Multigroup decodable STBCs from Clifford algebras

  • Authors:
  • Sanjay Karmakar;B. Sundar Rajan

  • Affiliations:
  • Electrical and Computer Science Engineering Department, University of Colorado at Boulder, Boulder, CO;Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

A space-time block code (STBC) in K symbols (variables) is called a g-group decodable STBC if its maximum-likelihood (ML) decoding metric can be written as a sum of g terms, for some positive integer g greater than one, such that each term is a function of a subset of the K variables and each variable appears in only one term. In this paper, we provide a general structure of the weight matrices of multigroup decodable codes using Clifford algebras. Without assuming that the number of variables in each group is the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal multigroup decodable codes is presented for arbitrary number of antennas. For the special case of 2a number of transmit antennas, we construct two subclass of2a codes: 1) a class of 2a-group decodable codes with rate a/2(a-1), which is, equivalently, a class of single-symbol decodable codes, and 2) a class of (2a-2) -group decodable codes with rate (a-1)/2(a-2), i.e., a class of double-symbol decodable codes.