Discrete Memoryless Interference Channel Research Articles

Treating Interference as Noise Is Optimal for Covert Communication Over Interference Channels

We study the covert communication over K-user-pair discrete memoryless interference channels (DM-ICs) with a warden. It is assumed that the warden's channel output distribution induced by K “off” input symbols, which are sent when no communication occurs, is not a convex combination of those induced by any other combination of input symbols (otherwise, the square-root law does not hold). We derive the exact covert capacity region and show that a simple point-to-point based scheme with treating interference as noise is optimal. In addition, we analyze the secret key length required for the reliable and covert communication with the desired rates, and present a channel condition where a secret key between each user pair is unnecessary. The results are extended to the Gaussian case and the case with multiple wardens.

Code Design for Discrete Memoryless Interference Channels

We study the design of explicit and implementable codes for the two-user discrete memoryless interference channels (DMICs). We consider Han–Kobayashi (HK) type encoding where both public and private messages are used and propose coding techniques utilizing a serial concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. Since exact analytical treatment of the BCJR decoder for the inner trellis-based code appears infeasible, we analytically investigate the iterative decoding process in the asymptotic regime where the probability of decoding error tends to zero. Based on this approximate analysis, we derive a stability condition for this type of a concatenated coding scheme for the first time in the literature. Furthermore, we use an extrinsic information transfer analysis to design the outer LDPC code while fixing the inner NLTC, and utilize the derived stability condition to accelerate the design process and to avoid code ensembles that potentially produce high error floors. Via numerical examples, we demonstrate that our designed codes achieve rate pairs close the optimal boundary of the HK subregion, which cannot be obtained without the use of nonlinear codes. Also, we verify that the estimated thresholds of the designed codes via finite block length simulations and show that our designs significantly outperform the point-to-point optimal codes, hence demonstrating the need for designs specifically tailored for DMICs.

The Discrete Memoryless Interference Channel with One-Sided Generalized Feedback and Secrecy

We study the interference channel with one-sided generalized feedback and secrecy requirement. In our model Message 1 that is known just to Encoder 1 should be decoded by both receivers. Message 2—known only to Encoder 2—should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an outer bound on the capacity-equivocation region for this model that is valid for the ”noisy cribbing” regime. The gap between this upper bound and the inner bound reported before is just in the Markov conditions satisfied by one of the auxiliary random variables. Furthermore, we consider a simplified causal cognitive interference model: the interference channel with a cribbing encoder. We show that when, conditioned on the input of Encoder 1, the interference channel is degraded our outer bound is tight thereby establishing the capacity-equivocation region for this case.

Multicoding Schemes for Interference Channels

The best known inner bound for the two-user discrete memoryless interference channel is the Han–Kobayashi rate region. The coding schemes that achieve this region are based on rate-splitting and superposition coding. In this paper, we develop a multicoding scheme to achieve the same rate region. A key advantage of the multicoding nature of the proposed coding scheme is that it can be naturally extended to more general settings, such as when encoders have state information or can overhear each other. In particular, we extend our coding scheme to characterize the capacity region of the state-dependent deterministic Z-interference channel when noncausal state information is available at the interfering transmitter. We specialize our results to the case of the linear deterministic model with ON/OFF interference, which models a wireless system where a cognitive transmitter is noncausally aware of the times it interferes with a primary transmission. For this special case, we provide an explicit expression for the capacity region and discuss some interesting properties of the optimal strategy. We also extend our multicoding scheme to find the capacity region of the deterministic Z-interference channel when the signal of the interfering transmitter can be overheard at the other transmitter (also known as unidirectional partial cribbing).

An Achievable Rate Region for the Three-User Interference Channel Based on Coset Codes

We consider the problem of communication over a three user discrete memoryless interference channel ($3-$IC). The current known coding techniques for communicating over an arbitrary $3-$IC are based on message splitting, superposition coding and binning using independent and identically distributed (iid) random codebooks. In this work, we propose a new ensemble of codes - partitioned coset codes (PCC) - that possess an appropriate mix of empirical and algebraic closure properties. We develop coding techniques that exploit algebraic closure property of PCC to enable efficient communication over $3-$IC. We analyze the performance of the proposed coding technique to derive an achievable rate region for the general discrete $3-$IC. Additive and non-additive examples are identified for which the derived achievable rate region is the capacity, and moreover, strictly larger than current known largest achievable rate regions based on iid random codebooks.

Communication With Disturbance Constraints

Motivated by the broadcast view of the interference channel, the new problem of communication with disturbance constraints is formulated. The rate-disturbance region is established for the single constraint case and the optimal encoding scheme turns out to be the same as the Han-Kobayashi scheme for the two user-pair interference channel. This result is extended to the Gaussian vector (multiple-input and multiple-output) case. For the case of communication with two disturbance constraints, inner and outer bounds on the rate-disturbance region for a deterministic model are established. The inner bound is achieved by an encoding scheme that involves rate splitting, Marton coding, and superposition coding, and is shown to be optimal in several nontrivial cases. This encoding scheme can be readily applied to discrete memoryless interference channels and motivates a natural extension of the Han-Kobayashi scheme to more than two user pairs.

Capacity Bounds and Sum Rate Capacities of a Class of Discrete Memoryless Interference Channels

This paper studies the capacity of a class of discrete memoryless interference channels (DMICs), where interference is defined analogous to that of a Gaussian interference channel with one-sided weak interference. The sum-rate capacity of this class of channels is determined. As with the Gaussian case, the sum-rate capacity is achieved by letting the transceiver pair subject to interference communicate at a rate such that its message can be decoded at the unintended receiver using single user detection. It is also established that this class of DMICs is equivalent in capacity region to certain degraded interference channels. This allows the construction of capacity outer-bounds using the capacity regions of associated degraded broadcast channels. The same technique is then used to determine the sum-rate capacity of DMICs with mixed interference as defined in this paper. The obtained capacity bounds and sum-rate capacities are used to resolve the capacities of several new DMICs.

Three‐user interference channel with common information: a rate splitting‐based achievability scheme

In this study, the three-user interference channel (IFC) with common information is considered, where each receiver decode not only the private message from the intended transmitter but also the common messages from the non-intended transmitters by applying a simultaneous decoding scheme. An achievable rate region is presented using rate splitting and superposition encoding at the transmitters and simultaneous joint decoding at the receivers in which the transmitters cooperatively send the split messages which allows the interference cancellation at the receivers. The implicit form of the achievable rate region is also extended to K-user IFC with common information. Finally the inner bound derived for the three-user discrete memoryless IFC with common information is generalised to the Gaussian case and is evaluated in a numerical example.

Interference Channel With a Causal Relay Under Strong and Very Strong Interference

In this paper, we study a two-user interference channel with a causal relay, where the relay's transmit symbol depends not only on its past received symbols, but also on its present received symbol. This is an appropriate model for studying amplify-and-forward type relaying when the bandwidth delay-spread product is much smaller than one. For the discrete memoryless interference channel with a causal relay, we derive a genie-aided outer bound. For the Gaussian interference channel with a causal relay, we define strong and very strong interference conditions and propose an outer bound for each case. We also propose an achievable scheme based on instantaneous amplify-and-forward (AF) relaying for the Gaussian interference channel with a causal relay and so it achieves capacity under some conditions. Our result extends the previous result by El Gamal, Hassanpour, and Mammen on the optimality of instantaneous AF relaying for the Gaussian relay channel with a causal relay to that of the Gaussian interference channel with a causal relay under strong and very strong interference.

The Discrete Memoryless Interference Channel With One-Sided Generalized Feedback

We study the interference channel with one-sided generalized feedback and secrecy requirements. In our model, Message 1 that is known just to Encoder 1 should be decoded by both receivers. Message 2 - known only to Encoder 2 - should be decoded by Decoder 2 and kept as secret as possible from Decoder 1. The uncertainty of Decoder 1 about Message 2 is measured by means of the equivocation rate. In addition, a noisy feedback is provided to Encoder 2. We derive an achievable rate-equivocation region for this model and an outer bound for the “noisy cribbing” regime without secrecy, the gap being the Markov conditions satisfied by one of the auxiliary random variables. Furthermore, we consider a simplified causal cognitive interference model: the interference channel with a cribbing encoder. We derive an inner bound on the rate region for this model and prove that when the interference channel is degraded conditionally on the input of Encoder 1, our inner bound is tight.

Interference Channels With Arbitrarily Correlated Sources

Communicating arbitrarily correlated sources over interference channels is considered in this paper. A sufficient condition is found for lossless transmission of a pair of correlated sources over a discrete memoryless interference channel. With independent sources, the sufficient condition reduces to the Han-Kobayashi achievable rate region for interference channels. For sources with a special correlation structure, the proposed region reduces to the known achievable region for interference channels with common information. Moreover, the proposed coding scheme is optimal for transmitting such set of correlated sources over a class of deterministic interference channels as defined in El Gamal and Costa, 1982.

Analysis of Deterministic Binary Interference Channels Via a General Outer Bound

We present a new outer bound for the general two-user discrete memoryless interference channel (IFC) and use it to establish the capacity region of the binary erasure IFC, whose determination was left open in . We also show that there are essentially two deterministic binary IFCs, in addition to the binary erasure IFC, whose capacity regions are not obvious from previous results. We determine the capacity region of one of these and apply the aforementioned general outer bound to obtain the best available bound on the maximum achievable sum-rate for the other. We also show that the new general outer bound is tight for one-sided deterministic IFCs that belong to the class studied by El Gamal and Costa.

The Capacity Region of a Class of Semideterministic Interference Channels

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.

Capacity of a Class of Cognitive Radio Channels: Interference Channels With Degraded Message Sets

This correspondence is motivated by two different scenarios. The first is a cognitive radio system where a cognitive radio knows a ldquodumbrdquo radio's message and the second is a sensor network in a correlated field where sensors possessing a nested message structure assist one another's information transmission. Both scenarios are modeled using the framework of discrete memoryless interference channels with degraded message sets (IFC-DMS), a setting where one of the two transmitters in an interference channel knows both the messages to be conveyed to the receivers. Both inner and outer bounds are provided for a class of IFC-DMS channels. The case of the Gaussian interference channels with degraded message sets is also investigated. In this case, achievability and converse arguments are presented for a class of ldquoweakrdquo interference channels, resulting in a characterization of this class' capacity region.

Outer Bounds on the Capacity of Gaussian Interference Channels

Two outer bounds on the capacity region of the two-user Gaussian interference channel (IFC) are derived. The idea of the first bound is to let a genie give each receiver just enough information to decode both messages. This bound unifies and improves the best known outer bounds of Sato and Carleial. Furthermore, the bound extends to discrete memoryless IFCs and is shown to be equivalent to another bound of Carleial. The second bound follows directly from existing results of Costa and Sato and possesses certain optimality properties for weak interference.

The capacity region of the discrete memoryless interference channel with strong interference (Corresp.)

The capacity region of the discrete memoryless interference channel with strong interference is established.

Outer bounds on the capacity of interference channels (Corresp.)

New outer bounds are demonstrated for the capacity regions of discrete memoryless interference channels and Gaussian interference channels. The bound for discrete channels coincides with the capacity region in special cases. The bound for Gaussian channels improves previous knowledge when the interference is of medium strength.

The capacity region of a class of deterministic interference channels (Corresp.)

The capacity region of a class of deterministic discrete memoryless interference channels is established. In this class of channels the outputs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y_{2}</tex> are (deterministic) functions of the inputs <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{2}</tex> such that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(Y_{1}|X_{1})=H(V_{2})</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(Y_{2}|X_{2})=H(V_{l})</tex> for all product probabiliW distributions on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{1}X_{2}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{1}</tex> is a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{2}</tex> a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{2}</tex> . The capacity, region for the case in which <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{2} \equiv 0</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y_{1}</tex> depends randomly on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X_{1}</tex> is also obtained and illustrated with an example.

Two-user interference channels with correlated information sources

Inner and outer bounds on the capacity region of two-user discrete memoryless interference channels (IFC) are obtained in the communication situation where private messages are sent by each sender as well as a common message by both senders to its corresponding receiver. A limiting expression for the capacity region is also derived. Special cases of the IFC are considered.

Interference channels

An interference channel is a communication medium shared by M sender-receiver pairs. Transmission of information from each sender to its corresponding receiver interferes with the communications between the other senders and their receivers. This corresponds to a frequent situation in communications, and defines an M -dimensional capacity region. In this paper, we obtain general bounds on the capacity region for discrete memoryless interference channels and for linear-superposition interference channels with additive white Gaussian noise. The capacity region is determined in special cases.