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 "on decoding irregular tanner codes with local optimality guarantees"):
  Abstract: We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality of a codeword in irregular Tanner codes with respect to any MBIOS channel. This characterization is based on a conical combination of normalized weighted subtrees in the computation trees of the Tanner graph. These subtrees may have any finite height h (even equal or greater than half of the girth of the Tanner graph). In addition, the degrees of local-code nodes in these subtrees are not restricted to two. We prove that local optimality in this new characterization implies maximum-likelihood (ML) optimality and LP optimality, and show that a certificate can be computed efficiently. #R##N#We also present a new message-passing iterative decoding algorithm, called normalized weighted min-sum (NWMS). NWMS decoding is a BP-type algorithm that applies to any irregular binary Tanner code with single parity-check local codes. We prove that if a locally-optimal codeword with respect to height parameter h exists (whereby notably h is not limited by the girth of the Tanner graph), then NWMS decoding finds this codeword in h iterations. The decoding guarantee of the NWMS decoding algorithm applies whenever there exists a locally optimal codeword. Because local optimality of a codeword implies that it is the unique ML codeword, the decoding guarantee also provides an ML certificate for this codeword. #R##N#Finally, we apply the new local optimality characterization to regular Tanner codes, and prove lower bounds on the noise thresholds of LP decoding in MBIOS channels. When the noise is below these lower bounds, the probability that LP decoding fails decays doubly exponentially in the girth of the Tanner graph.

Includes members:
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "convergence of weighted min sum decoding via dynamic programming on trees":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "hierarchies of local optimality characterizations in decoding of tanner codes")
  Member "correcting a fraction of errors in nonbinary expander codes with linear programming":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "local optimality guarantees for optimal decoding based on paths")
  Member "lp decoding of regular ldpc codes in memoryless channels":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the admm penalized decoder for ldpc codes")
  Member "error bounds for repeat accumulate codes decoded via linear programming":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "mathematical programming decoding of binary linear codes theory and algorithms")
  Member "probabilistic analysis of linear programming decoding":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the admm penalized decoder for ldpc codes")
  Member "on the block error probability of lp decoding of ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "impact of redundant checks on the lp decoding thresholds of ldpc codes")
  Member "graph cover decoding and finite length analysis of message passing iterative decoding of ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "efficient qp admm decoder for binary ldpc codes and its performance analysis")

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)