human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "tight bounds for ldpc and ldgm codes under map decoding"
  Abstract: A new method for analyzing low-density parity-check (LDPC) codes and low-density generator-matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is based on a rigorous approach to spin glasses developed by Francesco Guerra. It allows one to construct lower bounds on the entropy of the transmitted message conditional to the received one. Based on heuristic statistical mechanics calculations, we conjecture such bounds to be tight. The result holds for standard irregular ensembles when used over binary-input output-symmetric (BIOS) channels. The method is first developed for Tanner-graph ensembles with Poisson left-degree distribution. It is then generalized to "multi-Poisson" graphs, and, by a completion procedure, to arbitrary degree distribution

Connected through hyperedge HE-1 (induced by source paper "accuracy memory tradeoffs and phase transitions in belief propagation"):
  with members:
    - "the circuit complexity of inference"
    - "communication complexity of estimating correlations"
    - "geometric lower bounds for distributed parameter estimation under communication constraints"
    - "reducibility and computational lower bounds for problems with planted sparse structure"
    - "inference under information constraints i lower bounds from chi square contraction"
    - "extractor based time space lower bounds for learning"
    - "secret key generation with limited interaction"
    - "fast learning requires good memory a time space lower bound for parity learning"

Connected through hyperedge HE-2 (induced by source paper "information theoretic thresholds from the cavity method"):
  with members:
    - "planting colourings silently"
    - "mutual information in rank one matrix estimation"
    - "the condensation phase transition in random graph coloring"
    - "asymptotic mutual information for the two groups stochastic block model"
    - "semidefinite programs on sparse random graphs and their application to community detection"
    - "conditioning and covariance on caterpillars"
    - "chasing the k colorability threshold"
    - "on the complexity of random satisfiability problems with planted solutions"

Connected through hyperedge HE-3 (induced by source paper "adaptive path interpolation for sparse systems application to a simple censored block model"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "entropy and mutual information in models of deep neural networks"
    - "the committee machine computational to statistical gaps in learning a two layers neural network"
    - "information theoretic thresholds from the cavity method"
    - "the layered structure of tensor estimation and its mutual information"
    - "mutual information and optimality of approximate message passing in random linear estimation"
    - "the replica symmetric prediction for compressed sensing with gaussian matrices is exact"
    - "the mutual information in random linear estimation"

Connected through hyperedge HE-4 (induced by source paper "mutual information and optimality of approximate message passing in random linear estimation"):
  with members:
    - "approximate message passing decoder and capacity achieving sparse superposition codes"
    - "capacity achieving sparse superposition codes via approximate message passing decoding"
    - "the replica symmetric prediction for compressed sensing with gaussian matrices is exact"
    - "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels"
    - "the mutual information in random linear estimation"
    - "proof of threshold saturation for spatially coupled sparse superposition codes"
    - "mutual information in rank one matrix estimation"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"

Connected through hyperedge HE-5 (induced by source paper "the stochastic interpolation method a simple scheme to prove replica formulas in bayesian inference"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "entropy and mutual information in models of deep neural networks"
    - "the mutual information in random linear estimation beyond i i d matrices"
    - "adaptive path interpolation for sparse systems application to a simple censored block model"
    - "information theoretic thresholds from the cavity method"
    - "the layered structure of tensor estimation and its mutual information"
    - "i mmse relations in random linear estimation and a sub extensive interpolation method"
    - "mutual information and optimality of approximate message passing in random linear estimation"

Connected through hyperedge HE-6 (induced by source paper "the mutual information of ldgm codes"):
  with members:
    - "the computer science and physics of community detection landscapes phase transitions and hardness"
    - "multi layer generalized linear estimation"
    - "i mmse relations in random linear estimation and a sub extensive interpolation method"
    - "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels"
    - "phase transitions and sample complexity in bayes optimal matrix factorization"
    - "community detection thresholds and the weak ramanujan property"
    - "sharp bounds for optimal decoding of low density parity check codes"
    - "hiding satisfying assignments two are better than one"

Connected through hyperedge HE-7 (induced by source paper "analysis of regularized ls reconstruction and random matrix ensembles in compressed sensing"):
  with members:
    - "isotropically random orthogonal matrices performance of lasso and minimum conic singular values"
    - "on the performance of turbo signal recovery with partial dft sensing matrices"
    - "inference for generalized linear models via alternating directions and bethe free energy minimization"
    - "s amp approximate message passing for general matrix ensembles"
    - "signal recovery using expectation consistent approximation for linear observations"
    - "on sparse vector recovery performance in structurally orthogonal matrices via lasso"
    - "asymptotic mmse analysis under sparse representation modeling"
    - "statistical mechanics approach to sparse noise denoising"

Connected through hyperedge HE-8 (induced by source paper "concentration to zero bit error probability for regular ldpc codes on the binary symmetric channel proof by loop calculus"):
  with members:
    - "the bethe free energy allows to compute the conditional entropy of graphical code instances a proof from the polymer expansion"
    - "spatial coupling as a proof technique"
    - "beyond the bethe free energy of ldpc codes via polymer expansions"
    - "decay of correlations for sparse graph error correcting codes"
    - "sharp bounds for optimal decoding of low density parity check codes"
    - "the generalized area theorem and some of its consequences"

Question: Please tell me which class the center node 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)