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Register a new userInteractive Computation of Type-Threshold Functions in Collocated Broadcast-Superposition Networks
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Added by
Chien-Yi Wang
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on type-threshold functions, e.g., the maximum and indicator functions. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates converge to zero as the number of sensors increases. This paper considers two network models reflecting both the broadcast and superposition properties of wireless channels: the collocated linear finite field network and the collocated Gaussian network. A general multi-round coding scheme exploiting not only the broadcast property but particularly also the superposition property of the networks is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity.
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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 consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two decoders. Decoder 1 and decoder 2 have access to $X$ and $Y$ respectively, and they want to compute two functions $f(X,Y)$ and $g(X,Y)$ respectively using the encoded message and their respective side information. We want to find the optimum (minimum) encoding rate under the zero error and $epsilon$-error (i.e. vanishing error) criteria. For the special case of this problem with $f(X,Y) = Y$ and $g(X,Y) = X$, we show that the $epsilon$-error optimum rate is also achievable with zero error. This result extends to a more general `complementary delivery index coding problem with arbitrary number of messages and decoders. For other functions, we show that the cut-set bound is achievable under $epsilon$-error if $X$ and $Y$ are binary, or if the functions are from a special class of `compatible functions which includes the case $f=g$.
This paper reviews the theoretical and practical principles of the broadcast approach to communication over state-dependent channels and networks in which the transmitters have access to only the probabilistic description of the time-varying states while remaining oblivious to their instantaneous realizations. When the temporal variations are frequent enough, an effective long-term strategy is adapting the transmission strategies to the systems ergodic behavior. However, when the variations are infrequent, their temporal average can deviate significantly from the channels ergodic mode, rendering a lack of instantaneous performance guarantees. To circumvent a lack of short-term guarantees, the {em broadcast approach} provides principles for designing transmission schemes that benefit from both short- and long-term performance guarantees. This paper provides an overview of how to apply the broadcast approach to various channels and network models under various operational constraints.
Future wireless access networks will support simultaneously a large number of devices with heterogeneous service requirements. These include data rates, error rates, and latencies. While there exist achievable rate and capacity results for Gaussian broadcast channels in the asymptotic regime, the characterization of second-order achievable rate regions for different blocklength constraints are not available. Therefore, we investigate a two-user Gaussian broadcast channel (GBC) with heterogeneous blocklength constraints under a maximal input power constraint and an average error probability constraint. Unlike the traditional GBC where two users have the same blocklength constraints, here the user with higher output SNR has a shorter blocklength constraint. We show that with sufficiently large output SNR, the stronger user can invoke the technique named early decoding (ED) to decode the interference. Then the successive interference cancellation (SIC) can proceed. This leads to an improved achievable rate region compared to the state of the art. To achieve it, we derive an explicit lower bound on the necessary number of received symbols for a successful ED, using an independent and identically distributed Gaussian input. A second-order rate of the weaker user who suffers from an SNR change due to the heterogeneous blocklength constraint, is also derived. We then formulate the rate region of the considered setting with individual and also sum power constraints and compare to that of the hybrid non-orthogonal multiple access (HNOMA) scheme. Numerical results show that ED has a larger rate region than HNOMA partly when the gain of the better channel is sufficiently larger than the weaker one. Under the considered setting, about 7-dB SNR gain can be achieved. This makes ED with SIC a promising technique for future wireless network.
We study noisy broadcast networks with local cache memories at the receivers, where the transmitter can pre-store information even before learning the receivers requests. We mostly focus on packet-erasure broadcast networks with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. We present lower and upper bounds on the capacity-memory tradeoff of this network. The lower bound is achieved by a new joint cache-channel coding idea and significantly improves on schemes that are based on separate cache-channel coding. We discuss how this coding idea could be extended to more general discrete memoryless broadcast channels and to unequal cache sizes. Our upper bound holds for all stochastically degraded broadcast channels. For the described packet-erasure broadcast network, our lower and upper bounds are tight when there is a single weak receiver (and any number of strong receivers) and the cache memory size does not exceed a given threshold. When there are a single weak receiver, a single strong receiver, and two files, then we can strengthen our upper and lower bounds so as they coincide over a wide regime of cache sizes. Finally, we completely characterise the rate-memory tradeoff for general discrete-memoryless broadcast channels with arbitrary cache memory sizes and arbitrary (asymmetric) rates when all receivers always demand exactly the same file.
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