Completion time in broadcast channel and interference channel

Consider a multi-user channel, where each user has a large but non-replenishable bit pool to transmit. Completion time refers to the number of channel uses spent by each user to complete its transmission. In this paper, an information-theoretic formulation of completion time is based on the concept of constrained rates, which are defined over possibly different number of channel uses. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users’ completion times. For a two-user multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time regions (or inner and outer bounds) are established for a two-user Gaussian broadcast channel and a two-user Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally, optimization problems of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel are solved, demonstrating the utility of the completion time approach.

In this paper, we first look at the achievable rate regions of the Gaussian Multiple Access Channel (G-MAC) and Gaussian Broadcast Channel (G-BC) when discrete constellations are transmitted. Focusing on the two-user case and assuming uncoded Pulse Amplitude Modulation (PAM), we show that the rate regions of G-MAC and G-BC can be improved by power conservation at the transmitter, a factor ignored in the earlier derived rate regions. We then further investigate duality between the G-MAC and the G-BC and show that a rate pair achieved in the G-MAC can be translated to a rate pair in the dual G-BC, such that the equal sum power constraint be satisfied. Due to the similarity of the rate expressions to Shannon's capacity formula, for an appropriate choice of signal to noise ratio (SNR) gap, we show that when finite constellations are used for transmission, rate regions of these two channels also have a dual relationship (the known for Gaussian alphabets). The rate region of the G-BC can therefore be characterized from the rate region of the dual G-MAC and vice versa.

In this overview paper, we introduce an application of stochastic orders in wireless communications. In particular, we show how to use stochastic orders to investigate the ergodic capacity results for fast fading Gaussian memoryless multiuser channels when only the statistics of the channel state information are known at the transmitters (CSIT). In general, the characterization of the capacity region of multiuser channels with only statistical CSIT is open. To attain our goal, in this work we resort to classifying the random channels through their probability distributions by which we can obtain the capacity results. To be more precise, we derive sufficient conditions to attain some information theoretic channel orders such as degraded and very strong interference by exploiting the usual stochastic order and exploiting the same marginal property. After that, we apply the developed scheme to Gaussian interference channels and Gaussian broadcast channels. We also extend the framework to channels with multiple antennas. Possible scenarios for channel enhancement under statistical CSIT are also discussed. Several practical examples such as Rayleigh fading and Nakagami-m fading, etc., illustrate the application of the derived results.

In this paper, an efficient user selection method for traditional iterative Water-Filling algorithm in Gaussian multiuser broadcast channel is developed to reduce the computational complexity. The new algorithm selects some effective users from all the users, and then allocates the entire power among the selected users applying Water-Filling algorithm. The vector Gaussian broadcast channel and the matrix Gaussian broadcast channel are considered respectively and the corresponding user selection methods are proposed. Theoretical analysis and simulation results show that the new algorithm can significantly improve the computational efficiency of the traditional iterative Water-Filling power allocation and can obtain almost the optimal sum capacity.

This paper revisits the interference channels under strong interference and very strong interference, for both discrete memoryless and Gaussian channels. In particular, it is shown that for the classical definitions, while the conditions of strong interference for discrete and Gaussian cases coincide with each other, those of very strong interference are not consistent with each other in terms of mutual information inequalities. Based on this observation, a new class of discrete memoryless interference channels under very strong interference is introduced whose capacity region is characterized. This new class of channels is consistent with the Gaussian interference channel under very strong interference. Moreover, this new class of interference channels is not a subset of any existing classes of discrete memoryless interference channels with known capacity region.

The N +1 user, 1 ×N single-input multiple-output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The sum capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. On the achievability side, an interesting conclusion is that the GDOF regime where treating interference as noise is found to be optimal in the two-user interference channel, does not appear in the N + 1 user, 1 × N SIMO case. On the converse side, new multiuser outer bounds emerge out of this work that do not follow directly from the two-user case. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.

A Gaussian interference channel (IC) with a relay is considered. The relay is assumed to operate over an orthogonal band with respect to the underlying IC, and the overall system is referred to as IC with an out-of-band relay (IC-OBR). The system can be seen as operating over two parallel interference-limited channels: The first is a standard Gaussian IC and the second is a Gaussian relay channel characterized by two sources and destinations communicating through the relay without direct links. We refer to the second parallel channel as OBR Channel (OBRC). The main aim of this work is to identify conditions under which optimal operation, in terms of the capacity region of the IC-OBR, entails either signal relaying and/or interference forwarding by the relay, with either a separable or nonseparable use of the two parallel channels, IC, and OBRC. Here, “separable” refers to transmission of independent information over the two constituent channels. For a basic model in which the OBRC consists of four orthogonal channels from sources to relay and from relay to destinations (IC-OBR Type-I), a condition is identified under which signal relaying and separable operation is optimal. This condition entails the presence of a relay-to-destinations capacity bottleneck on the OBRC and holds irrespective of the IC. When this condition is not satisfied, various scenarios, which depend on the IC channel gains, are identified in which interference forwarding and nonseparable operation are necessary to achieve optimal performance. In these scenarios, the system exploits the “excess capacity” on the OBRC via interference forwarding to drive the IC-OBR system in specific interference regimes (strong or mixed). The analysis is then turned to a more complex IC-OBR, in which the OBRC consists of only two orthogonal channels, one from sources to relay and one from relay to destinations (IC-OBR Type-II). For this channel, some capacity resuls are derived that parallel the conclusions for IC-OBR Type-I and point to the additional analytical challenges.

We study the Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and private messages. We first obtain an outer bound for the capacity region of the two-user discrete memoryless broadcast channel with common and private messages. We next show that if jointly Gaussian random variables are sufficient to evaluate this outer bound for the Gaussian MIMO broadcast channel, the dirty-paper coding (DPC) region is the capacity region of the Gaussian MIMO broadcast channel with common and private messages. However, we can evaluate only a loosened version of this outer bound, which yields the result that extending the DPC region in the common message rate direction by a fixed amount is an outer bound for the capacity region of the Gaussian MIMO broadcast channel with common and private messages. However, this fixed amount, i.e., the gap, is not finite for all channels. We derive the necessary and sufficient conditions for this gap to be finite.

It has long been observed that cooperation between users in a communication network can improve its performance. Unfortunately, in practical ad-hoc networks, cooperation links can be unreliable, and in many cases part of the users in the system cannot be updated about their availability. In such a case we need robust coding schemes that exploit the cooperation links if they are present, but can still operate if cooperation is not possible. In this work we study the general broadcast channel with degraded message sets and cooperation link that may be absent, and derive its capacity region under such uncertainty conditions. A generalization of this model is studied, where the cooperation link capacity is one of k possible values, and its capacity region is derived. We examine the situation where the cooperation link capacity is random and suggest the following performance criterion: maximize the average rate of one user, subject to a constraint on the rate of the other user and the requirement that the system will operate in any realization of the (random) cooperation link. As examples to illustrate our results, the Gaussian broadcast channel is extensively examined, and its capacity is derived for the various cooperation models and assumptions suggested throughout.

Analog transmission of correlated information over Gaussian broadcast channels (BCs) using analog joint source–channel coding (JSCC) is addressed. This communication strategy has attractive advantages, such as low complexity, minimal delay, graceful degradation, and adaptation to time-varying environments. In this paper, we focus on the optimization of parametric continuous mappings that satisfy individual quality of service requirements over Gaussian BCs. This optimization is based on the balancing of the user distortions to ensure the feasibility of the resulting optimization problems. An analysis of the overall distortion corresponding to the considered mappings is carried out to design algorithms that determine the optimal values for the mappings parameters. Results show that the proposed analog JSCC scheme provides near optimal performance and an adequate balancing of the individual distortions.

Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC).This paper presents a DPC based code design for BCs.We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user.For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance.We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user.We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC.At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary.We also consider the performance of our scheme over a slow fading BC.For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively.

In a K-pair-user two-way Gaussian interference channel (IC), 2K messages and 2K transmitters/receivers form a Gaussian K-user IC in the forward direction (K messages) and another Gaussian K-user IC in the backward direction (K messages) which operate simultaneously in full-duplex mode. All nodes are permitted to interact, i.e. adapt current channel inputs to past received signals. We derive a new sum-rate outer bound for linear deterministic and Gaussian noise channels allowing for interaction, but show that for symmetric scenarios and certain interference regimes (moderately weak and strong), non-interactive schemes achieve to within a constant gap of this outer bound. That is, interaction for symmetric channels in certain interference regimes may only improve the sum-rate by a constant number of bits per channel use.

We consider two-user MIMO broadcast and interference channels in which confidential messages intended for each receiver are kept secret from the other receiver. The confidential secrecy rates are nonconvex functions of transmit covariance matrices, which makes it intractable to find optimal transmit covariance matrices analytically. In the MIMO broadcast channels, we prove the weighted secrecy sum rate maximization has zero duality gap and KKT conditions are necessary conditions for the optimal solution. We apply the block successive lower-bound maximization technique to nonconvex weighted secrecy sum rate maximization problems. We also derive numerical algorithms for MIMO interference channels and Gaussian wiretap channels with a cooperative jammer. Every limit point achieved by the proposed algorithms is a local optimal solution that satisfies the KKT conditions. Numerical results show that the proposed algorithms outperform existing suboptimal algorithms in terms of secrecy rates.

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis-based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error-rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi-static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

The capacity region of the symmetric multiple-input single-output (MISO) and single-input multiple-output (SIMO) Gaussian interference channels is studied. We characterize a low interference regime, where treating interference as noise using Gaussian inputs achieves sum capacity for both MISO and SIMO channels. We also characterize strong and very strong interference regimes for SIMO channel and a very strong interference regime for MISO channel.