On joint ml detection and decoding for linear block codes
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We consider joint maximum-likelihood (ML) detection and decoding in multiple-input multiple-output (MIMO) systems. The information data is encoded by a linear block error-correcting code and then transmitted across the MIMO channel in AWGN. Geometrically, the transmitted symbol is a
point in a high-dimensional lattice. The received symbol
is the lattice point perturbed by an additive noise.
The joint detection and decoding problem is equivalent
to the search for the closest lattice point that is
an admissible codeword. We propose an algorithm
which performs a search constrained by a sphere centered
at the observed point. The radius of the sphere
is determined according to the statistics of the noise.
Thus the computational complexity of the algorithm
is a random variable. We quantify it by means of its
first moment which, for binary codes, we And analytically.
The expected complexity of the proposed
algorithm is polynomial in the length of the uncoded
information word over a wide range of SNRs.
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