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Register a new userCapacity Regions of Two-Receiver Broadcast Erasure Channels with Feedback and Memory
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Michael Heindlmaier
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state 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.
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The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. 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 feedback sequences. 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.
This paper focuses on the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper provides a comparative overview of this channel model along the following lines: First, inner and outer bounds to the capacity region (set of achievable rates with backlogged arrivals) are presented: a) a new outer bound based on the idea of the physically degraded broadcast channel, and b) an inner bound of the LPE-BC with COF for the case of two users and any number of layers. Next, an inner bound on the stability region (set of exogenous arrival rates for which packet arrival queues are stable) for the same model is derived. The capacity region inner bound generalizes past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of inter-user and inter-layer network coding retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. For the case of $K = 2$ users and $Q geq 1$ layers, the inner bounds to the capacity region and the stability region coincide; both strategically employ the novel retransmission protocol. For the case of $Q = 2$ layers, sufficient conditions are derived by Fourier-Motzkin elimination for the inner bound on the stability region to coincide with the capacity outer bound, thus showing that in those cases the capacity and stability regions coincide.
Jolfaei et al. used feedback to create transmit signals that are simultaneously useful for multiple users in a broadcast channel. Later, Georgiadis and Tassiulas studied erasure broadcast channels with feedback, and presented the capacity region under certain assumptions. These results provided the fundamental ideas used in communication protocols for networks with delayed channel state information. However, to the best of our knowledge, the capacity region of erasure broadcast channels with feedback and with a common message for both receivers has never been presented. This latter problem shows up as a sub-problem in many multi-terminal communication networks such as the X-Channel, and the two-unicast problem. In this work, we present the capacity region of the two-user erasure broadcast channels with delayed feedback, private messages, and a common message. We consider arbitrary and possibly correlated erasure distributions. We develop new outer-bounds that capture feedback and quantify the impact of delivering a common message on the capacity region. We also propose a transmission strategy that achieves the outer-bounds. Our transmission strategy differs from prior results in that to achieve the capacity, it creates side-information at the weaker user such that the decodability is ensured even if we multicast the common message with a rate higher than its link capacity.
In this paper, the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of emph{inter-user & inter-layer network coding} retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. Analytical and numerical examples show that the proposed outer bound is optimal for some LPE-BCs.
In this paper, a class of broadcast interference channels (BIC) is investigated, where one of the two broadcast receivers is subject to interference coming from a point-to-point transmission. For a general discrete memoryless broadcast interference channel (DM-BIC), an achievable scheme based on message splitting, superposition and binning is proposed and a concise representation of the corresponding achievable rate region R is obtained. Two partial-order broadcast conditions interference-oblivious less noisy and interference-cognizant less noisy are defined, thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account. Under these conditions, a reduced form of R is shown to be equivalent to a rate region based on a simpler scheme, where the broadcast transmitter uses only superposition. Furthermore, if interference is strong for the interference-oblivious less noisy DM-BIC, the capacity region is given by the aforementioned two equivalent rate regions. For a Gaussian broadcast interference channel (GBIC), channel parameters are categorized into three regimes. For the first two regimes, which are closely related to the two partial-order broadcast conditions, achievable rate regions are derived by specializing the corresponding achievable schemes of DM-BICs with Gaussian input distributions. The entropy power inequality (EPI) based outer bounds are obtained by combining bounding techniques for a Gaussian broadcast channel (GBC) and a Gaussian interference channel (GIC). These inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions. For the remaining complementing regime, inner and outer bounds are also provided.
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