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 "decomposition methods for large scale lp decoding"):
  Abstract: When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode error-correcting codes at bit-error-rates comparable to state-of-the-art belief propagation (BP) decoders, but with significantly stronger theoretical guarantees. However, LP decoding when implemented with standard LP solvers does not easily scale to the block lengths of modern error correcting codes. In this paper we draw on decomposition methods from optimization theory, specifically the Alternating Directions Method of Multipliers (ADMM), to develop efficient distributed algorithms for LP decoding. #R##N#The key enabling technical result is a "two-slice" characterization of the geometry of the parity polytope, which is the convex hull of all codewords of a single parity check code. This new characterization simplifies the representation of points in the polytope. Using this simplification, we develop an efficient algorithm for Euclidean norm projection onto the parity polytope. This projection is required by ADMM and allows us to use LP decoding, with all its theoretical guarantees, to decode large-scale error correcting codes efficiently. #R##N#We present numerical results for LDPC codes of lengths more than 1000. The waterfall region of LP decoding is seen to initiate at a slightly higher signal-to-noise ratio than for sum-product BP, however an error floor is not observed for LP decoding, which is not the case for BP. Our implementation of LP decoding using ADMM executes as fast as our baseline sum-product BP decoder, is fully parallelizable, and can be seen to implement a type of message-passing with a particularly simple schedule.

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 "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "online alternating direction method":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "online learning a comprehensive survey")
  Member "error floor approximation for ldpc codes in the awgn channel":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a combinatorial methodology for optimizing non binary graph based codes theoretical analysis and applications in data storage")
  Member "improved linear programming decoding of ldpc codes and bounds on the minimum and fractional distance":
    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 "l1 projections with box constraints":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "predict and constrain modeling cardinality in deep structured prediction")
  Member "efficient implementation of linear programming decoding":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "adaptive linear programming decoding of nonbinary linear codes over prime fields")
  Member "probabilistic analysis of linear programming decoding":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the admm penalized decoder for ldpc 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)