2018/05/05 by Shanxiang Lyu, Lyu, Shanxiang, Antonio Campello +3
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1805.02073
openalex publication_date 2018/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers ℤ, Gaussian integers ℤ[i] or Eisenstein integers ℤ[ω], while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for Compute-and-Forward in block-fading channels without CSIT, which is referred to as Ring Compute-and-Forward because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Thanks to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional Compute-and-Forward based on ℤ-lattices. By investigating the effect of Diophantine approximation by algebraic conjugates, we prove that the degrees-of-freedom (DoF) of the optimized computation rate is n/L, where n is the number of blocks and L is the number of users.