By Topic

Two-Dimensional Maximum-Likelihood Sequence Detection Is NP Hard

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Ordentlich, E. ; Hewlett-Packard Labs., Palo Alto, CA, USA ; Roth, R.M.

A 2-D version of the classical maximum-likelihood sequence detection (MLSD) problem is considered for a binary antipodal signal that is corrupted by linear intersymbol interference (ISI) and then passed through a memoryless channel. For 1-D signals and fixed ISI, this detection problem is well-known to be solved using the Viterbi algorithm in time complexity that is linear in the sequence length. It is shown here that, in contrast, the 2-D MLSD problem is NP hard. Specifically, a decision formulation of the problem is shown to be NP complete for a particular 2-D ISI cascaded with either of two memoryless channels: one involving errors and erasures and the other corresponding to additive white Gaussian noise. The proof for the latter case is obtained through a reduction from a still NP complete restricted version of the former. These results are applied to proving the NP completeness of multi user detection under a Toeplitz constraint-a problem known to be equivalent to a variant of 1-D MLSD with growing ISI. This proves a conjecture posed by Verdú in 1989.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 12 )