# To see why only one path per state needs be kept

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Unformatted text preview: o compute. Additionally, there are still M n path costs that would need to be computed and stored. In general, for large M and n branch and path cost computation and storage is not feasible (e.g. for M = 8 and just n = 10, there would be over 1 × 109 paths). The Viterbi algorithm keeps only p · M L−1 paths at each stage, one for each state. ˆ To see why only one path per state needs be kept, consider two paths into a state S m at stage n. As these paths are extended to future stages, they transverse the same branches, and thus incur the same incremental costs. So the path into state S m at stage n with the lower cost will continue to have lower costs as it extends into the future. The path into state S m at stage n with higher cost can not possibly become the lowest-cost path in the future. Therefore it can be pruned (i.e. discarded) without loss of optimality at stage n. Thus the number of paths and corresponding computational cost remains constant through time. The steps to go from stage n to n + 1 are: 1. compute all branch costs from stage n to n1 ; 2. extend each of the...
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## This document was uploaded on 10/12/2009.

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