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Sequence error probability lower bounds for joint detection and estimation

A commonly used lower bound on the probability of error of joint detection and estimation (JDE) algorithms is derived under the assumption that estimation is performed using the transmitted sequence, in a genie-aided fashion. Although it seems reasonable that this genie-aided receiver performs better than the original receiver, a proof of this fact is not available in the literature. In this letter, the validity of this bound is established for a general class of JDE algorithms, as well as for an important special case when the maximum-likelihood sequence detection criterion is used. The results are then extended to a well-known suboptimal JDE algorithm, namely, the T-algorithm. It is shown, however, that the technique used to prove this bound is not sufficient for establishing the validity of the bound for the M-algorithm and the per-survivor processing algorithm.