Browsing by Author "Goldsmith, Andrea"

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A Unified Graphical Approach to Random Coding for Single-Hop Networks
(2016-01-01)
Rini, Stefano
;
Goldsmith, Andrea
;
電信工程研究所
;
Institute of Communications Engineering
A unified graphical approach to random coding for any memoryless, single-hop, K-user channel with or without common information is defined through two steps. The first step is user virtualization. Each user is divided into multiple virtual sub-users according to a chosen rate-splitting strategy. This results in an enhanced channel with a possibly larger number of users for which more coding possibilities are available and for which common messages to any subset of users can be encoded. Following user virtualization, the message of each user in the enhanced model is coded using a chosen combination of coded time-sharing, superposition coding, and joint binning. A graph is used to represent the chosen coding strategies. Nodes in the graph represent codewords, while edges represent coding operations. This graph is used to construct a graphical Markov model, which illustrates the statistical dependence among codewords that can be introduced by the superposition coding or joint binning. Using this statistical representation of the overall codebook distribution, the error probability of the code is shown to vanish through a unified analysis. The rate bounds that define the achievable rate region are obtained by linking the error analysis to the properties of the graphical Markov model. This proposed framework makes it possible to numerically obtain an achievable rate region by specifying a user virtualization strategy and describing a set of coding operations. The union of these rate regions defines the maximum achievable rate region of our unified coding strategy. The achievable rates obtained based on this unified graphical approach to random coding encompass the best random coding achievable rates for all memoryless single-hop networks known to date, including broadcast, multiple access, interference, and cognitive radio channels, as well as new results for topologies not previously studied, as we illustrate with several examples.
A Unified Graphical Approach to Random Coding for Single-Hop Networks
(2016-01)
Rini, Stefano
;
Goldsmith, Andrea
;
電信工程研究所
;
Institute of Communications Engineering
A unified graphical approach to random coding for any memoryless, single-hop, K-user channel with or without common information is defined through two steps. The first step is user virtualization. Each user is divided into multiple virtual sub-users according to a chosen rate-splitting strategy. This results in an enhanced channel with a possibly larger number of users for which more coding possibilities are available and for which common messages to any subset of users can be encoded. Following user virtualization, the message of each user in the enhanced model is coded using a chosen combination of coded time-sharing, superposition coding, and joint binning. A graph is used to represent the chosen coding strategies. Nodes in the graph represent codewords, while edges represent coding operations. This graph is used to construct a graphical Markov model, which illustrates the statistical dependence among codewords that can be introduced by the superposition coding or joint binning. Using this statistical representation of the overall codebook distribution, the error probability of the code is shown to vanish through a unified analysis. The rate bounds that define the achievable rate region are obtained by linking the error analysis to the properties of the graphical Markov model. This proposed framework makes it possible to numerically obtain an achievable rate region by specifying a user virtualization strategy and describing a set of coding operations. The union of these rate regions defines the maximum achievable rate region of our unified coding strategy. The achievable rates obtained based on this unified graphical approach to random coding encompass the best random coding achievable rates for all memoryless single-hop networks known to date, including broadcast, multiple access, interference, and cognitive radio channels, as well as new results for topologies not previously studied, as we illustrate with several examples.
DISTRIBUTED CONVEX OPTIMIZATION WITH LIMITED COMMUNICATIONS
(2019-01-01)
Rao, Milind
;
Rini, Stefano
;
Goldsmith, Andrea
;
交大名義發表
;
National Chiao Tung University
In this paper, a distributed convex optimization algorithm, termed distributed coordinate dual averaging (DCDA) algorithm, is proposed. The DCDA algorithm addresses the scenario of a large distributed optimization problem with limited communication among nodes in the network. Currently known distributed subgradient descent methods, such as the distributed dual averaging or the distributed alternating direction method of multipliers, assume that nodes can exchange messages of large cardinality. Such an assumption on the network communication capabilities is not valid in many scenarios of practical relevance. To address this setting, we propose the DCDA algorithm as a distributed convex optimization algorithm in which the communication between nodes in each round is restricted to a fixed number of dimensions. We bound the rate of convergence under different communication protocols and network architectures for this algorithm. We also consider the extensions to the cases of imperfect gradient knowledge and when transmitted messages are corrupted by additive noise or are quantized. Numerical simulations demonstrating the performance of DCDA in these different settings are also provided.
Distributed Sub-gradient Algorithms with Limited Communications
(2019-01-01)
Rini, Stefano
;
Rao, Milind
;
Goldsmith, Andrea
;
交大名義發表
;
National Chiao Tung University
We consider the distributed convex optimization scenario in which nodes in a network collectively find the minimum of a function utilizing only local communications and computations. Various sub-gradient algorithms have been developed for this optimization setting for the case in which the global function factorizes as the sum of local functions to be distributed to the nodes in network, including the distributed (i) online gradient descent, (ii) Nesterov gradient descent, and (iii) dual averaging algorithms. Generally speaking, these subgradient algorithms assume that, in each communication round, nodes can exchange messages of size comparable to that of the optimization variable. For many high-dimensional optimization problems, this communication requirement is beyond the capabilities of the communication network supporting the distributed optimization. For this reason, we propose a dimensionality reduction technique based on random projections to adapt these distributed optimization algorithms to networks with communication links of limited capacity. In particular, we analyze the performance of the proposed dimensionality reduction technique for the three algorithms above, i.e. (i)-(iii). Numerical simulations are presented that illustrate the performance of the proposed approach for these three algorithms.
On the Capacity of the Multiantenna Gaussian Cognitive Interference Channel
(2014-11-01)
Rini, Stefano
;
Goldsmith, Andrea
;
電信工程研究所
;
Institute of Communications Engineering
The capacity of the multiantenna Gaussian cognitive interference channel is studied. The cognitive interference channel is a variation of the classical two-users interference channel in which one of the transmitters, the cognitive transmitter, is also provided with the message of the second transmitter, the primary transmitter. We study the capacity of the multiple-input multiple-output Gaussian model, that is the channel in which the inputs are vectors and the outputs are obtained as linear combinations of the channel inputs plus an additive complex Gaussian noise. This channel models a wireless scenario in which transmitters and receivers have multiple antennas. For this channel, we derive capacity to within an additive gap, that is we show that inner and outer bounds to capacity lie to within a constant distance of each other. The gap between the inner and outer bounds depends on the number of antennas at the cognitive receiver and both bounds can be easily evaluated by considering jointly Gaussian inputs. We also derive capacity to within a constant multiplicative factor of two, that is we show that the ratio between inner and outer bound is at most two. The additive gap well-characterizes the capacity at high SNR, while the multiplicative gap is useful at low SNR. We also derive the exact capacity for a subset of the "strong interference" regime: in this subset, the primary transmitter can decode the cognitive message without loss of optimality. This new capacity result extends and generalizes previously known capacity results, in particular, the capacity in the "very strong interference" and the "primary decodes cognitive" regimes.