graph matching algorithms. However, hypergraph matching provides a throughput gain that increases with the number of sinks. Our results suggest that it is more advantageous to use hypergraph matching when the multicast group is large.
Table 3.2: Comparison of different algorithms in random networks with 10 nodes, 1 source and 2 sinks
HMsub HMalg1 HMalg2 HMalg3 HMalg5,1 Mopt Mlgd
Rate gain over Mlgd 9.45% 5.74% 4.32% -6.46% 5.44% 2.30% - Average w/wHMsub 1 0.9749 0.9593 0.8584 0.9714 0.9623 0.9593
Average time-slots - 13.38 13.46 5.88 9.63 - 6.15
Table 3.3: Comparison of different algorithms in random networks with 10 nodes, 1 source and 4 sinks
HMsub HMalg1 HMalg2 HMalg3 HMalg5,1 Mopt Mlgd
Rate gain over Mlgd 15.13% 8.78% 4.99% -1.42% 8.23% 4.49% - Average w/wHMsub 1 0.9737 0.9697 0.9310 0.9729 0.9707 0.9697
Average time-slots - 10.98 11.83 5.90 9.33 - 6.26
Table 3.4: Comparison of different algorithms in random networks with 10 nodes, 1 source and 6 sinks
HMsub HMalg1 HMalg2 HMalg3 HMalg5,1 Mopt Mlgd
Rate gain over Mlgd 23.47% 13.05% 5.50% 1.18% 12.15% 6.47% - Average w/wHMsub 1 0.9787 0.9776 0.9459 0.9785 0.9760 0.9776
Average time-slots - 10.40 11.95 5.91 9.10 - 6.57
Table 3.5: Comparison of different algorithms in random networks with 15 nodes, 1 source and 3 sinks
HMsub HMalg1 HMalg2 HMalg3 HMalg5,1 Mopt Mlgd
Rate gain over Mlgd 13.07% 7.79% 3.89% 1.39% 6.45% 4.73% - Average w/wHMsub 1 0.9813 0.9809 0.9769 0.9544 0.9806 0.9689
Average time-slots - 15.75 15.41 6.99 11.73 - 7.32
Chapter 4
Multiple Access Random Medium Access Control
In this chapter, we develop a new class of random medium access control protocol, which allows each user to transmit at multiple data rates. By using successive in- terference cancellation, multiple packets can be received simultaneously. To achieve the desired throughput optimal equilibrium in a distributed fashion, a game-theoretic framework is proposed. We investigate the design of random access games, charac- terize their equilibria, study their dynamics, and propose distributed algorithms to achieve the equilibria.
4.1 Introduction
The medium access control (MAC) layer decides when competing nodes may access the shared medium. Different from schedule-based medium access requiring a central authority, multiple nodes share the medium by using random access in contention based MAC. Most conventional random access protocols such as Aloha [6] and carrier sense multiple access (CSMA) [49] assume simple collision models, where the channel is noiseless, and reception failure is caused by collisions among users. Though the analysis and protocol design are simple in the collision model, the maximum achiev- able throughput of this model is limited. With more sophisticated physical layer approaches, simultaneous reception of multiple packets is possible, for example, by using code division multiple access (CDMA) and multiuser detection. In order to
represent such random access systems, a model for a channel with multipacket re- ception capability (MPR) with its stability property has been developed in [31]. A decentralized MAC protocol is proposed in [32]. In both works [31, 32], it is shown that the achievable throughput by using MPR is higher than that by using Aloha.
In MPR, each node transmits only at a single rate. On the other hand, a multiple access system withN users and one base station can be considered as a multiple access channel (mac). In the Gaussian noise case, if each user transmits with power P and the noise power at the base station is σ2, the maximum information theoretic sum rate of all users is 12log 1 + N Pσ2
, which can be achieved with multirate transmission capability and successive interference cancelation (SIC) [22].
In this chapter, we develop a new class of MAC protocol by applying a SIC based approach at the MAC layer. The MPR model in [31, 32] is generalized by allowing each user to transmit at different data rates chosen randomly from an appropriately determined set of rates. By using SIC, multiple packets can be received simultane- ously.
In slotted Aloha type networks with Gaussian channels, we show that the achiev- able sum rate of the new protocol using decentralized control is at least a constant frac- tion of that achievable by using centralized control, i.e., C2 log 1 + N Pσ2
, 0< C < 1, where C can be interpreted as the distributive loss due to contention and lack of cooperation between users. This result suggests that the total throughput increases with N as opposed to Aloha where the total throughput decreases with N.
The proposed protocol is also extended to CSMA. We consider a half duplex single cell wireless LAN. By maximizing the achievable sum rate, we can obtain a desired transmission probability for each data rate, which depends on the number of users in the network.
In order to adaptively adjust the channel access probability as nodes join and leave, we consider a general game-theoretic model, called random access game, whose equilibrium is the desired throughput maximizing point. Dynamic algorithms such as best response and gradient play are proposed to achieve the equilibrium distributively without the knowledge of the number of nodesN. We show that under mild conditions
S
1S
2(b)
I(X1;Y|X2) I(X2;Y|X1)
I(X2;Y)
I(X1;Y)
Y X
1X
2(a)
A B C
D
Figure 4.1: An illustration example.
all algorithms converge to the unique equilibrium. We also establish the convergence of gradient play under propagation delay and estimation error.
Finally, we consider extension of our multiple access scheme to rate splitting [69].
Rate splitting has been applied to Aloha in [14, 59]. We propose a new class of rate splitting algorithm where each virtual user can transmit at multiple potential transmission rates, which improves the achievable throughput.
Our simulation results support our analysis and show that the proposed proto- col achieves a significant throughput gain over conventional Aloha. In a single cell WLAN, the proposed protocol not only achieves a higher throughput over the stan- dard IEEE 802.11 DCF but also provides a better short term fairness.