Three-receiver broadcast channels with side information

Hajizadeh, Saeed; Hodtani, Ghosheh Abed

doi:10.1109/isit.2012.6284216

Cited by 8 publications

(5 citation statements)

References 30 publications

(52 reference statements)

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“…Consider ( M ) to be any random variable such that

M false\to X^{n}, S^{n} false\to Y^{n}, Z^{n}

forms a Markov chain, then we have

\begin{matrix} right leftthickmathspace.5em \\ I (Y^{i - 1}; Y_{i} | M, S^{n}) \geq I (Z^{i - 1}; Y_{i} | M, S^{n}) \\ I (Y^{i - 1}; Z_{i} | M, S^{n}) \geq I (Z^{i - 1}; Z_{i} | M, S^{n}) \end{matrix}

where 1 ≤ i ≤ n . Proof of the lemma is identical to what mentioned in [36] and is ignored. Now we start to prove the converse part.…”

Section: 3‐receiver Less Noisy Bc With Non‐causal Simentioning

confidence: 95%

On capacity region of certain classes of three‐receiver broadcast channels with side information

Bahrami

Hodtani

2015

IET Communications

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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. Index TermsThree-receiver broadcast channel, multilevel broadcast channel, less noisy broadcast channel, fading channel. I. INTRODUCTION BROADCAST channel is an important multiuser channel, first introduced by Cover [1]. Bergmans obtained an achievable rate region for degraded 2-receiver BC [2] using superposition coding and Gallager [3] and Ahlswede-Körner [4] showed that it is optimal. Special classes of BCs have been studied in [5] and [6]. By now, the best known capacity bounds for general 2-receiver BC are given by Marton [7] and Nair-El Gamal [8]. The results for BCs with two receivers are not generalizable to the BCs with more than two receivers and finding a closed form result for a broadcast channel with arbitrary number of receivers is not a straightforward problem. So some works focused on some special classes of BCs with more than two receivers such as multilevel broadcast channel [9] and 3-receiver less noisy broadcast channel [10]. For the first time, Borade et al.studied BCs with more than two receivers [11]. They guessed the straightforward extension of capacity region for 2-receiver BC with degraded message sets obtained by Körner and Marton [6], to multilevel broadcast channel, however Nair and El Gamal [9] showed that it is not in general optimal. Later, Nair and Wang [10] obtained the capacity region of the 3-receiver less noisy BC.Sajjad Bahrami is with the ). 2Shannon studied channels with side information (SI) [12], and found the capacity region of the single user channel when causal SI is available at the transmitter. Single user channel, when non-causal SI is available only at the transmitter, was studied by Gel'fand-Pinsker [13]. The results of [13] was generalized by Cover and Chiang [14] to the case where non-causal SI is available at both transmitter and receiver. Also single user channel with partial channel state information at the transmitter (CSIT) was studied in [15]. Multiuser channels e.g. multiple access channels, BCs, interference channels and relay channels in presence of SI were studied in [16], [17], [18] and [19], respectively and some works on multiuser channels with partial SI can be found in [20], [21], [22] and [23]. BC with SI was investigated in [17], in which inner and outer capacity bounds and capacity region for different cases of SI presence in degraded BC were obtained. The authors in [24] ...

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“…Consider ( M ) to be any random variable such that

M false\to X^{n}, S^{n} false\to Y^{n}, Z^{n}

forms a Markov chain, then we have

\begin{matrix} right leftthickmathspace.5em \\ I (Y^{i - 1}; Y_{i} | M, S^{n}) \geq I (Z^{i - 1}; Y_{i} | M, S^{n}) \\ I (Y^{i - 1}; Z_{i} | M, S^{n}) \geq I (Z^{i - 1}; Z_{i} | M, S^{n}) \end{matrix}

where 1 ≤ i ≤ n . Proof of the lemma is identical to what mentioned in [36] and is ignored. Now we start to prove the converse part.…”

Section: 3‐receiver Less Noisy Bc With Non‐causal Simentioning

confidence: 95%

On capacity region of certain classes of three‐receiver broadcast channels with side information

Bahrami

Hodtani

2015

IET Communications

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“…In that case, a confidential message can be encoded such that it can be reliably decoded at its intended destination while revealing almost no information to the eavesdropper. On this basis, physical (PHY) layer security derived from the information-theoretic perspective has attracted much attention recently as a promising approach for protecting against eavesdropping, without significantly increasing computational complexity [4][5][6][7][8]. The basic idea is to exploit the PHY characteristics of the wireless channels in order to mitigate eavesdropping attacks.…”

Section: A Backgroundmentioning

confidence: 99%

On the Security Analysis of a Cooperative Incremental Relaying Protocol in the Presence of an Active Eavesdropper

2019

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Physical layer security offers an efficient means to decrease the risk of confidential information leakage through wiretap links. In this paper, we address the physical-layer security in a cooperative wireless subnetwork that includes a source-destination pair and multiple relays, exchanging information in the presence of a malevolent eavesdropper. Specifically, the eavesdropper is active in the network and transmits artificial noise (AN) with a multiple-antenna transmitter to confound both the relays and the destination. We first analyse the secrecy capacity of the direct source-to-destination transmission in terms of intercept probability (IP) and secrecy outage probability (SOP). A decode-andforward incremental relaying (IR) protocol is then introduced to improve reliability and security of communications in the presence of the active eavesdropper. Within this context, and depending on the availability of channel state information, three different schemes (one optimal and two sub-optimal) are proposed to select a trusted relay to improve the achievable secrecy rate. For each one of these schemes, and for both selection and maximum ratio combining at the destination and eavesdropper, we derive new and exact closed-form expressions for the IP and SOP. Our analysis and simulation results demonstrate the superior performance of the proposed IR-based selection schemes for secure communication. They also confirm the existence of a floor phenomenon for the SOP in the absence of AN.Artificial noise, incremental relaying, network, physical-layer security.S. Vahidian is with the

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“…Gelf'and and Pinsker [6] found the capacity of a single-user channel with side information non-causally available at the encoders. State-dependent multiuser settings have been studied in [7], [8], [9], [10], and [11].…”

Section: Introductionmentioning

confidence: 99%

State-dependent Z channel

Hajizadeh

Monemizadeh

Bahmani

2014

2014 48th Annual Conference on Information Sciences and Systems (CISS)

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In this paper we study the "Z" channel with side information non-causally available at the encoders. We use Marton encoding along with Gelf'and-Pinsker random binning scheme and Chong-Motani-Garg-El Gamal (CMGE) jointly decoding to find an achievable rate region. We will see that our achievable rate region gives the achievable rate of the multiple access channel with side information and also degraded broadcast channel with side information. We will also derive an inner bound and an outer bound on the capacity region of the state-dependent degraded discrete memoryless Z channel and also will observe that our outer bound meets the inner bound for the rates corresponding to the second transmitter. Also, by assuming the high signal to noise ratio and strong interference regime, and using the lattice strategies, we derive an achievable rate region for the Gaussian degraded Z channel with additive interference non-causally available at both of the encoders. Our method is based on lattice transmission scheme, jointly decoding at the first decoder and successive decoding at the second decoder. Using such coding scheme we remove the effect of the interference completely. I. INTRODUCTIONThe Z channel is a two-transmitter two-receiver model shown in Fig. 1 where the first sender only wishes to send information to the first receiver whereas the second transmitter sends information to both of the receivers. The Z channel was first studied by Viswanath et al [1] where they introduced the model and found the capacity region of a specialclass of Z channels and the achievable rate of a special case of the Gaussian Z channel (GZC). In [2], Liu and Ulukus obtained several capacity bounds for a class of GZC. Chong-Motani-Garg (CMGE) [3] studied three different types of degraded Z channel and characterized the capacity region in one type. They also characterized the capacity region of GZC with moderately strong crossover link.The capacity region of the general Z channel is still an open problem. The best achievable rate region for the discrete memoryless Z channel until today is due to Do et al [4].Channels with side information were first studied by Shannon [5] where he characterized the capacity of a point-to-point channel with side information causally available at the transmitters. Gelf 'and and Pinsker [6] found the capacity of a single-user channel with side information non-causally available at the encoders. State-dependent multiuser settings have been studied in [7], [8], [9], [10], and [11].In this paper we study the Z channel with channel state information non-causally available at the encoders that is depicted in Fig. 2. The reason to study this channel model is buttressed by the applications it has in some wireless communication scenarios such as the case where two communication-involved cells are interfering with each other and thus suffer from a common interference modeled by some S non-causally available to two distinct destination base stations as shown in Fig. As in Fig. 2

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Three-receiver broadcast channels with side information

Cited by 8 publications

References 30 publications

On capacity region of certain classes of three‐receiver broadcast channels with side information

On capacity region of certain classes of three‐receiver broadcast channels with side information

On the Security Analysis of a Cooperative Incremental Relaying Protocol in the Presence of an Active Eavesdropper

State-dependent Z channel

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