2, · · · , N , compute the forward state probabilities (i,m′ ) M 1 l ′ (l,m) m′ =1 i=0 γ (rj , m , m) αj −1 (33) αj = (i,m′ ) M 1 M 1 l ′ m=1 l=0 m′ =1 i=0 γ (rj , m , m) αj −1 where for each j , m′ denotes the state index for stage j − 1 and m denotes the index for stage j . The γ (rj , m , m) = l ′ 0 (m) (m′ ) 1 P (rj /Sj , Sj −1 ) 2 Sj −1 , Sj f easible otherwise (m′ ) (m) (34) (l,m) are state transition probabilities1 . The Eq (33) denominator normalizes αj over l and m. ∗ Backward pass: For each j = N, N − 1, · · · , 1, compute the backward data probabilities (m) βj = M m=1 M 1 m′ =1 i=0 1 M l=0 m′ =1 γ l (rj +1 , m, m′ ) βj +1 1 i=0 (m′ ) (i,m′ ) γ l (rj +1, m′ , m) αj , (36) and the state probabilities λj (l,m) = αj (l,m) m βj . (37) Eqs(33 - 37) constitute the BCJR algorithm, where as stated earlier λj (m) (l) (l,m) = P (Sj /...
View Full Document

## This document was uploaded on 10/12/2009.

Ask a homework question - tutors are online