2014/11/17 by Roope Vehkalahti, Vehkalahti, Roope, Laura Luzzi +1
Computer Science · #Cellular Automata and Applications #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1411.4591
openalex publication_date 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proves that a family of number field lattice codes simultaneously\nachieves a constant gap to capacity in Rayleigh fast fading and Gaussian\nchannels.\n The key property in the proof is the existence of infinite towers of Hilbert\nclass fields with bounded root discriminant. The gap to capacity of the\nproposed families is determined by the root discriminant.\n The comparison between the Gaussian and fading case reveals that in Rayleigh\nfading channels the normalized minimum product distance plays an analogous role\nto the Hermite invariant in Gaussian channels.\n