Spherical lattice codes for lattice and lattice-reduction-aided decoders
AssigneeNEC Laboratories America, Inc.
InventorsNarayan Prasad, Xiaodong Wang, Mohammad Madihian
Life of this patent
Estimating the term…
Abstract
Methods and apparatus for designing spherical lattice codebooks for use in data transmission systems are provided. A spherical lattice codebook is constructed by determining the channel statistics of one or more channels, which can be accomplished by observing a sufficiently large set of channel realizations. After determining the channel statistics, an expression for the error probability of the decoder or expressions for bounds on the error probability and expressions for the corresponding gradients are determined. The gradient is then used in an optimization technique to produce a spherical lattice codebook which is subsequently used for transmission.
Claims31
A method of generating a spherical lattice codebook comprising:
- determining a set of lattice points closest to a translation vector;
- replacing the translation vector with a negative of a centroid of the codebook;
- repeating replacing the translation vector with a negative of the centroid until the translation vector converges on a final centroid;
- and,
- determining the final centroid as the translation vector for the spherical codebook;
- determining characteristics of a channel;
- determining an error probability of a decoder;
- determining a gradient of the error probability;
- and,
- producing a spherical lattice codebook for the received signal by optimizing the gradient of the error probability.
A method of generating a spherical lattice codebook for use in a multiple-input multiple-output data transmission system comprising:
- determining a set of lattice points closest to a translation vector;
- replacing the translation vector with a negative of a centroid of the codebook;
- repeating replacing the translation vector with a negative of the centroid until the translation vector converges on a final centroid;
- and,
- determining the final centroid as the translation vector for the spherical codebook;
- determining an error probability of a decoder;
- determining a function of the error probability;
- optimizing the function of the error probability;
- and,
- generating a spherical codebook from the optimized function.
A method of determining a spherical codebook satisfying a peak energy constraint comprising:
- determining a plurality of translation vectors;
- determining a set of lattice points from the plurality of translation vectors;
- and,
- generating a spherical code corresponding to the set of lattice points and satisfying the peak energy constraint;
- determining a set of lattice points closest to a translation vector;
- replacing the translation vector with a negative of a centroid of the codebook;
- repeating replacing the translation vector with a negative of the centroid until the translation vector converges on a final centroid;
- and,
- determining the final centroid as the translation vector for the spherical codebook.
A method of selecting a spherical codebook to reduce an average transmit energy constraint comprising:
- determining a set of lattice points closest to a translation vector;
- replacing the translation vector with a negative of a centroid of a codebook;
- repeating replacing the translation vector with a negative of the centroid until the translation vector converges on a final centroid;
- and,
- determining the final centroid as the translation vector for the spherical codebook.
An apparatus for generating a spherical lattice codebook for use in a multiple-input multiple-output data transmission system comprising:
- means for determining an error probability of a decoder;
- means for determining a function of the error probability;
- means for optimizing the function of the error probability;
- and,
- means for generating a spherical codebook from the optimized function;
- means for determining a set of lattice points closest to a translation vector;
- means for replacing the translation vector with a negative of a centroid of the codebook;
- repeating replacing the translation vector with a negative of the centroid until the translation vector converges on a final centroid;
- and,
- means for determining the final centroid as the translation vector for the spherical codebook.
Dependencies are inferred from the claim text.