Secrecy Capacity of Wiretap Channels with the Bit Error Rate Criterion

Hachiro Fujita

Ryutaroh Matsumoto

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.

Mustafa El-Halabi

R Rajesh, Shahid Mehraj Shah, Vinod Sharma

We consider secrecy obtained when one transmits on a Gaussian Wiretap channel above the secrecy capacity. Instead of equivocation, we consider probability of error as the criterion of secrecy. The usual channel codes are considered for transmission. The rates obtained can reach the channel capacity. We show that the “confusion” caused to the Eve when the rate of transmission is above capacity of the Eve's channel is similar to the confusion caused by using the wiretap channel codes used below the secrecy capacity.

Oussama Souihli, Tomoaki Otsuki Ohtsuki

Igor Bjelaković, Holger Boche, Jochen Sommerfeld

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.