The coding problem over wiretap channels is to realize an encoder and a decoder such that the legitimate receiver can correctly decode transmitted secret messages while the eavesdropper knows little about the secret messages. Traditionally, the secrecy of messages to the eavesdropper has been measured in terms of mutual information. Recently, several researches on the wiretap channels employ the bit error rate after decoding by the eavesdropper as a secrecy measure. In this note, we show that the secrecy capacity with respect to the bit error rate criterion is different from that with the traditional mutual information criterion. In addition to that, the encoder can be deterministic for the bit error rate criterion, while it must be stochastic for the mutual information criterion.
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.
The Gaussian wiretap channel with rate-limited help available at the legitimate receiver (decoder) is studied under various channel configurations (degraded, reversely degraded and non-degraded). In all considered cases but one, the rate-limited help results in a secrecy capacity boost equal to the help rate. This holds irrespective of whether the help is secure or not, so that secure help does not provide any advantage over non-secure one. The secrecy capacity is positive for the reversely-degraded channel (where the no-help secrecy capacity is zero) and no wiretap coding is needed to achieve it. More noise at the legitimate receiver can sometimes result in higher secrecy capacity. The same secrecy capacity boost also holds if non-secure help is available to the transmitter (encoder), in addition to or instead of the receiver help.
We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with
Mand
Nantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate
RN. The relationship between the average secrecy capacity
CˉNof Gaussian wiretap channel and the average secrecy rate
RˉNachieved by the null-space jamming scheme is investigated, and we prove that
RˉN≤CˉN≤RˉN+1. Based on this inequality and the derived lower and upper bounds on
RN, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when
N>M, the average secrecy capacity increases linearly with the total transmit power; while when
N≤M−1, there exists a performance ceiling on it.
We consider a system where an agent (Alice) aims at transmitting a message to a second agent (Bob) over a set of parallel channels, while keeping it secret from a third agent (Eve) by using physical layer security techniques. We assume that Alice perfectly knows the set of channels with respect to Bob, but she has only a statistical knowledge of the channels with respect to Eve. We derive bounds on the achievable outage secrecy rates, by considering coding either within each channel or across all parallel channels. Transmit power is adapted to the channel conditions, with a constraint on the average power over the whole transmission. We also focus on the maximum cumulative outage secrecy rate that can be achieved. Moreover, in order to assess the performance in a real life scenario, we consider the use of practical error correcting codes. We extend the definitions of security gap and equivocation rate, previously applied to the single additive white Gaussian noise channel, to Rayleigh distributed parallel channels, on the basis of the error rate targets and the outage probability. Bounds on these metrics are also derived, taking into account the statistics of the parallel channels. Numerical results are provided, that confirm the feasibility of the considered physical layer security techniques.
We consider a system where an agent (Alice) aims at transmitting a message to a second agent (Bob) over a set of parallel channels, while keeping it secret from a third agent (Eve) by using physical layer security techniques. We assume that Alice perfectly knows the set of channels with respect to Bob, but she has only a statistical knowledge of the channels with respect to Eve. We derive bounds on the achievable outage secrecy rates, by considering coding either within each channel or across all parallel channels. Transmit power is adapted to the channel conditions, with a constraint on the average power over the whole transmission. We also focus on the maximum cumulative outage secrecy rate that can be achieved. Moreover, in order to assess the performance in a real life scenario, we consider the use of practical error correcting codes. We extend the definitions of security gap and equivocation rate, previously applied to the single additive white Gaussian noise channel, to Rayleigh distributed parallel channels, on the basis of the error rate targets and the outage probability. Bounds on these metrics are also derived, considering the statistics of the parallel channels. Numerical results are provided, that confirm the feasibility of the considered physical layer security techniques.