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 "mutual information and optimality of approximate message passing in random linear estimation"):
  Abstract: We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a number of works considering the mutual information for this problem using the replica method from statistical physics. Here we put these considerations on a firm rigorous basis. First, we show, using a Guerra-Toninelli type interpolation, that the replica formula yields an upper bound to the exact mutual information. Secondly, for many relevant practical cases, we present a converse lower bound via a method that uses spatial coupling, state evolution analysis and the I-MMSE theorem. This yields a single letter formula for the mutual information and the minimal-mean-square error for random Gaussian linear estimation of all discrete bounded signals. In addition, we prove that the low complexity approximate message-passing algorithm is optimal outside of the so-called hard phase, in the sense that it asymptotically reaches the minimal-mean-square error. In this work spatial coupling is used primarily as a proof technique. However our results also prove two important features of spatially coupled noisy linear random Gaussian estimation. First there is no algorithmically hard phase. This means that for such systems approximate message-passing always reaches the minimal-mean-square error. Secondly, in a proper limit the mutual information associated to such systems is the same as the one of uncoupled linear random Gaussian estimation.

Includes members:
  Member "approximate message passing decoder and capacity achieving sparse superposition codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "capacity achieving sparse superposition codes via approximate message passing decoding":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "the replica symmetric prediction for compressed sensing with gaussian matrices is exact":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "unsourced multiuser sparse regression codes achieve the symmetric mac capacity")
  Member "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "compressed coding amp based decoding and analog spatial coupling")
  Member "the mutual information in random linear estimation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "bilinear recovery using adaptive vector amp")
  Member "proof of threshold saturation for spatially coupled sparse superposition codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "mutual information in rank one matrix estimation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "overlap matrix concentration in optimal bayesian inference")
  Member "mutual information for symmetric rank one matrix estimation a proof of the replica formula":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")

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)