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Efficient Algorithms for Look-Ahead Sigma-Delta Modulators

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Trellis Noise-Shaping Sigma-Delta modulators look forward at k samples of the signal before deciding to output a 'one' or a 'zero'. The Viterbi algorithm is then used to search the trellis of the exponential number of possibilities that such a procedure generates. Means of making the search more computationally efficient have been proposed. This paper describes alternative tree based algorithms that can also be used search the exponential number possibilities generated by lookahead noise-shaping S-D modulators. Tree based algorithms are simpler to implement because they do not require backtracking through an array of scores to determine the correct output value. They can also be made more efficient via the use of the 'Fano' or 'Stack' algorithms, which are described.

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