A novel distributed computing model called Multi-access Distributed Computing (MADC) was recently introduced in [B. Federico and P. Elia, "Multi-Access Distributed Computing," June 2022, [online] Available: ...
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A novel distributed computing model called Multi-access Distributed Computing (MADC) was recently introduced in [B. Federico and P. Elia, "Multi-Access Distributed Computing," June 2022, [online] Available: http://***:2206.12851]. The MADC models with Combinatorial Topology (CT) was studied, where there are Λ mapper nodes and K = (Λα ) reducer nodes with each reducer node connected to distinct α mapper nodes. In this paper, we represent MADC models via 2-layered bipartite graphs called Map-Reduce Graphs (MRGs) and a set of arrays called Map-Reduce Arrays (MRAs) inspired from the Placement Delivery Arrays (PDAs) used in the coded caching literature. The connection between MRAs and MRGs is established, thereby exploring new topologies and providing coded shuffling schemes for the MADC models with MRGs using the structure of MRAs. A novel Nearest Neighbor Connect-MRG (NNC-MRG) is explored and a coding scheme is provided for MADC models with NNC-MRG, exploiting the connections between MRAs and PDAs. Moreover, CT is generalized to Generalized Combinatorial-MRG (GC-MRG). A set of g−regular MRAs is provided which corresponds to the existing scheme for MADC models with CT and extended those to generate another set of MRAs to represent MADC models with GC-MRG. A lower bound on the computation-communication curve for MADC model with GC-MRG under homogeneous setting is derived and certain cases are explored where the existing scheme is optimal under CT. One of the major limitations of the existing scheme for CT is that it requires an exponentially large number of reducer nodes and input files for large Λ. This can be overcome by representing CT by MRAs, where coding schemes can be derived even if some of the reducer nodes are not present. Another way of tackling this is by using a different MRG, specifically NNC-MRG, where the number of reducer nodes and files required are significantly smaller compared to CT. Hence, the advantages are two-fold, which is achievable at th
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length N can...
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