5 research outputs found
Cooperative Compute-and-Forward
We examine the benefits of user cooperation under compute-and-forward. Much
like in network coding, receivers in a compute-and-forward network recover
finite-field linear combinations of transmitters' messages. Recovery is enabled
by linear codes: transmitters map messages to a linear codebook, and receivers
attempt to decode the incoming superposition of signals to an integer
combination of codewords. However, the achievable computation rates are low if
channel gains do not correspond to a suitable linear combination. In response
to this challenge, we propose a cooperative approach to compute-and-forward. We
devise a lattice-coding approach to block Markov encoding with which we
construct a decode-and-forward style computation strategy. Transmitters
broadcast lattice codewords, decode each other's messages, and then
cooperatively transmit resolution information to aid receivers in decoding the
integer combinations. Using our strategy, we show that cooperation offers a
significant improvement both in the achievable computation rate and in the
diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor
Secure Compute-and-Forward in a Bidirectional Relay
We consider the basic bidirectional relaying problem, in which two users in a
wireless network wish to exchange messages through an intermediate relay node.
In the compute-and-forward strategy, the relay computes a function of the two
messages using the naturally-occurring sum of symbols simultaneously
transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the
computed function value is forwarded to the user nodes in an ensuing broadcast
phase. In this paper, we study the problem under an additional security
constraint, which requires that each user's message be kept secure from the
relay. We consider two types of security constraints: perfect secrecy, in which
the MAC channel output seen by the relay is independent of each user's message;
and strong secrecy, which is a form of asymptotic independence. We propose a
coding scheme based on nested lattices, the main feature of which is that given
a pair of nested lattices that satisfy certain "goodness" properties, we can
explicitly specify probability distributions for randomization at the encoders
to achieve the desired security criteria. In particular, our coding scheme
guarantees perfect or strong secrecy even in the absence of channel noise. The
noise in the channel only affects reliability of computation at the relay, and
for Gaussian noise, we derive achievable rates for reliable and secure
computation. We also present an application of our methods to the multi-hop
line network in which a source needs to transmit messages to a destination
through a series of intermediate relays.Comment: v1 is a much expanded and updated version of arXiv:1204.6350; v2 is a
minor revision to fix some notational issues; v3 is a much expanded and
updated version of v2, and contains results on both perfect secrecy and
strong secrecy; v3 is a revised manuscript submitted to the IEEE Transactions
on Information Theory in April 201
Cooperative Strategies for Near-Optimal Computation in Wireless Networks
Computation problems, such as network coding and averaging consen- sus, have become increasingly central to the study of wireless networks. Network coding, in which intermediate terminals compute and forward functions of others’ messages, is instrumental in establishing the capacity of multicast networks. Averaging consensus, in which terminals compute the mean of others’ measurements, is a canonical building block of dis- tributed estimation over sensor networks. Both problems, however, are typically studied over graphical networks, which abstract away the broad- cast and superposition properties fundamental to wireless propagation. The performance of computation in realistic wireless environments, there- fore, remains unclear.
In this thesis, I seek after near-optimal computation strategies under realistic wireless models. For both network coding and averaging con- sensus, cooperative communications plays a key role. For network cod- ing, I consider two topologies: a single-layer network in which users may signal cooperatively, and a two-transmitter, two-receiver network aided by a dedicated relay. In the former topology, I develop a decode-and- forward scheme based on a linear decomposition of nested lattice codes. For a network having two transmitters and a single receiver, the proposed
scheme is optimal in the diversity-multiplexing tradeo↵; otherwise it pro- vides significant rate gains over existing non-cooperative approaches. In the latter topology, I show that an amplify-and-forward relay strategy is optimal almost everywhere in the degrees-of-freedom. Furthermore, for symmetric channels, amplify-and-forward achieves rates near capacity for a non-trivial set of channel gains.
For averaging consensus, I consider large networks of randomly-placed nodes. Under a path-loss wireless model, I characterize the resource de- mands of consensus with respect to three metrics: energy expended, time elapsed, and time-bandwidth product consumed. I show that existing con- sensus strategies, such as gossip algorithms, are nearly order optimal in the energy expended but strictly suboptimal in the other metrics. I propose a new consensus strategy, tailored to the wireless medium and cooperative in nature, termed hierarchical averaging. Hierarchical averaging is nearly order optimal in all three metrics for a wide range of path-loss exponents. Finally, I examine consensus under a simple quantization model, show- ing that hierarchical averaging achieves a nearly order-optimal tradeo↵ between resource consumption and estimation accuracy
Coding and Signal Processing for Secure Wireless Communication
Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel