2011/04/04 by Lakshmi Prasad Natarajan, Natarajan, Lakshmi Prasad, K. Pavan Srinath +3
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1104.0640
openalex publication_date 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the landmark paper by Hassibi and Hochwald, it is claimed without proof that the upper triangular matrix R encountered during the sphere decoding of any linear dispersion code is full-ranked whenever the rate of the code is less than the minimum of the number of transmit and receive antennas. In this paper, we show that this claim is true only when the number of receive antennas is at least as much as the number of transmit antennas. We also show that all known families of high rate (rate greater than 1 complex symbol per channel use) multigroup ML decodable codes have rank-deficient R matrix even when the criterion on rate is satisfied, and that this rank-deficiency problem arises only in asymmetric MIMO with number of receive antennas less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the average sphere decoding complexity of the STBCs whose R matrix is rank-deficient is polynomial in the constellation size. We derive the sphere decoding complexity of most of the known high rate multigroup ML decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.