# The complexity of the algorithm grows exponentially

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Unformatted text preview: /s ,s , · · · , s(k+D) ) P (s(k+D)) s(k−1) (k −1) (k ) (k −1+D ) p k (s ,s ,···,s (25) ) where pk (s(k) , s(k+1) , · · · , s(k+D) ) is the probability of state {s(k) , s(k+1) , · · · , s(k+D) } at time k . L is the system memory. The Figure 4 illustrates this time-recursive computation in the form of a trellis diagram. 2.5.2 Forward/Backward Symbol-by-Symbol MAP A disadvantage of forward-only symbol-by-symbol MAP is that the estimator of s(k) uses data only up to time k + D . The complexity of the algorithm grows exponentially with the delay parameter D . For example, there are M D states/stage in the trellis diagram. Thus D can not be selected too large. Given a block of data/symbols over time k = 1, 2, · · · , N , with N &gt;&gt; D, performance can be improved (especially for the early symbols) using a block processing symbol-bysymbol MAP algorithm which maximizes P (s(k) = Am /r1 , r2 , · · · , rN ) . (26) Kevin Buckley - 2007 stage k−1 stage k p(r k+D / s P (s =A 1 , .... , s k−1 (k) (k+D) (k+D−L) 13 , ....
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## This document was uploaded on 10/12/2009.

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