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 "reed muller codes for random erasures and errors"):
  Abstract: This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels. Necessarily, the paper also studies properties of evaluations of multi-variate $GF(2)$ polynomials on random sets of inputs. #R##N#For erasures, we prove that RM codes achieve capacity both for very high rate and very low rate regimes. For errors, we prove that RM codes achieve capacity for very low rate regimes, and for very high rates, we show that they can uniquely decode at about square root of the number of errors at capacity. #R##N#The proofs of these four results are based on different techniques, which we find interesting in their own right. In particular, we study the following questions about $E(m,r)$, the matrix whose rows are truth tables of all monomials of degree $\leq r$ in $m$ variables. What is the most (resp. least) number of random columns in $E(m,r)$ that define a submatrix having full column rank (resp. full row rank) with high probability? We obtain tight bounds for very small (resp. very large) degrees $r$, which we use to show that RM codes achieve capacity for erasures in these regimes. #R##N#Our decoding from random errors follows from the following novel reduction. For every linear code $C$ of sufficiently high rate we construct a new code $C'$, also of very high rate, such that for every subset $S$ of coordinates, if $C$ can recover from erasures in $S$, then $C'$ can recover from errors in $S$. Specializing this to RM codes and using our results for erasures imply our result on unique decoding of RM codes at high rate. #R##N#Finally, two of our capacity achieving results require tight bounds on the weight distribution of RM codes. We obtain such bounds extending the recent \cite{KLP} bounds from constant degree to linear degree polynomials.

Includes members:
  Member "recursive decoding and its performance for low rate reed muller codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reed muller codes theory and algorithms")
  Member "from polar to reed muller codes a technique to improve the finite length performance":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "polar codes and their quantum domain counterparts")
  Member "polar codes speed of polarization and polynomial gap to capacity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "polar codes simplicity random codes durability")
  Member "smoothed analysis of tensor decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "improper learning for non stochastic control")
  Member "efficient density estimation via piecewise polynomial approximation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "em algorithm is sample optimal for learning mixtures of well separated gaussians")
  Member "threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "randomness and dependencies extraction via polarization with applications to slepian wolf coding and secrecy":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "polar codes simplicity random codes durability")
  Member "channel polarization a method for constructing capacity achieving codes for symmetric binary input memoryless channels":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "reed muller codes theory and algorithms")

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)