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 "phasecode fast and efficient compressive phase retrieval based on sparse graph codes"):
  Abstract: We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of the $K$ non-zero signal components using only slightly more than $4K$ measurements when the support of the signal is uniformly random, with order-optimal time and memory complexity of $\Theta(K)$. It is known that the fundamental limit for the number of measurements in compressive phase retrieval problem is $4K - o(K)$ to recover the signal exactly and with no assumptions on its support distribution. This shows that under mild relaxation of the conditions, our algorithm is the first constructive \emph{capacity-approaching} compressive phase retrieval algorithm: in fact, our algorithm is also order-optimal in complexity and memory. Next, motivated by some important practical classes of optical systems, we consider a Fourier-friendly constrained measurement setting, and show that its performance matches that of the unconstrained setting. In the Fourier-friendly setting that we consider, the measurement matrix is constrained to be a cascade of Fourier matrices and diagonal matrices. We further demonstrate how PhaseCode can be robustified to noise. Throughout, we provide extensive simulation results that validate the practical power of our proposed algorithms for the sparse unconstrained and Fourier-friendly measurement settings, for noiseless and noisy scenarios. A key contribution of our work is the novel use of coding-theoretic tools like density evolution methods for the design and analysis of fast and efficient algorithms for compressive phase-retrieval problems.

Includes members:
  Member "compressive phase retrieval via generalized approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "phase retrieval via wirtinger flow theory and algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "reliable deniable and hidable communication over multipath networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "stealthy communication over adversarially jammed multipath networks")
  Member "super sparse signals with unknown phases efficiently recovered":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "stronger l2 l2 compressed sensing without iterating")
  Member "phase retrieval for sparse signals":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "stable phaseless sampling and reconstruction of real valued signals with finite rate of innovations")
  Member "new conditions for sparse phase retrieval":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "almost optimal phaseless compressed sensing with sublinear decoding time")
  Member "computing a k sparse n length discrete fourier transform using at most 4k samples and o k log k complexity":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "an adaptive sublinear time block sparse fourier transform")
  Member "near optimal phase retrieval of sparse vectors":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "almost optimal phaseless compressed sensing with sublinear decoding time")

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)