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 International Symposium on Information Theory (ISIT)

Wiretap channels: Roles of rate splitting and channel prefixing

Omur Ozel, Şennur Ulukuş

Published Jul 1, 2011• 9 citations
Publisher

Abstract

Csiszár and Körner's characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: U, which represents rate splitting and V, which represents channel prefixing. For some channels, one or both of these auxiliary random variables are unnecessary, simplifying the expression and evaluation of the rate-equivocation region. In this paper, we provide new conditions under which channel prefixing or rate splitting does not improve the rate-equivocation region. In particular, we show that when the main channel is more capable than the eavesdropping channel, channel prefixing is unnecessary; the entire rate-equivocation region can be achieved by rate splitting alone. Conversely, we show under a mild assumption that if the main receiver is not more capable, then channel prefixing is strictly necessary. Moreover, we show that if the main channel is more capable but not less noisy, then rate splitting is strictly necessary. Next, we focus on the set of cyclic shift symmetric channels. We prove that for these channels, if in addition I(X; Y) - I(X;Z) is maximized at the uniform distribution, then rate splitting is unnecessary. Our results apply to BSC-BEC and BEC-BSC wiretap channels. We identify the conditions on the parameters of the BSC and BEC under which channel prefixing and/or rate splitting are unnecessary.

DOI
10.1109/isit.2011.6034206

Related papers

Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

Omur Ozel, Şennur Ulukuş

Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables:U, for rate splitting andV, for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable,V=Xis optimal and the boundary of the rate-equivocation region is achieved by varying rate splittingUalone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, thenV=Xis strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splittingUthat achieves the boundary of the rate-equivocation region is uniform with cardinality |X| and the prefix channel between optimalUandVis expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for whichU=φ is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.

arXiv:1110.4613•IEEE Transactions on Information Theory•Dec 4, 2012•13 citations

Rate-equivocation region of cyclic shift symmetric wiretap channels

Omur Ozel, Şennur Ulukuş

In this paper, we study cyclic shift symmetric wiretap channels in which the channels between Alice and Bob and Alice and Eve are both cyclic shift symmetric. We characterize the rate-equivocation region by determining the optimal selection of rate splitting U and channel prefixing V for these channels. We show that optimal U and V are determined via cyclic shifts of the solution of an auxiliary optimization problem that involves only one auxiliary random variable. We find the cardinality bound on the necessary auxiliary variable and formulate the problem as a constrained optimization problem. We determine the optimality conditions for the binary-input cyclic shift symmetric wiretap channels. We find the optimum by inspecting each point of the I(X;Y) - I(X; Z) function and ruling out the sub-optimal candidates that satisfy the optimality conditions. In particular, we address BSC-BEC and BEC-BSC wiretap channels. By using the optimality conditions, we determine the optimal selections of U and V for the rate-equivocation regions of these channels.

Allerton Conference on Communication, Control, and Computing•Sep 1, 2011•2 citations

E - Capacity - Equivocation Region of Wiretap Channel

Mariam E. Haroutunian

One of the problems of information - theoretic security concerns secure communication over a wiretap channel. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). We introduce and investigate the E - capacity - equivocation region and the E - secrecy capacity function for the wiretap channel, which are, correspondingly, the generalizations of the capacity - equivocation region and secrecy - capacity studied by Csiszár and Körner (1978). The E - capacity equivocation region is the closure of the set of all achievable rate - reliability and equivocation pairs, where the rate - reliability function represents the optimal dependence of rate on the error probability exponent (reliability). By analogy with the notion of E - capacity, we consider the E - secrecy capacity function that for the given E is the maximum rate at which the message can be transmitted being kept perfectly secret from the wiretapper.

JUCS - Journal of Universal Computer Science•Nov 28, 2021•1 citation

Capacity-Equivocation Region of the Gaussian MIMO Wiretap Channel

Ersen Ekrem, Şennur Ulukuş

We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.

arXiv:1005.0419•May 3, 2010•2 citations

Capacity-Equivocation Region of the Gaussian MIMO Wiretap Channel

Ersen Ekrem, Şennur Ulukuş

We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar–Korner.

IEEE Transactions on Information Theory•Jun 12, 2012•25 citations

Outer Bound for E-Capacity–Equivocation Region of Compound Wiretap Channel

Mariam E. Haroutunian

Investigation of communication over a wiretap channel is one of the problems of information–theoretic security. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). Here we consider the compound wiretap channel model, when the channels to the legitimate receiver and to the wiretapper depends on the number of possible states. We investigate the $$E$$ -capacity–equivocation region which is the closure of the set of all achievable rate-reliability and equivocation pairs, where the rate-reliability function represents the optimal dependence of rate on the error probability exponent (reliability). Here the outer bound of this region is constructed in the case, when the states are not known to all terminals.

Pattern Recognition and Image Analysis•Mar 1, 2024•0 citations
Csiszár and Körner's characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: U, which represents rate splitting and V, which represents channel prefixing. For some channels, one or both of these auxiliary random variables are unnecessary, simplifying the expression and evaluation of the rate-equivocation region. In this paper, we provide new conditions under which channel prefixing or rate splitting does not improve the rate-equivocation region. In particular, we show that when the main channel is more capable than the eavesdropping channel, channel prefixing is unnecessary; the entire rate-equivocation region can be achieved by rate splitting alone. Conversely, we show under a mild assumption that if the main receiver is not more capable, then channel prefixing is strictly necessary. Moreover, we show that if the main channel is more capable but not less noisy, then rate splitting is strictly necessary. Next, we focus on the set of cyclic shift symmetric channels. We prove that for these channels, if in addition I(X; Y) - I(X;Z) is maximized at the uniform distribution, then rate splitting is unnecessary. Our results apply to BSC-BEC and BEC-BSC wiretap channels. We identify the conditions on the parameters of the BSC and BEC under which channel prefixing and/or rate splitting are unnecessary.
Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables:U, for rate splitting andV, for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable,V=Xis optimal and the boundary of the rate-equivocation region is achieved by varying rate splittingUalone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, thenV=Xis strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splittingUthat achieves the boundary of the rate-equivocation region is uniform with cardinality |X| and the prefix channel between optimalUandVis expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for whichU=φ is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.
In this paper, we study cyclic shift symmetric wiretap channels in which the channels between Alice and Bob and Alice and Eve are both cyclic shift symmetric. We characterize the rate-equivocation region by determining the optimal selection of rate splitting U and channel prefixing V for these channels. We show that optimal U and V are determined via cyclic shifts of the solution of an auxiliary optimization problem that involves only one auxiliary random variable. We find the cardinality bound on the necessary auxiliary variable and formulate the problem as a constrained optimization problem. We determine the optimality conditions for the binary-input cyclic shift symmetric wiretap channels. We find the optimum by inspecting each point of the I(X;Y) - I(X; Z) function and ruling out the sub-optimal candidates that satisfy the optimality conditions. In particular, we address BSC-BEC and BEC-BSC wiretap channels. By using the optimality conditions, we determine the optimal selections of U and V for the rate-equivocation regions of these channels.
One of the problems of information - theoretic security concerns secure communication over a wiretap channel. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). We introduce and investigate the E - capacity - equivocation region and the E - secrecy capacity function for the wiretap channel, which are, correspondingly, the generalizations of the capacity - equivocation region and secrecy - capacity studied by Csiszár and Körner (1978). The E - capacity equivocation region is the closure of the set of all achievable rate - reliability and equivocation pairs, where the rate - reliability function represents the optimal dependence of rate on the error probability exponent (reliability). By analogy with the notion of E - capacity, we consider the E - secrecy capacity function that for the given E is the maximum rate at which the message can be transmitted being kept perfectly secret from the wiretapper.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar–Korner.
Investigation of communication over a wiretap channel is one of the problems of information–theoretic security. The aim in the general wiretap channel model is to maximize the rate of the reliable communication from the source to the legitimate receiver, while keeping the confidential information as secret as possible from the wiretapper (eavesdropper). Here we consider the compound wiretap channel model, when the channels to the legitimate receiver and to the wiretapper depends on the number of possible states. We investigate the EEE -capacity–equivocation region which is the closure of the set of all achievable rate-reliability and equivocation pairs, where the rate-reliability function represents the optimal dependence of rate on the error probability exponent (reliability). Here the outer bound of this region is constructed in the case, when the states are not known to all terminals.