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A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. In general, networks or graphs are used to capture relationships between entities or objects. A typical graphing representation consists of a set of nodes connected by edges. As early as 1736 Leonhard Euler analyzed a real-world issue known as the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930's-1950's the study of random graphs were developed.
Reed–Muller codes are error-correcting codes that are used in wireless communications applications, particularly in deep-space communication. Moreover, the proposed 5G standard relies on the closely related polar codes for error correction in the control channel. Due to their favorable theoretical and mathematical properties, Reed–Muller codes have also been extensively studied in theoretical computer science. Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code.
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a system into varying degrees of interdependence and independence across and "hide the complexity of each part behind an abstraction and interface". However, the concept of modularity can be extended to multiple disciplines, each with their own nuances.
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively dec
Various embodiments are directed to Reed-Muller decoding systems and methods based on recursive projections and aggregations of cosets decoding, exploiting the self-similarity of RM codes, and extende
Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the em