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Register a new userComputation Over Gaussian Networks With Orthogonal Components
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Added by
Sang-Woon Jeon
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.
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In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.
We introduce clustered millimeter wave networks with invoking non-orthogonal multiple access~(NOMA) techniques, where the NOMA users are modeled as Poisson cluster processes and each cluster contains a base station (BS) located at the center. To provide realistic directional beamforming, an actual antenna array pattern is deployed at all BSs. We propose three distance-dependent user selection strategies to appraise the path loss impact on the performance of our considered networks. With the aid of such strategies, we derive tractable analytical expressions for the coverage probability and system throughput. Specifically, closed-form expressions are deduced under a sparse network assumption to improve the calculation efficiency. It theoretically demonstrates that the large antenna scale benefits the near user, while such influence for the far user is fluctuant due to the randomness of the beamforming. Moreover, the numerical results illustrate that: 1) the proposed system outperforms traditional orthogonal multiple access techniques and the commonly considered NOMA-mmWave scenarios with the random beamforming; 2) the coverage probability has a negative correlation with the variance of intra-cluster receivers; 3) 73 GHz is the best carrier frequency for near user and 28 GHz is the best choice for far user; 4) an optimal number of the antenna elements exists for maximizing the system throughput.
A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Martons coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all ranges of bit-pipe capacities.
In this work, we study bounds on the capacity of full-duplex Gaussian 1-2-1 networks with imperfect beamforming. In particular, different from the ideal 1-2-1 network model introduced in [1], in this model beamforming patterns result in side-lobe leakage that cannot be perfectly suppressed. The 1-2-1 network model captures the directivity of mmWave network communications, where nodes communicate by pointing main-lobe beams at each other. We characterize the gap between the approximate capacities of the imperfect and ideal 1-2-1 models for the same channel coefficients and transmit power. We show that, under some conditions, this gap only depends on the number of nodes. Moreover, we evaluate the achievable rate of schemes that treat the resulting side-lobe leakage as noise, and show that they offer suitable solutions for implementation.
There is a local ring $E$ of order $4,$ without identity for the multiplication, defined by generators and relations as $E=langle a,b mid 2a=2b=0,, a^2=a,, b^2=b,,ab=a,, ba=brangle.$ We study a special construction of self-orthogonal codes over $E,$ based on combinatorial matrices related to two-class association schemes, Strongly Regular Graphs (SRG), and Doubly Regular Tournaments (DRT). We construct quasi self-dual codes over $E,$ and Type IV codes, that is, quasi self-dual codes whose all codewords have even Hamming weight. All these codes can be represented as formally self-dual additive codes over $F_4.$ The classical invariant theory bound for the weight enumerators of this class of codesimproves the known bound on the minimum distance of Type IV codes over $E.$
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