Constrained-complexity equalizer design for fixed delay tree search with decision feedback

Fixed delay tree search with decision feedback (FDTS/DF) is a hybrid detection scheme which incorporates a sequence detector into the decision feedback equalizer (DFE). When applied to minimum-runlength-limited channels, the FDTS/DP provides near-optimal detection performance with a reasonable complexity requirement. It has been shown recently that for the special case of search depth 1 and the channel subject to the d=1 run length constraint, a simpler structure arises for the decision elements of the FDTS/DF, which provides asymptotically-equivalent performance to the originally proposed FDTS/DF structure. We demonstrate the asymptotic optimality of this reduced FDTS/DF based on a simple signal-to-noise ratio argument. We also introduce a design criterion for choosing tap weights for the constrained-complexity FDTS/DF, which assumes the finite impulse response (FIR) structure for its forward and feedback filters. A method to compute optimal tap weights for the forward and feedback filters is then presented for a magnetic recording channel subject to the popular minimum runlength constraint, d=1. Results show that under the d=1 constraint, the FDTS/DF with one-bit decision delay achieves a large performance improvement over the DFE