Capacity of Time-Slotted ALOHA Packetized Multiple-Access Systems Over the AWGN Channel

Abstract

We study different notions of capacity for time-slotted ALOHA systems. In these systems multiple users synchronously send packets in a bursty manner over a common additive white Gaussian noise (AWGN) channel. The users do not coordinate their transmissions, which may collide at the receiver. For such a system we define both single-slot capacity and multiple-slot capacity. We then construct a coding and decoding scheme for single-slot capacity that achieves any rate within this capacity region. This coding and decoding scheme for a single time slot combines aspects of multiple access rate splitting and of broadcast codes for degraded AWGN channels. This design allows some bits to be reliably received even when collisions occur, and more bits to be reliably received in the absence of collisions. The exact number of bits reliably received under both of these scenarios is part of the code design process, which we optimize to maximize the expected rate in each slot.Next, we examine the behavior of the system asymptotically over multiple slots. We show that there exist coding and decoding strategies such that regardless of the burstiness of the * Laboratory for Information and Decision Systems, Massachusetts Institute of Technology (medard@mit.edu). traffic, the system is stable as long as the average rate of the users is within the multiple access capacity region of the channel. In other words, we show that bursty traffic does not decrease the Cover-Wyner capacity region of the multiple access channel. A vast family of codes, which includes the type of codes we introduce for the single-slot transmission, achieve the capacity region, in a sense we define, for multiple-slot transmissions. These codes are stabilizing, using only local information at each of the individual queues. The use of information regarding other queues or the use of scheduling does not improve the multiple-slot capacity region.

Bounded-Contention Coding for the additive network model

“…Issues of synchronization, SNR determination and identification of users are in practice handled often jointly, since a signature serves for initial synchronization in acquiring the signal of a user, for measuring the received SNR and also for identification of the transmitting user. Finally note that, as long as we have appropriate coding, then the Cover-Wyner region represents the region not only for coordinated transmissions, but also for uncoordinated packetized transmissions, such as exemplified in the classical ALOHA scheme [34]. This result, which may seem counterintuitive, is due in effect to the fact that the system will be readily shown to be stable as long as the individual and sum rates of the Cover-Wyner region will exceed the absolute value of the derivative of an appropriately defined Lyapunov function based on the queue length of a packetized ALOHA system.…”

Random Access: An Information-Theoretic Perspective

“…Definition 5.5: A rate tuple {r i (A)} is said to be achievable if there exists a sequence of n codes such that the average probability of a decoding error (17) for each decoder vanishes to zero as the block size n tends to infinity. …”

“…Previously, Medard et al [17] studied the performance of Gaussian superposition coding in a two-user additive white Gaussian noise (AWGN) system, but did not investigate the information-theoretic optimality of such a scheme. In the present work, we present coding schemes with guaranteed gaps to the information-theoretic capacity.…”

On multiple access random medium access control

“…This result suggests that the total throughput increases with N as opposed to Aloha where the total throughput decreases with N. Finally, we consider extension to rate splitting [6]. Rate splitting has been applied to Aloha in [7], [8]. We propose a new class of rate splitting algorithm which generalizes that in [8].…”