LATTICE CODING FOR CONTINUOUS CHANNELS,
Abstract
A class of explicit codes for time-discrete amplitude-continuous channels is presented. These codes, called lattice codes, can maintain positive transmission rates over such channels while simultaneously reducing the probability of error to zero, providing only that the channel noise variance is finite. A lattice in n-dimensional Euclidean space is the set of all integer linear combinations of some n independent basis vectors. A lattice code for a given time-discrete amplitude-continuous channel is formed from a lattice by taking for codes words all those vectors of the lattice which satisfy the channel constraints. Communication over memoryless time-discrete amplitude-continuous channels with either amplitude or average power constraints using lattice codes is considered. An analysis is given for such channels when lattice codes are used together with bounded distance decoding. Bounds on the channel capacity are found, and for fixed transmission rates less than capacity, bounds are found for the best attainable probability of error as a function of the code length n. The construction of lattice codes using positive definite quadratic forms is considered. A sequential decoding algorithm which has a probability of error less than that of bounded distance decoding for any lattice code is given. Finally, some examples are given of lattice codes for which this algorithm may be replaced by a simple algebraic procedure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0663808
Entities
People
- Robert J. Tracey
Organizations
- University of Illinois Urbana–Champaign