Two-Way Writing on Dirty Paper

Trans. Emerging Tel. Tech.

2014

In this paper, we characterize capacity region of the Gaussian doubly dirty two-way channel (TWC) with partial side information at users, where there are two additive interference signals that, although similar to the channel noise sequences, corrupt the transmitted signals but are non-causally and partially known to the users. First, by employing adaptation (considering the previously received signals in encoding process), we derive an adaptive outer bound on the capacity region of the channel. Then, we utilize lattice strategies and obtain a non-adaptive inner bound that coincides with the adaptive outer bound and hence gives the capacity region. This also shows that for the doubly dirty TWC with partial side information, adaptation is useless and cannot increase the capacity region. Finally, we prove that Costa's dirty paper coding is optimal like lattice strategies and therefore, the Gaussian doubly dirty TWC is an instance of multi-user channels in which lattice strategy and Costa's strategy have the same performance from the capacity region perspective. It is worth noting that our results subsume the previous related works as special cases.

“…Therefore, the proof of Theorem follows by considering , , , and . Remark By setting

P_{E_{1}} = P_{E_{2}} = 0

, we can obtain the capacity region of the doubly dirty TWC with full SI , Theorem ]:

C = \{\begin{matrix} 0 \leq R_{1} \leq \frac{1}{2} \log_{2} ((), 1 + \frac{h_{21}^{2} P_{X_{1}}}{P_{Z_{2}}}) \\ 0 \leq R_{2} \leq \frac{1}{2} \log_{2} ((), 1 + \frac{h_{12}^{2} P_{X_{2}}}{P_{Z_{1}}}) \end{matrix}\}

Section: Resultsmentioning

confidence: 63%

“…Therefore, is proved. Similarly, by using the same procedure and considering , we can show that the equality

h ((), U_{2} | U_{1}, {\overset{S}{true}}_{1}, Y_{1}) = h ((), U_{2} | U_{1}, {\overset{S}{true}}_{1}, Y_{1}, {\overset{S}{true}}_{2})

\begin{matrix} R_{1} & \leq I (U_{1}; Y_{2} | U_{2}, {\tilde{S}}_{2}) - I (U_{1}; {\tilde{S}}_{1} | U_{2}, {\tilde{S}}_{2}) \\ = I (U_{1}; Y_{2}, {\tilde{S}}_{1} | U_{2}, {\tilde{S}}_{2}) - I (U_{1}; {\tilde{S}}_{1} | U_{2}, {\tilde{S}}_{2}) \\ = I (...) \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

“…Remark 1. By setting P E 1 D P E 2 D 0, we can obtain the capacity region of the doubly dirty TWC with full SI [11,Theorem 2]:…”

Section: Non-adaptive Inner Bound Based On Lattice Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Capacity region of the Gaussian doubly dirty two‐way channel in the presence of partial side information

Monemizadeh

Trans. Emerging Tel. Tech.

2014

“…YoungHan Kim et al extended [21] to degraded BC, MAC, and Relay Channel (RC) [22]. Reza Khosravi-Farsani [23] also extended [21] to the two-way channel, which was first studied by Shannon [24].…”

Section: Introductionmentioning

confidence: 99%

Three-receiver broadcast channels with side information

Hajizadeh

2012 IEEE International Symposium on Information Theory Proceedings

2012

Abstract-Three-Receiver broadcast channels (BC) are of interest due to their information-theoretic differences with tworeceiver one. In this paper, we derive achievable rate regions for two classes of 3-receiver BC with side information (SI), i.e. Multilevel BC (MBC) and 3-receiver less noisy BC, using a combination of superposition coding, Gelf'and-Pinsker binning scheme and Nair-El Gamal indirect decoding. Our rate region for MBC subsumes Steinberg's rate region for 2-receiver degraded BC with SI as its special case. We will also show that the obtained achievable rate regions in the first two cases are tight for several classes of non-deterministic, semi-deterministic, and deterministic 3-receiver BC when SI is available both at the transmitter and at the receivers. We also prove that as far as a receiver is deterministic in the three-receiver less noisy BC, the presence of side information at that receiver does not affect the capacity region. We have also provided the writing on dirty paper (WDP) property for 3-receiver BC is provided as an example. In the last section, we provide simple bounds on the capacity region of the Additive Exponential noise three-receiver broadcast channels with Additive Exponential interference (AEN-3BC-EI).Index Terms-Three-receiver broadcast channel, Less noisy, Multilevel broadcast channel, Deterministic broadcast channel, Semi-deterministic broadcast channel.

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

Bahrami

2015

IET Communications

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] ...