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 "generalized sphere packing bound"):
  Abstract: Kulkarni and Kiyavash recently introduced a new method to establish upper bounds on the size of deletion-correcting codes. This method is based upon tools from hypergraph theory. The deletion channel is represented by a hypergraph whose edges are the deletion balls (or spheres), so that a deletion-correcting code becomes a matching in this hypergraph. Consequently, a bound on the size of such a code can be obtained from bounds on the matching number of a hypergraph. Classical results in hypergraph theory are then invoked to compute an upper bound on the matching number as a solution to a linear-programming problem. #R##N#The method by Kulkarni and Kiyavash can be applied not only for the deletion channel but also for other error channels. This paper studies this method in its most general setup. First, it is shown that if the error channel is regular and symmetric then this upper bound coincides with the sphere packing bound and thus is called the generalized sphere packing bound. Even though this bound is explicitly given by a linear programming problem, finding its exact value may still be a challenging task. In order to simplify the complexity of the problem, we present a technique based upon graph automorphisms that in many cases reduces the number of variables and constraints in the problem. We then apply this method on specific examples of error channels. We start with the $Z$ channel and show how to exactly find the generalized sphere packing bound for this setup. Next studied is the non-binary limited magnitude channel both for symmetric and asymmetric errors, where we focus on the single-error case. We follow up on the deletion and grain-error channels and show how to improve upon the existing upper bounds for single deletion/error. Finally, we apply this method for projective spaces and find its generalized sphere packing bound for the single-error case.

Includes members:
  Member "upper bounds on the size of grain correcting codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "linear programming based converses for finite blocklength lossy joint source channel coding")
  Member "bounds for projective codes from semidefinite programming":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "semidefinite programming bounds for error correcting codes")
  Member "correcting grain errors in magnetic media":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "linear programming based converses for finite blocklength lossy joint source channel coding")
  Member "non asymptotic upper bounds for deletion correcting codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "duplication correcting codes")
  Member "on the non existence of lattice tilings by quasi crosses":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "some new results on splitter sets")
  Member "linearity and complements in projective space":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the lattice structure of linear subspace codes")
  Member "write channel model for bit patterned media recording":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "graph based encoders and their performance for finite state channels with feedback")
  Member "coding for high density recording on a 1 d granular magnetic medium":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the capacity of channels with timing synchronization errors")

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)