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 "sharp bounds for optimal decoding of low density parity check codes"):
  Abstract: Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the average input-output conditional entropy per bit in the infinite block length limit. Montanari proved a lower bound for this entropy, in the case of LDPC ensembles with convex check degree polynomial, which matches the replica formula. Here we extend this lower bound to any irregular LDPC ensemble. The new feature of our work is an analysis of the second derivative of the conditional input-output entropy with respect to noise. A close relation arises between this second derivative and correlation or mutual information of codebits. This allows us to extend the realm of the interpolation method, in particular we show how channel symmetry allows to control the fluctuations of the overlap parameters.

Includes members:
  Member "on universal properties of capacity approaching ldpc code ensembles":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "one and two bit message passing for sc ldpc codes with higher order modulation")
  Member "decay of correlations for sparse graph error correcting codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a scaling law to predict the finite length performance of spatially coupled ldpc codes")
  Member "maxwell construction the hidden bridge between iterative and maximum a posteriori decoding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reed muller codes theory and algorithms")
  Member "tight bounds for ldpc and ldgm codes under map decoding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "accuracy memory tradeoffs and phase transitions in belief propagation")

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)