In wireless data networks, communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multi-antenna transmitter sends independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multi-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound prove to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.
Deep Dive into Secrecy Capacity Region of a Multi-Antenna Gaussian Broadcast Channel with Confidential Messages.
In wireless data networks, communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multi-antenna transmitter sends independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multi-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound prove to be consistent with the
In this work, we consider multiple antenna secret broadcast in wireless networks. This research is inspired by the seminal paper [1], in which Wyner introduced the so-called wiretap channel and proposed an information theoretic approach to secret communication schemes. Under the assumption that the channel to the eavesdropper is a degraded version of that to the desired receiver, Wyner characterized the capacitysecrecy tradeoff for the discrete memoryless wiretap channel and showed that secret communication is possible without sharing a secret key. Later, the result was extended by Csiszár and Körner who determined the secrecy capacity for the non-degraded broadcast channel (BC) with a single confidential message intended for one of the users [2].
In more general wireless network scenarios, secret communication may involve multiple users and multiple antennas. Motivated by wireless communication, where transmitted signals are broadcast and can be received by all users within the communication range, a significant research effort has been invested
in the study of the information-theoretic limits of secret communication in different wireless network environments including multi-user communication with confidential messages [3]- [11], secret wireless communication on fading channels [12]- [15], and the Gaussian multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) wiretap channels [16]- [21].
These issues motivate us to study the multi-antenna Gaussian BC with confidential messages (MGBC-CM), in which independent confidential messages from a multi-antenna transmitter are to be communicated to two users. The corresponding broadcast communication model is shown in Fig. 1. Each user would like to obtain its own message reliably and confidentially.
To give insight into this problem, we first consider a single-antenna Gaussian BC. Note that this channel is degraded [22], which means that if a message can be successfully decoded by the inferior user, then the superior user is also ensured of decoding it. Hence, the secrecy rate of the inferior user is zero and this problem is reduced to the scalar Gaussian wiretap channel problem [23] whose secrecy capacity is now the maximum rate achievable by the superior user. This analysis gives rise to the question: can the transmitter, in fact, communicate with both users confidentially at nonzero rate under some other conditions? Roughly
speaking, the answer is in the affirmative. In particular, the transmitter can communicate when equipped with sufficiently separated multiple antennas.
We here have two goals motivated directly by questions arising in practice. The first is to determine the condition under which both users can obtain their own confidential messages in a reliable and safe manner.
This is equivalent to evaluating the secrecy capacity region for the MGBC-CM. The second is to show how the transmitter should broadcast confidentially, which is equivalent to designing an achievable secret coding scheme. To this end, we first describe a secret dirty-paper coding (DPC) scheme and derive the corresponding achievable secrecy rate region based on Gaussian codebooks. The secret DPC is based on double-binning [24] which enables both joint encoding and preserving confidentiality. Next, a computable Sato-type outer bound on the secrecy capacity region is developed for the MGBC-CM. Furthermore, the Sato-type outer bound prove to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally,
two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.
The remainder of this paper is organized as follows. The system model and definitions are introduced in Section II. The main results on the secrecy capacity region of the MGBC-CM is state in Section III.
The achievability proof associated with the secret DPC scheme is established in Section IV. The converse proof is derived in Section V based on the Sato-type outer bound. Finally, Section VI shows numerical examples and Section VII points our our conclusions.
We consider the communication of confidential messages to two users over a Gaussian BC via t ≥ 2 transmit-antennas. Each user is equipped with a single receive-antenna. As shown in Fig. 1, the transmitter sends independent confidential messages W 1 and W 2 in n channel uses with nR 1 and nR 2 bits, respectively.
The message W 1 is destined for user 1 and eavesdropped by user 2, whereas the message W 2 is destined for user 2 and eavesdropped by user 1. This communication scenario is referred to as the multi-antenna Gaussian BC with confidential messages. The Gaussian BC is an additive noise channel and the received symbols at user 1 and user 2 are represented using the following expression:
where x i ∈ C t is a complex input vector at time i, {z 1,i } a
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