Capacity Region Of Broadcast Channel Research Articles

Blahut-Arimoto Algorithms for Inner and Outer Bounds on Capacity Regions of Broadcast Channels.

The celebrated Blahut-Arimoto algorithm computes the capacity of a discrete memoryless point-to-point channel by alternately maximizing the objective function of a maximization problem. This algorithm has been applied to degraded broadcast channels, in which the supporting hyperplanes of the capacity region are again cast as maximization problems. In this work, we consider general broadcast channels and extend this algorithm to compute inner and outer bounds on the capacity regions. Our main contributions are as follows: first, we show that the optimization problems are max-min problems and that the exchange of minimum and maximum holds; second, we design Blahut-Arimoto algorithms for the maximization part and gradient descent algorithms for the minimization part; third, we provide convergence analysis for both parts. Numerical experiments validate the effectiveness of our algorithms.

Time-Division is Optimal for Covert Communication Over Some Broadcast Channels

We consider a covert communication scenario where a transmitter wishes to communicate simultaneously to two legitimate receivers while ensuring that the communication is not detected by an adversary, the warden. The legitimate receivers and the adversary observe the transmission from the transmitter via a three-user discrete or Gaussian memoryless broadcast channel. We focus on the case where the “no-input” symbol is not redundant, i.e., the output distribution at the warden induced by the no-input symbol is not a mixture of the output distributions induced by other input symbols, so that the covert communication is governed by the square root law, i.e., at most $\Theta (\sqrt {n})$ bits can be transmitted over $n$ channel uses. We show that for such a setting, a simple time-division strategy achieves the optimal throughputs for a non-trivial class of broadcast channels; this is not true for communicating over broadcast channels without the covert communication constraint. Our result implies that a code that uses two separate optimal point-to-point codes each designed for the constituent channels and each used for a fraction of the time is optimal in the sense that it achieves the best constants of the $\sqrt {n}$ -scaling for the throughputs. Our proof strategy combines several elements in the network information theory literature, including concave envelope representations of the capacity regions of broadcast channels and El Gamal’s outer bound for more capable broadcast channels.

On the Achievable Rate Region of NOMA Under Outage Probability Constraints

In this letter, we study the outage achievable rate region of non-orthogonal multiple access (NOMA), which is defined as the achievable rate region when all users are required to satisfy their outage probability constraints. First, we formally define the outage achievable rate region of NOMA assuming a slow fading channel model. Then, we introduce a successive interference cancelation (SIC) order under the assumption of statistical channel information. Under this assumption, we find that the outage capacity region of broadcast channel (BC) is also ϵ-achievable by NOMA, which requires the use of SIC, though the definition of outage in NOMA is different from that in BC. Combining the converse result, we get a full characterization of the outage achievable rate region of NOMA, which also shows the optimality of the SIC order used here. Then, we give some discussions about power allocation and the practical insights derived from the characterization. Finally, numerical simulations are provided.

Optimal and Near-Optimal Online Strategies for Energy Harvesting Broadcast Channels

We consider an energy harvesting broadcast channel where a transmitter powered by energy harvested from the environment serves data to two receivers on the downlink. Energy harvests occur randomly over time as an independent and identically distributed (i.i.d.) random process; the battery at the transmitter in which the harvested energy is stored is of finite size. We focus on online transmission schemes where the transmitter knows the energy arrivals only causally as they happen. We first consider the case where the energy arrivals follow a Bernoulli distribution, where the incoming energy is either zero or it fills the battery completely. For this case, we determine the optimum online strategy that allocates power over time and between users optimally. We note that the optimum total transmit power is not equal to the optimum single-user transmit power as it depends on the receiver noise variance; this is unlike the offline problem, where the optimum total transmit power in the broadcast channel equals the optimum single-user transmit power. We then consider the case of general i.i.d. energy arrivals, and propose a sub-optimum strategy coined fractional power constant cut-off (FPCC) policy. We develop a lower bound for the performance of the proposed FPCC policy. In addition, we develop a universal upper bound for the broadcast channel capacity region that depends only on the average recharge rate. We show that the FPCC policy is near-optimal in that it yields rates that are within a constant gap from the developed upper bound, and therefore, from the actual capacity region, for all system parameters.

On Marton's Inner Bound and Its Optimality for Classes of Product Broadcast Channels

Marton's inner bound is the tightest known inner bound on the capacity region of the broadcast channel. It is not known, however, if this bound is tight in general. One approach to settle this key open problem in network information theory is to investigate the multiletter extension of Marton's bound, which is known to be tight in general. This approach has become feasible only recently through the development of a new method for bounding cardinalities of auxiliary random variables by Gohari and Anantharam. This paper undertakes this long overdue approach to establish several new results, including 1) establishing the optimality of Marton's bound for new classes of product broadcast channels, 2) showing that the best-known outer bound by Nair and El Gamal is not tight in general, and 3) finding sufficient conditions for a global maximizer of Marton's bound that imply that the 2-letter extension does not increase the achievable rate. Motivated by the new capacity results, we establish a new outer bound on the capacity region of product broadcast channels.

Optimal offline broadcast scheduling with an energy harvesting transmitter

We consider an energy harvesting transmitter broadcasting individual data to two receivers. Data packets intended for each user are assumed to arrive at arbitrary but known instants. The goal is to minimize the total transmission time of the packets arriving within a certain time window, using the energy harvested during this time. Energy harvests are also modelled to occur at known discrete instants. An achievable rate region with structural properties satisfied by the two-user additive white Gaussian noise broadcast channel capacity region is assumed. Structural properties of power and rate allocations are established, as well as the uniqueness of the optimal policy. An iterative algorithm, DuOpt, is devised for efficient solution of this offline problem. DuOpt is compared with the sequential unconstrained minimization (SUMT) solution technique on randomly generated problem instances and is observed to solve the problem two orders of magnitude faster on average than SUMT.

Optimal Packet Scheduling on an Energy Harvesting Broadcast Link

The minimization of transmission completion time for a given number of bits per user in an energy harvesting communication system, where energy harvesting instants are known in an offline manner is considered. An achievable rate region with structural properties satisfied by the 2-user AWGN Broadcast Channel capacity region is assumed. It is shown that even though all data are available at the beginning, a non-negative amount of energy from each energy harvest is deferred for later use such that the transmit power starts at its lowest value and rises as time progresses. The optimal scheduler ends the transmission to both users at the same time. Exploiting the special structure in the problem, the iterative offline algorithm, FlowRight, from earlier literature, is adapted and proved to solve this problem. The solution has polynomial complexity in the number of harvests used, and is observed to converge quickly on numerical examples.

Variable-Rate Channel Capacity

This paper introduces the notions of variable-to-fixed and fixed-to-variable channel capacity, without feedback. For channels that satisfy the strong converse, these notions coincide with the conventional Shannon capacity. For channels that do not behave ergodically, the conventional fixed-rate Shannon capacity only depends on least-favorable channel conditions, while the variable-rate capacity notions are able to capture the whole range of channel states and their likelihood, even in the absence of any side information about channel state at the transmitter. Particular emphasis is placed on memoryless channels that are governed by finitely valued states. We show that (single-user) variable-to-fixed channel capacity is intimately connected to the capacity region of broadcast channels with degraded message sets, and we give an expression for the fixed-to-variable capacity.

Rate Regions for Relay Broadcast Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner bound reduces to an inner bound on the capacity region of broadcast channels that includes an inner bound of Marton, and Gel'fand and Pinsker. The outer bound reduces to a new outer bound on the capacity region of broadcast channels that generalizes an outer bound of Marton to include a common message, and that generalizes an outer bound of Gel'fand and Pinsker to apply to general discrete memoryless broadcast channels. The proof for the outer bound simplifies the proof of Gel'fand and Pinsker that was based on a recursive approach. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels. </para>

The capacity region of broadcast channels with intersymbol interference and colored Gaussian noise

We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models.

Partial feedback for two-way and broadcast channels

Two examples are presented showing that partial feedback can increase the capacity regions of broadcast channels and also the capacity regions even of those two-way channels which give equal outputs on both terminals.

An outer bound to the capacity region of broadcast channels (Corresp.)

An outer bound to the capacity region of broadcast channels for the transmission of separate messages is derived. This bound improves upon Cover's outer bound by taking into consideration the total throughput information rate and the fact that the capacity region depends only on the marginal transition probabilities.