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arXiv:1103.0135 · IEEE Information Theory Workshop (ITW)

Capacity results for compound wiretap channels

Igor Bjelaković, Holger Boche, Jochen Sommerfeld

Published Oct 1, 2011• 6 citations
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Abstract

We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower bound and a multi-letter converse to the secrecy capacity of the compound wiretap channel without channel state information.

DOI
10.1109/itw.2011.6089569

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We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower bound and a multi-letter converse to the secrecy capacity of the compound wiretap channel without channel state information.
We derive a lower bound on the secrecy capacity of the compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. and thus establishing a full coding theorem in this case. We achieve this with a quite strong secrecy criterion and with a decoder that is robust against the effect of randomisation in the encoding. This relieves us from the need of decoding the randomisation parameter which is in general not possible within this model. Moreover we prove a lower bound and a multi-letter converse to the secrecy capacity of the compound wiretap channel without channel state information.
We derive a lower bound on the secrecy capacity of a compound wiretap channel with channel state information at the transmitter which matches the general upper bound on the secrecy capacity of general compound wiretap channels given by Liang et al. [1], thus establishing a full coding theorem in this case. We achieve this with a stronger secrecy criterion and the maximum error probability criterion, and with a decoder that is robust against the effect of randomization in the encoding. This relieves us from the need of decoding the randomization parameter, which is in general impossible within this model. Moreover, we prove a lower bound on the secrecy capacity of a compound wiretap channel without channel state information and derive a multiletter expression for the capacity in this communication scenario.
We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a proof for a lower bound on the entanglement generating capacity of the compound quantum channel. We also derive a proof for the formula for entanglement generating capacity of the compound quantum channel with channel state information at the encoder which was given in additional information [Bjelakovi\ifmmode \acute{c}\else \'{c}\fi{}, Boche, and N\"otzel, in Proceedings of International Symposium on Information Theory ISIT, Korea, 2009 (IEEE, New York, 2009), pp. 1889--1893].
The wiretap channel with secret keys models the problem of secure communication in the presence of a non-legitimate eavesdropper, where the transmitter and legitimate receiver share a secret key of finite rate. This communication scenario is studied for compound channels. An achievable strong secrecy rate is presented and a multi-letter upper bound is derived. For degraded compound wiretap channels with secret keys the strong secrecy capacity is established. Finally, the case of channel state information at the transmitter is discussed and the secrecy capacity is established for this case as well.
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.
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.