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On joint detection and decoding of linear block codes on Gaussian vector channels

Vikalo, Haris and Hassibi, Babak (2006) On joint detection and decoding of linear block codes on Gaussian vector channels. IEEE Transactions on Signal Processing, 54 (9). pp. 3330-3342. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:VIKieeetsp06b

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Abstract

Optimal receivers recovering signals transmitted across noisy communication channels employ a maximum-likelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In systems that employ error-correcting coding for data protection, the symbol space forms a sparse lattice, where the sparsity structure is determined by the code. In such systems, ML data recovery may be geometrically interpreted as a search for the closest point in the sparse lattice. In this paper, motivated by the idea of the "sphere decoding" algorithm of Fincke and Pohst, we propose an algorithm that finds the closest point in the sparse lattice to the given vector. This given vector is not arbitrary, but rather is an unknown sparse lattice point that has been perturbed by an additive noise vector whose statistical properties are known. The complexity of the proposed algorithm is thus a random variable. We study its expected value, averaged over the noise and over the lattice. For binary linear block codes, we find the expected complexity in closed form. Simulation results indicate significant performance gains over systems employing separate detection and decoding, yet are obtained at a complexity that is practically feasible over a wide range of system parameters.


Item Type:Article
Additional Information:© Copyright 2006 IEEE. Reprinted with permission. Manuscript received December 28, 2004; revised September 7, 2005. [Posted online: 2006-08-21] The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Chong-Yung Chi.
Subject Keywords:Expected complexity, integer least squares, joint detection and decoding, lattice problems, multiantenna systems, NP hard, sphere decoding (SD), wireless communications
Issue or Number:9
Record Number:CaltechAUTHORS:VIKieeetsp06b
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:VIKieeetsp06b
Alternative URL:http://dx.doi.org/10.1109/TSP.2006.877675
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4996
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:18 Sep 2006
Last Modified:26 Dec 2012 09:03

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