5 kevin buckley 2007 6 242 the viterbi algorithm

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Unformatted text preview: iterbi algorithm for MLSE, this development of HMM’s in not required since Eq (16) does not require the S n be a Markov chain. However, the HMM assumption is necessary for the development of other digital communications algorithms, including the forward/backward symbol-by-symbol MAP algorithm described later in Subsection 2.5. Kevin Buckley - 2007 6 2.4.2 The Viterbi Algorithm Applied to Digital Comm. Problems The trellis representation, by itself, does not save us computation. It is simply a representation of the possible symbol sequences and their MLSE costs. The number of possible paths through the trellis is equal to the number of possible symbol sequences, and this grows exponentially with time. Into stage n of the trellis there are M n paths corresponding to M n possible symbol sequences at symbol time n. Concerning branches and states, with CPM (for example) there are p · M L−1 states per stage, so there are as many as (ˆ · M L−1 )2 branches and ˆ p corresponding costs t...
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