Encoding and decoding binary product lattices

Amir J. Salomon, Ofer Amrani

Research output: Contribution to journalArticlepeer-review

Abstract

A binary product lattice is generated from two binary component lattices of lower dimensions by employing the Kronecker product. This work focuses on codes carved from binary product lattices. Defined as such, an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points. A novel approach is disclosed yielding an explicit connection between source bits and lattice points. Decoding methods typically used for binary product codes do not apply for product lattices. Several alternative decoding approaches are discussed. In particular, a provably bounded-distance decoder is presented. It relies on the fact that a product lattice code point may be regarded as a two-dimensional array whose rows and columns are points in the component lattices. The obtained results are compared with classical lattices known in the art.

Original languageEnglish
Pages (from-to)5485-5495
Number of pages11
JournalIEEE Transactions on Information Theory
Volume52
Issue number12
DOIs
StatePublished - Dec 2006

Keywords

  • Barnes-Wall lattice
  • Binary code
  • Binary lattice
  • Bounded-distance decoding
  • Lattice
  • Maximum-likelihood (ML) decoding
  • Nearest neighbors
  • Product code
  • Product lattice
  • Reed-Muller code

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