General Fractional Repetition Codes From Combinatorial Designs

Bounds on Fractional Repetition Codes using Hypergraphs

“…• FR codes are generalized to Weak [10], [29], General [7], [42] or Irregular [43] FR codes, where different number of packets are stored in each node. Those FR codes are constructed using partial regular graphs [10] and group divisible designs [7].…”

“…In [29], FR codes are constructed using ring construction, where all the replicated packets are distributed to nodes in specific order. In [42], the FR code is constructed using packings, coverings, and pairwise balanced designs. In [43], FR codes are studied as uniform hypergraphs.…”

“…FR code [3], [17], [33] ρ-uniform and α-regular hypergraph HFR code [8] Linear and α-regular hypergraph IFR code [43] ρ-uniform hypergraph VFR code [44] α-regular hypergraph with |E| ∈ {ρ 1 , ρ 2 }, for each E ∈ E GFR code [7], [42] ρ-uniform and linear hypergraph WFR code [10] ρ-uniform hypergraph FR code [18]- [20] ρ-uniform, α-regular and [12], [14], [16], [24], [26] linear hypergraph Adaptive FR code [5] ρ-uniform α-regular hypergraph s.t. induced sub-hypergraph is again ρ ′ -uniform α ′ -regular hypergraph FFR code [45] Linear hypergraph FR code [29] ρ-uniform hypergraph FR code [9] Hypergraph FR code [6], [11] ρ-uniform and α-regular hypergraph FR code [34],…”