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 achievable rates and complexity of ldpc codes for parallel channels with application to puncturing"):
  Abstract: This paper considers the achievable rates and decoding complexity of low-density parity-check (LDPC) codes over statistically independent parallel channels. The paper starts with the derivation of bounds on the conditional entropy of the transmitted codeword given the received sequence at the output of the parallel channels; the component channels are considered to be memoryless, binary-input, and outputsymmetric (MBIOS). These results serve for the derivation of an upper bound on the achievable rates of ensembles of LDPC codes under optimal maximum-likelihood (ML) decoding when their transmission takes place over parallel MBIOS channels. The paper relies on the latter bound for obtaining upper bounds on the achievable rates of ensembles of randomly and intentionally punctured LDPC codes over MBIOS channels. For ensembles of punctured LDPC codes, the calculation of bounds on their thresholds under ML decoding and their exact thresholds under iterative decoding (based on density evolution analysis) is of interest in the sense that it enables to assess the degradation in the asymptotic performance which is attributed to the sub-optimality of iterative decoding (as compared to ML decoding), and also to assess the inherent loss in the asymptotic performance which is attributed to the structure of these ensembles, even if ML decoding could be applied to decode LDPC codes. The paper also provides a lower bound on the decoding complexity (per iteration) of ensembles of LDPC codes under message-passing iterative decoding over parallel MBIOS channels; the bound is given in terms of the gap between the rate of these codes for which reliable communication is achievable and the channel capacity. Similarly to the case of a single MBIOS channel, this lower bound grows like the log of the inverse of the gap to capacity. The latter bound is used for the derivation of lower bounds on the decoding complexity of punctured LDPC codes over MBIOS channels; looser versions of these bounds suggest a simplifled re-derivation of previously reported bounds on the decoding complexity of randomly punctured LDPC codes. The paper presents a diagram which shows interconnections between the theorems introduced in this paper and some other previously reported results. The setting which serves for the derivation of the bounds on the achievable rates and decoding complexity is general, and the bounds can be applied to punctured LDPC codes, non-uniformly error protected LDPC codes, and LDPC-coded modulation where all these scenarios can be treated as difierent forms of communication over parallel channels.

Includes members:
  Member "maxwell construction the hidden bridge between iterative and maximum a posteriori decoding":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reed muller codes theory and algorithms")
  Member "improved bounds on the parity check density and achievable rates of binary linear block codes with applications to ldpc codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "performance versus complexity per iteration for low density parity check codes an information theoretic approach")
  Member "capacity achieving ensembles for the binary erasure channel with bounded complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "log logarithmic time pruned polar coding")

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)