On the Complexity of Scheduling in Half-Duplex Diamond Networks

We consider an n-relay Gaussian diamond network where a source communicates to a destination with the help of n half-duplex relays. Achieving rates close to the capacity of this network requires to employ all the n relays under an optimal transmit/receive schedule. Even for the moderate values of n, this can have significant operational complexity as the optimal schedule may possibly have 2(n) different states for the network (since each of the relays can be in either transmitting or receiving mode). In this paper, we investigate whether a significant fraction of the network capacity can be achieved by using transmit/receive schedules that have only few active states and by using only few relays. First, we conjecture that the approximately optimal schedule has at most n+1 states instead of the 2(n) possible states. We prove this conjecture for networks of size n

Low Complexity Scheduling and Coding for Wireless Networks

Siddhartha Brahma

The advent of wireless communication technologies has created a paradigm shift in the accessibility of communication. With it has come an increased demand for throughput, a trend that is likely to increase further in the future. A key aspect of these challenges is to develop low complexity algorithms and architectures that can take advantage of the nature of the wireless medium like broadcasting and physical layer cooperation. In this thesis, we consider several problems in the domain of low complexity coding, relaying and scheduling for wireless networks. We formulate the Pliable Index Coding problem that models a server trying to send one or more new messages over a noiseless broadcast channel to a set of clients that already have a subset of messages as side information. We show through theoretical bounds and algorithms, that it is possible to design short length codes, poly-logarithmic in the number of clients, to solve this problem. The length of the codes are exponentially better than those possible in a traditional index coding setup. Next, we consider several aspects of low complexity relaying in half-duplex diamond networks. In such networks, the source transmits information to the destination through

n

half-duplex intermediate relays arranged in a single layer. The half-duplex nature of the relays implies that they can either be in a listening or transmitting state at any point of time. To achieve high rates, there is an additional complexity of optimizing the schedule (i.e. the relative time fractions) of the relaying states, which can be

2^n

in number. Using approximate capacity expressions derived from the quantize-map-forward scheme for physical layer cooperation, we show that for networks with

n\leq 6

relays, the optimal schedule has atmost

n+1

active states. This is an exponential improvement over the possible

2^n

active states in a schedule. We also show that it is possible to achieve at least half the capacity of such networks (approximately) by employing simple routing strategies that use only two relays and two scheduling states. These results imply that the complexity of relaying in half-duplex diamond networks can be significantly reduced by using fewer scheduling states or fewer relays without adversely affecting throughput. Both these results assume centralized processing of the channel state information of all the relays. We take the first steps in analyzing the performance of relaying schemes where each relay switches between listening and transmitting states randomly and optimizes their relative fractions using only local channel state information. We show that even with such simple scheduling, we can achieve a significant fraction of the capacity of the network. Next, we look at the dual problem of selecting the subset of relays of a given size that has the highest capacity for a general layered full-duplex relay network. We formulate this as an optimization problem and derive efficient approximation algorithms to solve them. We end the thesis with the design and implementation of a practical relaying scheme called QUILT. In it the relay opportunistically decodes or quantizes its received signal and transmits the resulting sequence in cooperation with the source. To keep the complexity of the system low, we use LDPC codes at the source, interleaving at the relays and belief propagation decoding at the destination. We evaluate our system through testbed experiments over WiFi.

EPFL2015

Structure of optimal schedules in diamond networks

Siddhartha Brahma, Christina Fragouli

We consider Gaussian diamond networks with n half-duplex relays. At any point of time, a relay can either be in a listening (L) or transmitting (T) state. The capacity of such networks can be approximated to within a constant gap (independent of channel SNRs) by solving a linear program that optimizes over the 2(n) relaying states. We recently conjectured, and proved for the cases of n = 2, 3, that there exist optimal schedules with at most n+1 active states, instead of the possible 2(n). In this paper we develop a computational proof strategy that relies on submodularity properties of information flow across cuts in the network and linear programming duality to resolve the conjecture. We implement the strategy for n = 4, 5, 6 and show that indeed there exist optimal schedules with at most n+1 active states in these cases (1).

Ieee2014