2024/11/28 by Adrián Fidalgo-Díaz, Umberto Martínez-Peñas, Fidalgo-Díaz, Adrián +1
Computer Science · Mathematics · #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Stochastic Gradient Optimization Techniques #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2411.19065
openalex publication_date 2024/11/28 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ Reed-Muller-type codes for explicitly constructing the desired algorithms and study their parameters by translating the problem into a combinatorial problem involving sums of discrete convex sets. We generalize polynomial codes and matdot codes, discussing the impossibility of the latter being applicable for very small field sizes, while providing optimal solutions for some regimes of parameters in both cases.