On the inner and outer bounds for 2-receiver discrete memoryless broadcast channels

We study the best known general inner bound[MAR '79] and outer bound[N-EG'07] for the capacity region of the two user discrete memory less channel. We prove that a seemingly stronger outer bound is identical to a weaker form of the outer bound that was also presented in [N-EG'07]. We are able to further express the best outer bound in a form that is computable, i.e. there are bounds on the cardinalities of the auxiliary random variables. The inner and outer bounds coincide for all channels for which the capacity region is known and it is not known whether the regions described by these bounds are same or different. We present a channel, where assuming a certain conjecture backed by simulations and partial theoretical results, one can show that the bounds are different.Comment: 4 pages, 2 figures, ITA Workshop San Diego 200

Discrete Memoryless Interference and Broadcast Channels with Confidential Messages: Secrecy Rate Regions

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers with information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a double-binning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, the two bound bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.Comment: to appear Special Issue of IEEE Transactions on Information Theory on Information Theoretic Securit

Multi-receiver Wiretap Channel with Public and Confidential Messages

We study the multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless multi-receiver wiretap channel as well as its Gaussian multi-input multi-output (MIMO) instance. First, we consider the degraded discrete memoryless channel, and obtain an inner bound for the capacity region by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound, and show that this outer bound partially matches the inner bound, providing a partial characterization for the capacity region of the degraded channel model. Second, we obtain an inner bound for the general, not necessarily degraded, discrete memoryless channel by using Marton's inner bound, superposition coding, rate-splitting and binning. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel. Finally, we provide an inner bound for the capacity region of the general, not necessarily degraded, Gaussian MIMO multi-receiver wiretap channel.Comment: Submitted to IEEE Transactions on Information Theory, June 201

Capacity Bounds and a Certain Capacity Region for Special Three-Receiver Broadcast Channels with Side Information

The fact that the results for 2-receiver broadcast channels (BCs) are not generalized to the 3-receiver ones is of information theoretical importance. In this paper we study two classes of discrete memoryless BCs with non-causal side information (SI), i.e. multilevel BC (MBC) and 3-receiver less noisy BC. First, we obtain an achievable rate region and a capacity outer bound for the MBC. Second, we prove a special capacity region for the 3-receiver less noisy BC. Third, the obtained special capacity region for the 3-receiver less noisy BC is extended to continuous alphabet fading Gaussian version. It is worth mentioning that the previous works are special cases of our works.Comment: 24 pages, 2 figures, Submitted to IET Communications Journal for possible publicatio

Multiple-Access Relay Wiretap Channel

In this paper, we investigate the effects of an additional trusted relay node on the secrecy of multiple-access wiretap channel (MAC-WT) by considering the model of multiple-access relay wiretap channel (MARC-WT). More specifically, first, we investigate the discrete memoryless MARC-WT. Three inner bounds (with respect to decode-forward (DF), noise-forward (NF) and compress-forward (CF) strategies) on the secrecy capacity region are provided. Second, we investigate the degraded discrete memoryless MARC-WT, and present an outer bound on the secrecy capacity region of this degraded model. Finally, we investigate the Gaussian MARC-WT, and find that the NF and CF strategies help to enhance Tekin-Yener's achievable secrecy rate region of Gaussian MAC-WT. Moreover, we find that if the noise variance of the transmitters-relay channel is smaller than that of the transmitters-receiver channel, the DF strategy may also enhance Tekin-Yener's achievable secrecy rate region of Gaussian MAC-WT, and it may perform even better than the NF and CF strategies.Comment: Accepted by IEEE Transactions on Information Forensics & Security. arXiv admin note: text overlap with arXiv:1312.6784; text overlap with arXiv:cs/0612044 by other author

Distortion Bounds for Source Broadcast Problems

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for the degraded broadcast channel case. When specialized to the Gaussian or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also generate some new results. Besides, we also extend the inner bound and outer bounds to the Wyner-Ziv source broadcast problem, i.e., source broadcast with side information available at decoders. Some new bounds are obtained when specialized to the Wyner-Ziv Gaussian and Wyner-Ziv binary cases.Comment: Accepted by IEEE Transactions on Information Theor

Bounds and Capacity Theorems for Cognitive Interference Channels with State

A class of cognitive interference channel with state is investigated, in which two transmitters (transmitters 1 and 2) communicate with two receivers (receivers 1 and 2) over an interference channel. The two transmitters jointly transmit a common message to the two receivers, and transmitter 2 also sends a separate message to receiver 2. The channel is corrupted by an independent and identically distributed (i.i.d.) state sequence. The scenario in which the state sequence is noncausally known only at transmitter 2 is first studied. For the discrete memoryless channel and its degraded version, inner and outer bounds on the capacity region are obtained. The capacity region is characterized for the degraded semideterministic channel and channels that satisfy a less noisy condition. The Gaussian channels are further studied, which are partitioned into two cases based on how the interference compares with the signal at receiver 1. For each case, inner and outer bounds on the capacity region are derived, and partial boundary of the capacity region is characterized. The full capacity region is characterized for channels that satisfy certain conditions. The second scenario in which the state sequence is noncausally known at both transmitter 2 and receiver 2 is further studied. The capacity region is obtained for both the discrete memoryless and Gaussian channels. It is also shown that this capacity is achieved by certain Gaussian channels with state noncausally known only at transmitter 2.Comment: Submitted to the IEEE Transactions on Information Theor

On the Capacity of the Cognitive Interference Channel with a Common Cognitive Message

In this paper the cognitive interference channel with a common message, a variation of the classical cognitive interference channel in which the cognitive message is decoded at both receivers, is studied. For this channel model new outer and inner bounds are developed as well as new capacity results for both the discrete memoryless and the Gaussian case. The outer bounds are derived using bounding techniques originally developed by Sato for the classical interference channel and Nair and El Gamal for the broadcast channel. A general inner bound is obtained combining rate-splitting, superposition coding and binning. Inner and outer bounds are shown to coincide in the "very strong interference" and the "primary decodes cognitive" regimes. The first regime consists of channels in which there is no loss of optimality in having both receivers decode both messages while in the latter regime interference pre-cancellation at the cognitive receiver achieves capacity. Capacity for the Gaussian channel is shown to within a constant additive gap and a constant multiplicative factor.Comment: submitted to Transactions on Emerging Telecommunications Technologies (ETT). arXiv admin note: substantial text overlap with arXiv:1202.097

Multiple Access Channel with Common Message and Secrecy constraint

In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a special case called the switch channel. As well, for a Gaussian version of MAWC-CM, we derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, we illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.Comment: 11 pages, 7 figures, Accepted in IET Communication

Degrees of Freedom of the Broadcast Channel with Hybrid CSI at Transmitter and Receivers

In general, the different links of a broadcast channel may experience different fading dynamics and, potentially, unequal or hybrid channel state information (CSI) conditions. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that CSI is stale or unavailable at the transmitter. Disparity of link fading dynamics in the presence of CSI limitations can be modeled by a multi-user broadcast channel with both non-identical link fading block lengths as well as dissimilar link CSIR/CSIT conditions. This paper investigates a MISO broadcast channel where some receivers experience longer coherence intervals (static receivers) and have CSIR, while some other receivers experience shorter coherence intervals (dynamic receivers) and do not enjoy free CSIR. We consider a variety of CSIT conditions for the above mentioned model, including no CSIT, delayed CSIT, or hybrid CSIT. To investigate the degrees of freedom region, we employ interference alignment and beamforming along with a product superposition that allows simultaneous but non-contaminating transmission of pilots and data to different receivers. Outer bounds employ the extremal entropy inequality as well as a bounding of the performance of a discrete memoryless multiuser multilevel broadcast channel. For several cases, inner and outer bounds are established that either partially meet, or the gap diminishes with increasing coherence times.Comment: 36 pages, 8 figures, submitted to IEEE Transactions on Information Theor