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

arXiv:1109.0696 · IEEE Information Theory Workshop (ITW)

Hybrid digital/analog schemes for secure transmission with side information

Joffrey Villard, Pablo Piantanida, Shlomo Shitz Shamai

Published Oct 1, 2011• 1 citation
arXivHTMLPDF

Abstract

Recent results on source-channel coding for secure transmission show that separation holds in several cases under some less-noisy conditions. However, it has also been proved through a simple counterexample that pure analog schemes can be optimal and hence outperform digital ones. According to these observations and assuming matched-bandwidth, we present a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. An application example to binary symmetric sources with side information is also investigated.

DOI
10.1109/itw.2011.6089583

Related papers

Secure Transmission of Sources Over Noisy Channels With Side Information at the Receivers

Joffrey Villard, Pablo Piantanida, Shlomo Shitz Shamai

This paper investigates the problem of source-channel coding for secure transmission with arbitrarily correlated side informations at both receivers. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the problems of secure source coding with (uncoded) side information at the decoders and the wiretap channel. A general outer bound on the rate-distortion-equivocation region, as well as an inner bound based on a pure digital scheme, is derived for arbitrary channels and side informations. In some special cases of interest, it is proved that this digital scheme is optimal and that separation holds. However, it is also shown through a simple counterexample with a binary source that a pure analog scheme can outperform the digital one while being optimal. According to these observations and assuming matched bandwidth, a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones is then presented. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. Through an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.

arXiv:1201.2315•IEEE Transactions on Information Theory•Nov 19, 2013•25 citations

Secure Hybrid Digital-Analog Coding With Side Information at the Receiver

Ghadamali Bagherikaram, Konstantinos N. Plataniotis

In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information available at the intended receiver is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR, compared to the intended receiver. The objective is to minimize the distortion of source reconstruction at the intended receiver. In this work, it is shown that the source-channel separation coding scheme is optimum in the sense of achieving minimum distortion. Two hybrid digital-analog Wyner-Ziv coding schemes are then proposed which achieve the minimum distortion. These secure joint source-channel coding schemes are based on the Wyner-Ziv coding scheme and wiretap channel coding scheme when the analog source is not explicitly quantized. The proposed secure hybrid digital-analog schemes are analyzed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, i.e., when the actual SNR is larger than the designed SNR.

arXiv:1110.3365•Oct 15, 2011•0 citations

Secure transmission of a Gaussian source over Gaussian channels with side information

Joffrey Villard, Pablo Piantanida, Shlomo Shitz Shamai

This paper investigates the problem of source-channel coding for secure transmission of a Gaussian source over a Gaussian wiretap channel in presence of arbitrarily correlated side informations at both receivers. By means of an appropriate coding scheme (either hybrid digital/analog or pure digital), the optimal rate-distortion-equivocation region is characterized for most of the scenarios. These results provide the best achievable tradeoff between the requirement on the distortion level at the legitimate receiver and the equivocation rate at the eavesdropper.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2012•1 citation

Secure Joint Source-Channel Coding With Side Information

Ghadamali Bagherikaram, Konstantinos N. Plataniotis

In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is minimizing the distortion of source reconstruction at the intended receiver. In this work, it is shown that unlike the Gaussian wiretap channel without side information, Shannon's source-channel separation coding scheme is not optimum in the sense of achieving the minimum distortion. Three hybrid digital-analog secure joint source channel coding schemes are then proposed which achieve the minimum distortion. The first coding scheme is based on Costa's dirty paper coding scheme and wiretap channel coding scheme when the analog source is not explicitly quantized. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital-analog signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wiretap channel with side information, there exists an infinite family of optimum secure joint source-channel coding scheme. In the third coding scheme, the quantized signal and the analog error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of optimum secure joint source-channel channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital-analog schemes are analyzed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, i.e., when the actual SNR is larger than the designed SNR.

arXiv:1008.0223•Aug 2, 2010•1 citation

Secure joint source–channel coding with interference known at the transmitter

Ghadamali Bagherikaram, Konstantinos N. Plataniotis

In this study, the problem of transmitting an independent and identically distributed (i.i.d.) Gaussian source over an i.i.d. Gaussian wire-tap channel, with an i.i.d. Gaussian known interference available at the transmitter is considered. The intended receiver is assumed to have a certain minimum signal-to-noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is to minimise the distortion of source reconstruction at the intended receiver. In this study, an achievable distortion is derived when Shannon's source–channel separation coding scheme is used. Three hybrid digital–analogue secure joint source–channel coding schemes are then proposed, which achieve the same distortion. The first coding scheme is based on Costa's dirty-paper-coding scheme and wire-tap channel coding scheme, when the analogue source is not explicitly quantised. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital–analogue signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wire-tap channel with side information, there exists an infinite family of secure joint source–channel coding schemes. In the third coding scheme, the quantised signal and the analogue error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of secure joint source–channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital–analogue schemes are analysed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, that is, when the actual SNR is larger than the designed SNR.

IET Communications•Nov 27, 2012•9 citations

Secure Multiterminal Source Coding With Side Information at the Eavesdropper

Joffrey Villard, Pablo Piantanida

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.

arXiv:1105.1658•IEEE Transactions on Information Theory•Feb 6, 2013•78 citations
Recent results on source-channel coding for secure transmission show that separation holds in several cases under some less-noisy conditions. However, it has also been proved through a simple counterexample that pure analog schemes can be optimal and hence outperform digital ones. According to these observations and assuming matched-bandwidth, we present a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. An application example to binary symmetric sources with side information is also investigated.
This paper investigates the problem of source-channel coding for secure transmission with arbitrarily correlated side informations at both receivers. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the problems of secure source coding with (uncoded) side information at the decoders and the wiretap channel. A general outer bound on the rate-distortion-equivocation region, as well as an inner bound based on a pure digital scheme, is derived for arbitrary channels and side informations. In some special cases of interest, it is proved that this digital scheme is optimal and that separation holds. However, it is also shown through a simple counterexample with a binary source that a pure analog scheme can outperform the digital one while being optimal. According to these observations and assuming matched bandwidth, a novel hybrid digital/analog scheme that aims to gather the advantages of both digital and analog ones is then presented. In the quadratic Gaussian setup when side information is only present at the eavesdropper, this strategy is proved to be optimal. Furthermore, it outperforms both digital and analog schemes and cannot be achieved via time-sharing. Through an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information available at the intended receiver is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR, compared to the intended receiver. The objective is to minimize the distortion of source reconstruction at the intended receiver. In this work, it is shown that the source-channel separation coding scheme is optimum in the sense of achieving minimum distortion. Two hybrid digital-analog Wyner-Ziv coding schemes are then proposed which achieve the minimum distortion. These secure joint source-channel coding schemes are based on the Wyner-Ziv coding scheme and wiretap channel coding scheme when the analog source is not explicitly quantized. The proposed secure hybrid digital-analog schemes are analyzed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, i.e., when the actual SNR is larger than the designed SNR.
This paper investigates the problem of source-channel coding for secure transmission of a Gaussian source over a Gaussian wiretap channel in presence of arbitrarily correlated side informations at both receivers. By means of an appropriate coding scheme (either hybrid digital/analog or pure digital), the optimal rate-distortion-equivocation region is characterized for most of the scenarios. These results provide the best achievable tradeoff between the requirement on the distortion level at the legitimate receiver and the equivocation rate at the eavesdropper.
In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is minimizing the distortion of source reconstruction at the intended receiver. In this work, it is shown that unlike the Gaussian wiretap channel without side information, Shannon's source-channel separation coding scheme is not optimum in the sense of achieving the minimum distortion. Three hybrid digital-analog secure joint source channel coding schemes are then proposed which achieve the minimum distortion. The first coding scheme is based on Costa's dirty paper coding scheme and wiretap channel coding scheme when the analog source is not explicitly quantized. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital-analog signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wiretap channel with side information, there exists an infinite family of optimum secure joint source-channel coding scheme. In the third coding scheme, the quantized signal and the analog error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of optimum secure joint source-channel channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital-analog schemes are analyzed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, i.e., when the actual SNR is larger than the designed SNR.
In this study, the problem of transmitting an independent and identically distributed (i.i.d.) Gaussian source over an i.i.d. Gaussian wire-tap channel, with an i.i.d. Gaussian known interference available at the transmitter is considered. The intended receiver is assumed to have a certain minimum signal-to-noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is to minimise the distortion of source reconstruction at the intended receiver. In this study, an achievable distortion is derived when Shannon's source–channel separation coding scheme is used. Three hybrid digital–analogue secure joint source–channel coding schemes are then proposed, which achieve the same distortion. The first coding scheme is based on Costa's dirty-paper-coding scheme and wire-tap channel coding scheme, when the analogue source is not explicitly quantised. The second coding scheme is based on the superposition of the secure digital signal and the hybrid digital–analogue signal. It is shown that for the problem of communicating a Gaussian source over a Gaussian wire-tap channel with side information, there exists an infinite family of secure joint source–channel coding schemes. In the third coding scheme, the quantised signal and the analogue error signal are explicitly superimposed. It is shown that this scheme provides an infinite family of secure joint source–channel coding schemes with a variable number of binning. Finally, the proposed secure hybrid digital–analogue schemes are analysed under the main channel SNR mismatch. It is proven that the proposed schemes can give a graceful degradation of distortion with SNR under SNR mismatch, that is, when the actual SNR is larger than the designed SNR.
The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.