
Click here for full text:
On the Computational Complexity of 2D Maximum Likelihood Sequence Detection
Ordentlich, Erik; Roth, Ron M.
HPL200669
Keyword(s): twodimensional; maximumlikelihood; sequence detection; intersymbol interference; multiuser detection; Viterbi algorithm; NP completeness
Abstract: We consider a twodimensional version of the classical maximumlikelihood sequence detection problem for a binary antipodal signal that is corrupted by linear intersymbol interference (ISI) and then passed through a memoryless channel. For onedimensional signals and fixed ISI, this detection problem is wellknown to be efficiently solved using the Viterbi algorithm. We show that the twodimensional version is, in general, intractable, in the sense that a decision formulation of the problem is NP complete for a certain fixed two dimensional ISI and memoryless channel with errors and erasures. We also extend the result to the additive white Gaussian noise channel and the same fixed ISI as in the previous case. Finally, we show how our proof of NP completeness for the twodimensional case can also be used to prove the NP completeness of multiuser detection under a Toeplitz constraint, shown in [4] to be equivalent to a variant of onedimensional maximum likelihood sequence detection when the ISI is not fixed, thereby proving Conjecture 1 in [4]. Notes: Presented in part at the ITA Workshop, 8 February 2006, San Diego, CA, USA
14 Pages
Back to Index
