Capacity Regions of Two-Receiver Broadcast Erasure Channels With Feedback and Memory

Abstract

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finitestate Markov chain representing a channel state. Two scenarios are considered: (i) when the transmitter has causal knowledge of the channel state (i.e., the state is visible), and (ii) when the channel state is unknown at the transmitter, but observations of it are available at the transmitter through feedback (i.e., the state is hidden). In both scenarios, matching outer and inner bounds on the rates of communication are derived and the capacity region is determined. It is shown that similar results carry over to channels with memory and delayed feedback and memoryless compound channels with feedback.When the state is visible, the capacity region has a single-letter characterization and is in terms of a linear program. Two optimal coding schemes are devised that use feedback to keep track of the sent/received packets via a network of queues: a probabilistic scheme and a deterministic backpressure-like algorithm. The former bases its decisions solely on the past channel state information and the latter follows a max-weight queue-based policy. The performance of the algorithms are analyzed using the frameworks of rate stability in networks of queues, max-flow min-cut duality in networks, and finite-horizon Lyapunov drift analysis.When the state is hidden, the capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past L acknowledgments and its achievable rate region approaches the capacity region exponentially fast in L. The second algorithm is a backpressure-like algorithm that performs optimally in the long run.Michael Heindlmaier is with the

Three-terminal Erasure Source-Broadcast with Feedback

“…Previously, there have been two primary techniques in deriving a rate region for queue-based coding schemes, which we have found to be insufficient for our purposes. The first technique was derived from a channel coding problem involving erasure channels with feedback and memory [5]. In [5], the authors use a queue stability criterion to set up a system of inequalities involving the achievable rates and flow variables that represent the number of packets that are transferred between queues.…”

“…The first technique was derived from a channel coding problem involving erasure channels with feedback and memory [5]. In [5], the authors use a queue stability criterion to set up a system of inequalities involving the achievable rates and flow variables that represent the number of packets that are transferred between queues. When this technique is applied to the chaining algorithm of Section III-B2 however, we find that our system of inequalities is over-specified.…”

Benefits of Coding on Age of Information in Broadcast Networks

“…In this work, we aim to shed light on the interplay between AoI and (channel/network) coding in the context of broadcast packet erasure channels (BPECs) with feedback. BPECs and their variants have been investigated in previous work such as [35]- [39] and rate-optimal coding algorithms are designed using (network) coding ideas. The key idea is due to [35] where it is shown that the entire capacity region of two-user BPECs with feedback can be attained by XORing overheard packets.…”

Exploiting Location Information to Enhance Throughput in Downlink V2I Systems

“…Although the theoretical result is well beyond the V2I scenario, we do believe that this scenario is one of the few cases for which the underlying assumptions of the general result can be realistic. In contrast to previous works on similar setups [9], [10] which use queuing-theoretic tools, we adopt an Information-Theoretic (IT) approach to derive the achievable rate region. Our scheme is based on standard IT tools such as random coding arguments, block Markov coding, joint source-channel coding and typicality decoding.…”