For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR)=K/2log(SNR)+o(log(SNR)) . Thus, the K user time-varying interference channel almost surely has K/2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values.

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Interference Alignment and Degrees of Freedom of the $K$ -User Interference Channel

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

Gaussian Interference Channel Capacity to Within One Bit

The capacity of the two-user Gaussian interference channel has been open for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high SNR regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

The capacity region of the two-user Gaussian interference channel (IC) is studied. Three classes of channels are considered: weak, one-sided, and mixed Gaussian ICs. For the weak Gaussian IC, a new outer bound on the capacity region is obtained that outperforms previously known outer bounds. The sum capacity for a certain range of channel parameters is derived. For this range, it is proved that using Gaussian codebooks and treating interference as noise are optimal. It is shown that when Gaussian codebooks are used, the full Han-Kobayashi achievable rate region can be obtained by using the naive Han-Kobayashi achievable scheme over three frequency bands (equivalently, three subspaces). For the one-sided Gaussian IC, an alternative proof for the Sato's outer bound is presented. We derive the full Han-Kobayashi achievable rate region when Gaussian codebooks are utilized. For the mixed Gaussian IC, a new outer bound is obtained that outperforms previously known outer bounds. For this case, the sum capacity for the entire range of channel parameters is derived. It is proved that the full Han-Kobayashi achievable rate region using Gaussian codebooks is equivalent to that of the one-sided Gaussian IC for a particular range of channel parameters.

Capacity Bounds for the Gaussian Interference Channel

In this correspondence, we derive a simplified description of the Han-Kobayashi rate region for the general interference channel. Using this result, we establish that the recently discovered Chong-Motani-Garg rate region is a new representation of the Han-Kobayashi region. Moreover, a tighter bound for the cardinality of the time-sharing auxiliary random variable emerges from our simplified description.

On The Han–Kobayashi Region for theInterference Channel

WiFi offloading is regarded as one of the most promising techniques for dealing with the explosive data increase in cellular networks due to its high data transmission rate and low requirement on devices. In this paper, we investigate the mobile data offloading problem through a third-party WiFi access point (AP) for a cellular mobile system. From the cellular operator's perspective, by assuming a usage-based charging model, we formulate the problem as a utility maximization problem. In particular, we consider three scenarios: 1) successive interference cancellation (SIC) available at both the base station (BS) and the AP; 2) SIC available at neither the BS nor the AP; and 3) SIC available at only the BS. For scenario 1, we show that the utility maximization problem can be solved by considering its relaxation problem, and the proposed data offloading scheme is near-optimal when the number of users is large. For scenario 2, we prove that with high probability the optimal solution is One-One-Association, i.e., one user connects to the BS and one user connects to the AP. For scenario 3, we show that with high probability there is at most one user connecting to the AP, and all the other users connect to the BS. By comparing these three scenarios, we prove that SIC decoders help the cellular operator maximize its utility. To relieve the computational burden of the BS, we propose a threshold-based distributed data offloading scheme. We show that the proposed distributed scheme performs well if the threshold is properly chosen.

Mobile Data Offloading Through A Third-Party WiFi Access Point: An Operator's Perspective

This correspondence studies coding strategies for a three-node relay channel. We start with the basic coding strategies of Cover and El Gamal: the relay decodes the source message and forward it to the destination (cooperation); the relay transmits its compressed channel outputs to the destination (facilitation); or the relay superimposes both cooperation and facilitation (generalized). In this paper, two new generalized strategies superimposing cooperation and facilitation are introduced and investigated on the general relay channel. The first strategy makes use of sequential backward (SeqBack) decoding while the second strategy makes use of simultaneous backward (SimBack) decoding. The achievable rate for the second strategy is shown to include that of the generalized strategy of Cover and El Gamal. Assuming zero-mean, jointly Gaussian random variables, the two new strategies give higher achievable rates than the generalized strategy of Cover and El Gamal for certain parameters on the Gaussian relay channel

Generalized Backward Decoding Strategies for the Relay Channel

We consider the two-user "Z" channel (ZC), where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver), while the other sender transmits information to both receivers. The complete characterization of the discrete memoryless ZC remains unknown to date. For the Gaussian ZC, the capacity has only been established for a crossover link gain of 1. In this work, we study both the discrete memoryless ZC and the Gaussian ZC. We first establish achievable rates for the general discrete memoryless ZC. The coding strategy uses rate-splitting and superposition coding at the sender with information for both receivers. At the receivers, we use joint decoding. We then specialize the rates obtained to two different types of degraded discrete memoryless ZCs and also derive respective outer bounds to their capacity regions. We show that as long as a certain condition is satisfied, the achievable rate region is the capacity region for one type of degraded discrete memoryless ZC. The results are then extended to the two-user Gaussian ZC with different crossover link gains. We determine an outer bound to the capacity region of the Gaussian ZC with strong crossover link gain and establish the capacity region for moderately strong crossover link gain

Capacity Theorems for the “Z” Channel

The capacity region of a class of discrete memoryless interference channels with common information is established. The setup is similar to the class of deterministic interference channels without common information studied by El Gamal and Costa, which was later extended to the class of deterministic interference channels with common information. In this paper, certain conditions that were originally imposed by El Gamal and Costa are relaxed and it is shown, by a specific example, that this new class of interference channels is strictly larger than the class of deterministic interference channels previously studied. In fact, the result of this paper is obtained by combining the class of deterministic interference channels with the class of discrete memoryless interference channels with strong interference. Hence, it also includes the capacity region of the class of discrete memoryless interference channels with strong interference as a special case.

Hon-Fah Chong

Papers

On The Han–Kobayashi Region for theInterference Channel

Mobile Data Offloading Through A Third-Party WiFi Access Point: An Operator's Perspective

Generalized Backward Decoding Strategies for the Relay Channel

Capacity Theorems for the “Z” Channel

The Capacity Region of a Class of Semideterministic Interference Channels