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 "the admm penalized decoder for ldpc codes"):
  Abstract: Linear programming (LP) decoding for low-density parity-check codes was introduced by Feldman  et al.  and has been shown to have theoretical guarantees in several regimes. Furthermore, it has been reported in the literature—via simulation and via instanton analysis—that LP decoding displays better error rate performance at high signal-to-noise ratios (SNR) than does belief propagation (BP) decoding. However, at low SNRs, LP decoding is observed to have worse performance than BP. In this paper, we seek to improve LP decoding at low SNRs while maintaining LP decoding’s high SNR performance. Our main contribution is a new class of decoders obtained by applying the alternating direction method of multipliers (ADMM) algorithm to a set of non-convex optimization problems. These non-convex problems are constructed by adding a penalty term to the objective of LP decoding. The goal of the penalty is to make pseudocodewords, which are non-integer vertices of the LP relaxation, more costly. We name this class of decoders—ADMM penalized decoders. For low and moderate SNRs, we simulate ADMM penalized decoding with    $\ell _{1}$    and    $\ell _{2}$    penalties. We find that these decoders can outperform both BP and LP decoding. For high SNRs, where it is difficult to obtain data via simulation, we use an instanton analysis and find that, asymptotically, ADMM penalized decoding performs better than BP but not as well as LP. Unfortunately, since ADMM penalized decoding is not a convex program, we have not been successful in developing theoretical guarantees. However, the non-convex program can be approximated using a sequence of linear programs; an approach that yields a reweighted LP decoder. We show that a two-round reweighted LP decoder has an improved theoretical recovery threshold when compared with LP decoding. In addition, we find via simulation that reweighted LP decoding significantly attains lower error rates than LP decoding at low SNRs.

Includes members:
  Member "hierarchical and high girth qc ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "multi dimensional spatially coupled code design enhancing the cycle properties")
  Member "linear programming decoding of spatially coupled codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lp decoding excess over symmetric channels")
  Member "an improved three weight message passing algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a distributed admm approach to informative trajectory planning for multi target tracking")
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "mathematical programming decoding of binary linear codes theory and algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "efficient qp admm decoder for binary ldpc codes and its performance analysis")
  Member "error floor approximation for ldpc codes in the awgn channel":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a combinatorial methodology for optimizing non binary graph based codes theoretical analysis and applications in data storage")
  Member "adaptive cut generation algorithm for improved linear programming decoding of binary linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "admm based decoder for binary linear codes aided by deep learning")
  Member "decomposition methods for large scale lp decoding":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "admm based decoder for binary linear codes aided by deep learning")

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)