Results 1  10
of
18
Lattice codes for the Gaussian relay channel: DecodeandForward and CompressandForward
, 2013
"... Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
(Show Context)
Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that lattice codes may be used to achieve the same performance as known i.i.d. Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks. In particular, we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decodeandforward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present two examples of how this DF scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known Gaussian random coding techniques in multisource relay channels. That is, we derive a new achievable rate region for the twoway relay channel with direct links and compare it to existing schemes, and derive a new achievable rate region for the multiple access relay channel. We furthermore present a lattice compressandforward (CF) scheme for the Gaussian relay channel which exploits a lattice Wyner–Ziv binning scheme and achieves the same rate as the Cover–El Gamal CF rate evaluated for Gaussian random codes. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks.
Approximate ergodic capacity of a class of fading 2user 2hop networks
, 2012
"... We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a constant num ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a constant number of bits/sec/Hz, independent of signaltonoise ratio. The achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into K pairs, and interference is neutralized separately by each pair of relays. For K =1, we previously proved a gap of 4 bits/sec/Hz for i.i.d. uniform phase fading and approximately 4.7 bits/sec/Hz for i.i.d. Rayleigh fading. In this paper, we give a result for general K. In the limit of large K, we characterize the ergodic sum capacity within 4((log π) − 1) ≃ 2.6 bits/sec/Hz for i.i.d. uniform phase fading and 4(4 − log 3π) ≃ 3.1 bits/sec/Hz for i.i.d. Rayleigh fading.
On the Ergodic Rate for ComputeandForward
"... Abstract—A key issue in computeandforward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i] n to a l ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Abstract—A key issue in computeandforward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z[i] n to a line in the ndimensional complex Euclidean space, within a bounded region around the origin. We then use the complex version of the LLL lattice basis reduction (CLLL) algorithm to provide a reduced complexity suboptimal solution as well as an upper bound to the minimum distance of the lattice point from the line. Using this bound we are able to find a lower bound to the ergodic rate and a union bound estimate on the error performance of a lattice constellation used for lattice network coding. We compare performance of the CLLL with a more complex iterative optimization method as well as with a simple quantized search. Simulations show how CLLL can trade some performance for a lower complexity. Index Terms—Ergodic rate, computeandforward, CLLL algorithm, quantized error, successive refinement. I.
Computation in Multicast Networks: Function Alignment and Converse Theorems
, 2012
"... The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an iden ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an identical function of the original messages. For a countably infinite class of twotransmitter tworeceiver singlehop linear deterministic networks, the computing capacity is characterized for a linear function (modulo2 sum) of Bernoulli sources. Inspired by the geometric concept of interference alignment in networks, a new achievable coding scheme called function alignment is introduced. A new converse theorem is established that is tighter than cutset based and genieaided bounds. Computation (vs. communication) over multicast networks requires additional analysis to account for multiple receivers sharing a network’s computational resources. We also develop a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality. The decomposition theorem provides a conceptuallys impler algebraic proof of achievability that generalizes to Ltransmitter Lreceiver networks.
Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach
, 2011
"... A classical result in undirected wireline networks is the near optimality of routing (flow) for multipleunicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
A classical result in undirected wireline networks is the near optimality of routing (flow) for multipleunicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we “extend” the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: local physicallayer schemes combined with global routing. We use the reciprocity of the wireless channel critically in this result. Our formal result is in the context of channel models for which “good ” local schemes, that achieve the cutset bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks). Layered architectures, common in the engineeringdesign of wireless networks, can have nearoptimal performance if the locality over which physicallayer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected “polymatroidal” network, for which we establish a maxflow mincut approximation theorem.
Multisession Function Computation and Multicasting in Undirected Graphs
"... In the function computation problem, certain nodes of an undirected graph have access to independent data, while some other nodes of the graph require certain functions of the data; this model, motivated by sensor networks and cloud computing, is the focus of this paper. We study the maximum rates ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In the function computation problem, certain nodes of an undirected graph have access to independent data, while some other nodes of the graph require certain functions of the data; this model, motivated by sensor networks and cloud computing, is the focus of this paper. We study the maximum rates at which function computation is possible on a capacitated graph; the capacities on the edges of the graph impose constraints on the communication rate. We consider a simple class of computation strategies based on Steinertree packing (socalled computation trees), which does not involve block coding and has minimal delay. With a single terminal requiring function computation, computation trees are known to be optimal when the underlying graph is itself a directed tree, but have arbitrarily poor performance in general directed graphs. Our main result is that computation trees are near optimal for a wide class of function computation requirements even at multiple terminals in undirected graphs. The key technical contribution involves connecting approximation algorithms for Steiner cuts in undirected graphs to the function computation problem. Furthermore, we show that existing algorithms for Steiner tree packings allow us to compute approximately optimal packings of computation trees in polynomial time. We also show a close connection between the function computation problem and a communication problem involving multiple multicasts.
Capacity Approximations for Gaussian Relay Networks
, 2014
"... Consider a Gaussian relay network where a source node communicates to a destination node with the help of several layers of relays. Recent work has shown that compressandforward based strategies can achieve the capacity of this network within an additive gap. Here, the relays quantize their receiv ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Consider a Gaussian relay network where a source node communicates to a destination node with the help of several layers of relays. Recent work has shown that compressandforward based strategies can achieve the capacity of this network within an additive gap. Here, the relays quantize their received signals at the noise level and map them to random Gaussian codebooks. The resultant gap to capacity is independent of the SNRs of the channels in the network and the topology but is linear in the total number of nodes. In this paper, we provide an improved lower bound on the rate achieved by compressandforward based strategies (noisy network coding in particular) in arbitrary Gaussian relay networks, whose gap to the cutset upper bound depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut of the network. We illustrate that for many networks this refined lower bound can lead to a better approximation of the capacity. In particular, we demonstrate that it leads to a logarithmic rather than linear capacity gap in the total number of nodes for certain classes of layered networks. The improvement comes from quantizing the received signals of the relays at a resolution decreasing with the total number of nodes in the network. This suggests that the ruleofthumb in literature of quantizing the received signals at the noise level can be highly suboptimal.
Optimized Noisy Network Coding for Gaussian Relay
 Networks, International Zurich Seminar on Communications
, 2014
"... Abstract—In this paper, we provide an improved lower bound on the rate achieved by noisy network coding in arbitrary Gaussian relay networks, whose gap to the cutset upper bound depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut o ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract—In this paper, we provide an improved lower bound on the rate achieved by noisy network coding in arbitrary Gaussian relay networks, whose gap to the cutset upper bound depends on the network not only through the total number of nodes but also through the degrees of freedom of the min cut of the network. We illustrate that for many networks this refined lower bound can lead to a better approximation of the capacity. The improvement is based on a judicious choice of the quantization resolutions at the relays. I.