2019/09/17 by Mahdi Soleymani, Soleymani, Mahdi, Hessam Mahdavifar +1 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #Advanced Wireless Communication Techniques #Algorithm #Artificial intelligence #Block code #Coding (social sciences) #Coding theory #Combinatorics #Computer network #Computer science #Cooperative Communication and Network Coding #Decoding methods #Discrete mathematics #FOS: Computer and information sciences #Finite field #Grassmannian #Information Theory (cs.IT) #Linear network coding #Linear subspace #Mathematics #Pure mathematics #Robustness (evolution) #Subspace topology #Theoretical computer science #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1909.07533
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/09/17 · arxiv created 2022/01/28 · arxiv updated 2022/01/31 · openalex created_date 2022/07/23 · openalex updated_date 2026/08/08
We provide a novel framework to study subspace codes for non-coherent communications in wireless networks. To this end, an analog operator channel is defined with inputs and outputs being subspaces of ℂn. Then a certain distance is defined to capture the performance of subspace codes in terms of their capability to recover from interference and rank-deficiency of the network. We also study the robustness of the proposed model with respect to an additive noise. Furthermore, we propose a new approach to construct subspace codes in the analog domain, also regarded as Grassmann codes, by leveraging polynomial evaluations over finite fields together with characters associated to finite fields that map their elements to the unit circle in the complex plane. The constructed codes, referred to as character-polynomial (CP) codes, are shown to perform better comparing to other existing constructions of Grassmann codes in terms of the trade-off between the rate and the normalized minimum distance, for a wide range of values for n.