Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Information Forensics and Security

On the Secrecy Capacity of Wiretap Channels With Side Information at the Transmitter

Hachiro Fujita

Published Jun 20, 2016• 12 citations
Publisher

Abstract

The wiretap channel with causal/noncausal side information at the transmitter is an extension of the original wiretap channel of Wyner to the multi-user case and has been investigated by several authors. Although much effort has been made to establish the secrecy capacity, it is still elusive even if the wiretap channel is physically degraded. In this paper, for a physically degraded wiretap channel, we show a lower bound on the secrecy capacity for the causal case and an upper bound for the noncausal case. We also show that under a certain condition, the secrecy capacity for the causal case is the same as that for the noncausal case. To illustrate the usefulness of our theoretical result, we introduce the concept of a symmetric wiretap channel with state, for which the above condition is easily checked, and we give some examples in which the secrecy capacity can be computed numerically.

DOI
10.1109/tifs.2016.2582558

Related papers

Some New Results on the Wiretap Channel with Side Information

Bin Dai, Yuan Luo

In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information.

Entropy•Sep 7, 2012•24 citations

Wiretap channel with strictly causal side information at encoder

Amir Sonee, Ghosheh Abed Hodtani

In this paper, the wiretap channel with side information studied in [2] is revisited for the case in which the side information is available only at the encoder and in a strictly causal manner. We derive a lower bound on the secrecy capacity of the channel based on a coding scheme which consists of block Markov encoding and key generation using the strictly causal state information available at the encoder. In order to provide the secrecy of messages, at the end of each block a description of the state sequence obtained by the encoder is used to generate the key which encrypts the whole or part of the message to be transmitted in the next block. Moreover, for the decoder to be able to decrypt the messages, the description of the sate sequence of each block is sent in common with the message of that block. Also, an upper bound on the secrecy capacity is developed which assumes that the state is noncausally known at the encoder and we prove that it would coincide the lower bound for a special case and results in the secrecy capacity.

Iran Workshop on Communication and Information Theory (IWCIT)•May 1, 2014•7 citations

Wiretap Channel With Causal State Information and Secure Rate-Limited Feedback

Alejandro Cohen, Asaf Cohen

In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded, the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszár, and Körner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.

IEEE Transactions on Communications•Jan 7, 2016•24 citations

Wiretap channel with causal state information

Yeow-Khiang Chia, Abbas El Gamal

A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2010•10 citations

Wiretap Channel with Causal State Information

Yeow-Khiang Chia, Abbas El Gamal

A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.

arXiv:1001.2327•Jan 13, 2010•5 citations

Wiretap Channel With Causal State Information

Yeow-Khiang Chia, Abbas El Gamal

A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and the decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and the decoder is established and is shown to coincide with the aforementioned lower bound for several classes of wiretap channels with state.

IEEE Transactions on Information Theory•Jan 31, 2012•78 citations
The wiretap channel with causal/noncausal side information at the transmitter is an extension of the original wiretap channel of Wyner to the multi-user case and has been investigated by several authors. Although much effort has been made to establish the secrecy capacity, it is still elusive even if the wiretap channel is physically degraded. In this paper, for a physically degraded wiretap channel, we show a lower bound on the secrecy capacity for the causal case and an upper bound for the noncausal case. We also show that under a certain condition, the secrecy capacity for the causal case is the same as that for the noncausal case. To illustrate the usefulness of our theoretical result, we introduce the concept of a symmetric wiretap channel with state, for which the above condition is easily checked, and we give some examples in which the secrecy capacity can be computed numerically.
In this paper, the model of wiretap channel has been reconsidered for the case that the main channel is controlled by channel state information (side information), and it is available at the transmitter in a noncausal manner (termed here noncausal side information) or causal manner (termed here causal side information). Inner and outer bounds are derived on the capacity-equivocation regions for the noncausal and causal manners, and the secrecy capacities for both manners are described and bounded, which provide the best transmission rate with perfect secrecy. Moreover, for the case that the side information is available at the transmitter in a memoryless manner (termed here memoryless side information), both the capacity-equivocation region and the secrecy capacity are determined. The results of this paper extend the previous work on wiretap channel with noncausal side information by providing an outer bound on the capacity-equivocation region. In addition, we find that the memoryless side information can not help to obtain the same secrecy capacity as that of the causal case, and this is different from the well known fact that the memoryless manner can achieve the capacity of the channel with causal side information.
In this paper, the wiretap channel with side information studied in [2] is revisited for the case in which the side information is available only at the encoder and in a strictly causal manner. We derive a lower bound on the secrecy capacity of the channel based on a coding scheme which consists of block Markov encoding and key generation using the strictly causal state information available at the encoder. In order to provide the secrecy of messages, at the end of each block a description of the state sequence obtained by the encoder is used to generate the key which encrypts the whole or part of the message to be transmitted in the next block. Moreover, for the decoder to be able to decrypt the messages, the description of the sate sequence of each block is sent in common with the message of that block. Also, an upper bound on the secrecy capacity is developed which assumes that the state is noncausally known at the encoder and we prove that it would coincide the lower bound for a special case and results in the secrecy capacity.
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and the legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf. We derive upper and lower bounds on the secrecy capacity and show that, when the channel to the eavesdropper is degraded, the bounds are tight and the secrecy capacity is completely characterized. The capacity achieving scheme is based on Wyner, Csiszár, and Körner wiretap coding and two steps of shared-key generation: one from the state information and one via the noiseless feedback. The upper bound is more involved and requires a nontrivial recursive lemma extending previous results in the literature to include both state and feedback. We conclude the paper by showing that a few interesting known results can be seen as special cases of the above, as well as discussing the case where the source of local randomness at the encoder is limited.
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key, which is used to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and decoder is established and is shown to coincide with the lower bound for several classes of wiretap channels with state.
A lower bound on the secrecy capacity of the wiretap channel with state information available causally at both the encoder and the decoder is established. The lower bound is shown to be strictly larger than that for the noncausal case by Liu and Chen. Achievability is proved using block Markov coding, Shannon strategy, and key generation from common state information. The state sequence available at the end of each block is used to generate a key to enhance the transmission rate of the confidential message in the following block. An upper bound on the secrecy capacity when the state is available noncausally at the encoder and the decoder is established and is shown to coincide with the aforementioned lower bound for several classes of wiretap channels with state.