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 polarize"):
  Abstract: Reed-Muller (RM) codes and polar codes are generated by the same matrix $G_m= \bigl[\begin{smallmatrix}1 & 0 \\ 1 & 1 \\ \end{smallmatrix}\bigr]^{\otimes m}$ but using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in $G_m$; while this is a more elaborate and channel-dependent rule, the top-to-down ordering has the advantage of making the conditional mutual information polarize, giving directly a capacity-achieving code on any binary memoryless symmetric channel (BMSC). RM codes are yet to be proved to have such property. #R##N#In this paper, we reconnect RM codes to polarization theory. It is shown that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in $G_m$, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that $G_m$ contains another code, different than the polar code and called here the twin code, that is provably capacity-achieving on any BMSC. This proves a necessary condition for RM codes to achieve capacity on BMSCs. It further gives a sufficient condition if the rows with the largest conditional mutual information correspond to the heaviest rows, i.e., if the twin code is the RM code. We show here that the two codes bare similarity with each other and give further evidence that they are likely the same.

Includes members:
  Member "recursive projection aggregation decoding of reed muller codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reed muller codes theory and algorithms")
  Member "general strong polarization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "reed muller codes theory and algorithms")
  Member "on the performance of reed muller codes with respect to random errors and erasures":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reed muller codes theory and algorithms")
  Member "decoding reed muller codes using minimum weight parity checks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "reed muller codes theory and algorithms")
  Member "almost optimal scaling of reed muller codes on bec and bsc channels":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "reed muller codes theory and algorithms")
  Member "recursive decoding and its performance for low rate reed muller codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "reed muller codes theory and algorithms")
  Member "algebraic properties of polar codes from a new polynomial formalism":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "polar decreasing monomial cartesian codes")
  Member "high girth matrices and polarization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the fractality of polar and reed muller codes")

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)