human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "the explicit coding rate region of symmetric multilevel diversity coding"):
  Abstract: It is well known that {\em superposition coding}, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear optimization problem. Thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple. In this paper, we first obtain closed-form expressions of these uncountably many inequalities. Then we identify a finite subset of inequalities that is sufficient for characterizing the coding rate region. This gives an explicit characterization of the coding rate region. We further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple. Yet, the cardinality of this smaller set grows at least exponentially fast with $L$. We also present a subset entropy inequality, which together with our explicit characterization of the coding rate region, is sufficient for proving the optimality of superposition coding.

Includes members:
  Member "distributed multilevel diversity coding":
    also connected through other hyperedges:
      (none)
  Member "multilevel diversity coding with regeneration":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "an open source toolbox for computer aided investigation on the fundamental limits of information systems version 0 1")
  Member "symmetrical multilevel diversity coding and subset entropy inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "multilevel diversity coding with secure regeneration separate coding achieves the mbr point")
  Member "multilevel diversity coding systems rate regions codes computation forbidden minors":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "an open source toolbox for computer aided investigation on the fundamental limits of information systems version 0 1")
  Member "secure symmetrical multilevel diversity coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "multilevel diversity coding with secure regeneration separate coding achieves the mbr point")
  Member "asymmetric multilevel diversity coding and asymmetric gaussian multiple descriptions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "multilevel diversity coding with secure regeneration separate coding achieves the mbr point")
  Member "information inequalities for joint distributions with interpretations and applications":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "dual loomis whitney inequalities via information theory")
  Member "approximating the gaussian multiple description rate region under symmetric distortion constraints":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the storage cost of private information retrieval")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)