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The authors address the design of low-complexity algorithms for soft-output detection over channels impaired by intersymbol interference. Unlike most works with similar aims, which assume the presence of the whitened matched filter at the receiver (Forney approach), algorithms that can directly work on the matched filter output (Ungerboeck approach) are considered. They introduce a novel (cyclic) factor graph describing the channel and, by applying the sum-product algorithm to it, they derive soft-output detection schemes that can provide impressive complexity reductions with respect to the benchmark algorithms, since their complexity is linear, instead of exponential, in the channel memory.
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