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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Recent results on compound wire-tap channels

Yingbin Liang, Gerhard G. Kramer, H. Vincent Poor, Shlomo Shitz Shamai

Published Sep 1, 2008• 19 citations
Publisher

Abstract

The compound wire-tap channel is studied, which is based on Wynerpsilas wire-tap model with both the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states. No matter which states occur for the two channels, the source wishes to guarantee that the destination decodes its message successfully and that the wire-tapper does not obtain the source message. The semideterministic compound wire-tap channel is first studied, in which the channel from the source to the destination is deterministic and has only one state. The secrecy capacity is obtained. An example parallel Gaussian compound wire-tap channel is then studied, in which both channels have two states. Three schemes are studied, and it is shown that introducing randomness either into the source message or into the encoder achieves the maximal secrecy degree of freedom. Both channels studied in this paper demonstrate that creating an auxiliary input, and hence adding a prefix channel from this auxiliary input to the actual channel input, improves the secrecy rate.

DOI
10.1109/pimrc.2008.4699909

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The compound wire-tap channel is studied, which is based on Wynerpsilas wire-tap model with both the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states. No matter which states occur for the two channels, the source wishes to guarantee that the destination decodes its message successfully and that the wire-tapper does not obtain the source message. The semideterministic compound wire-tap channel is first studied, in which the channel from the source to the destination is deterministic and has only one state. The secrecy capacity is obtained. An example parallel Gaussian compound wire-tap channel is then studied, in which both channels have two states. Three schemes are studied, and it is shown that introducing randomness either into the source message or into the encoder achieves the maximal secrecy degree of freedom. Both channels studied in this paper demonstrate that creating an auxiliary input, and hence adding a prefix channel from this auxiliary input to the actual channel input, improves the secrecy rate.
The compound wire-tap channel is studied, which is based on the classical wire-tap channel with the channel from the source to the destination and the channel from the source to the wire-tapper taking a number of states, respectively. This channel can also be viewed as the wire-tap channel with mul-tiple destinations and multiple wire-tappers, i.e., multicast with multiple wire-tappers. The source wishes to transmit information to all destinations and wants to keep the information secret from all wire-tappers. For the discrete memoryless compound wire-tap channel, lower and upper bounds on the secrecy capacity are derived and are shown to match for the degraded channel. The parallel Gaussian compound wire-tap channel is further studied, for which the secrecy capacity and the characterization of an optimal power allocation are obtained. The secrecy degree of freedom (s.d.o.f.) is also derived, which connects the secure communication rate in the high SNR regime to secure networking coding for deterministic networks. Finally, the multi-antenna (i.e., MIMO) compound wire-tap channel is studied. The secrecy capacity is established for the degraded MIMO compound wire-tap channel and an achievable s.d.o.f. is given for the general MIMO compound wire-tap channel.
This paper considers the compound wiretap channel, which generalizes Wyner's wiretap model to allow the channels to the (legitimate) receiver and to the eavesdropper to take a number of possible states. No matter which states occur, the transmitter guarantees that the receiver decodes its message and that the eavesdropper is kept in full ignorance about the message. The compound wiretap channel can also be viewed as a multicast channel with multiple eavesdroppers, in which the transmitter sends information to all receivers and keeps the information secret from all eavesdroppers. For the discrete memoryless channel, lower and upper bounds on the secrecy capacity are derived. The secrecy capacity is established for the degraded channel and the semideterministic channel with one receiver. The parallel Gaussian channel is further studied. The secrecy capacity and the secrecy degree of freedom ( ) are derived for the degraded case with one receiver. Schemes to achieve the for the case with two receivers and two eavesdroppers are constructed to demonstrate the necessity of a prefix channel in encoder design. Finally, the multi-antenna (i.e., MIMO) compound wiretap channel is studied. The secrecy capacity is established for the degraded case and an achievable is given for the general case.
The fading wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an information-theoretic model for the fading wire-tap channel. The secrecy capacity of the parallel wire-tap channel is established. This result is then specialized to give the secrecy capacity of the fading wire-tap channel, which is achieved with the source node dynamically changing the power allocation according to the channel state realization. An optimal source power allocation is obtained to achieve the secrecy capacity.
In this paper, we study the problem of secret communication over a Multiple Access Wire-tap Channel with Common Message. In this channel, we assume that two transmitters have confidential messages which must be kept secret from the eavesdropper (receiver 2), and both of them have a common message which can be decoded by two receivers. For this setting, in the discrete memoryless case we derive general inner and outer bounds on the secrecy capacity region. Also, we derive inner and outer bounds on the secrecy capacity region for the Gaussian case. Providing numerical examples for the Gaussian case, we illustrate the comparison between derived achievable rate regions, outer bounds and the capacity region of compound multiple access channel.
In this paper, we first consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-taper also receives the transmitted signal. We assume that the signals are transmitted over additive white Gaussian noise channels. We characterize the secrecy capacity region of this channel. Our achievable coding scheme is based on superposition coding and the random binning. We refer to this scheme as secret superposition coding. The converse proof combines the converse proof for the conventional Gaussian broadcast channel and the perfect secrecy constraint. This capacity region matches the capacity region of the broadcast channel without security constraint. It also matches the secrecy capacity of the wire-tap channel. Based on the rate characterization of the secure Gaussian broadcast channel, we then use a multilevel coding approach for the slowly fading wire-tap. We assume that the transmitter only knows the eavesdropper's channel. In this approach, source node sends secure layered coding and the receiver viewed as a continuum ordered users. We derive optimum power allocation for the layers which maximizes the total average rate.
This paper studies secrecy capacity in a semi-deterministic setting, in which the channel between legitimate users (called Alice and Bob) is deterministic, while that between Alice and the eavesdropper (called Eve) is a discrete memoryless channel. Such a model is particularly relevant when a pre-existing error correcting code tailored to the legitimate channel is in use on top of which secret information is to be shared. First, a point-to-point setting is considered with a single wiretapper, a situation in which the secrecy capacity has an elegant characterization. Next, a generalized multiple access setting with confidential messages is considered in which each user wishes to communicate secret information to a common destination without the other determining its message. In this latter situation, outer bounds on the secrecy capacity are obtained.