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 "finite length scaling for polar codes"):
  Abstract: Consider a binary-input memoryless output-symmetric channel W. Such a channel has a capacity, call it I(W), and for any R <; I(W) and strictly positive constant Pe we know that we can construct a coding scheme that allows transmission at rate R with an error probability not exceeding P#N# e#N#. Assume now that we let the rate R tend to I(W) and we ask how we have to scale the blocklength N in order to keep the error probability fixed to P#N# e#N#. We refer to this as the finite-length scaling behavior. This question was addressed by Strassen as well as Polyanskiy, Poor, and Verdu, and the result is that N must grow at least as the square of the reciprocal of I(W) - R. Polar codes are optimal in the sense that they achieve capacity. In this paper, we are asking to what degree they are also optimal in terms of their finite-length behavior. Since the exact scaling behavior depends on the choice of the channel, our objective is to provide scaling laws that hold universally for all binary-input memoryless output-symmetric channels. Our approach is based on analyzing the dynamics of the un-polarized channels. More precisely, we provide bounds on (the exponent of) the number of subchannels whose Bhattacharyya constant falls in a fixed interval [a, b]. Mathematically, this can be stated as bounding the sequence {1/n logPr(Z#N# n#N# ∈ [a, b])}#N# n∈N#N#, where Z#N# n#N# is the Bhattacharyya process. We then use these bounds to derive tradeoffs between the rate and the block-length. The main results of this paper can be summarized as follows. Consider the sum of Bhattacharyya parameters of subchannels chosen (by the polar coding scheme) to transmit information. If we require this sum to be smaller than a given value P#N# e#N# > 0, then the required block-length N scales in terms of the rate R <; I(W) as N ≥ α/(I(W) - R)#N# μ#N#, where α is a positive constant that depends on P#N# e#N# and I(W). We show that μ = 3.579 is a valid choice, and we conjecture that indeed the value of μ can be improved to μ = 3.627, the parameter for the binary erasure channel. Also, we show that with the same requirement on the sum of Bhattacharyya parameters, the blocklength scales in terms of the rate like N ≤ β/(I(W) - R)#N# μ#N#, where β is a constant that depends on P#N# e#N# and I(W), and μ = 6.

Includes members:
  Member "performance limits and practical decoding of interleaved reed solomon polar concatenated codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "threshold secure coding with shared key")
  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 "improved successive cancellation decoding of polar codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "polar codes and their quantum domain counterparts")
  Member "improved bounds on the finite length scaling of polar codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "polar codes simplicity random codes durability")
  Member "polar codes with dynamic frozen symbols and their decoding by directed search":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "polar codes and their quantum domain counterparts")
  Member "on the correlation between polarized becs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "polar code moderate deviation recovering the scaling exponent")
  Member "scaling exponent of list decoders with applications to polar codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "polar codes and their quantum domain counterparts")

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)