This paper strengthens the known secrecy results for a k-transmitter multiple access channel (MAC) with an external eavesdropper from weak to strong without any rate loss on the achievable region. More specifically, the results are derived under a strong secrecy metric defined by the information leakage to the eavesdropper, instead of the weaker secrecy criteria defined by the information leakage rate or the (average) variation distance. To this end, different approaches are taken to analyze the information leakage and the decoding error probability. Interestingly, both the secrecy and error exponents could be characterized by the (conditional) Rényi mutual information in a concise form. Thus, the region is guaranteed with both information leakage and decoding error probability decreasing exponentially in the code length. Our technique for strong secrecy analysis reflects the resolvability for the k-transmitter MAC; while our error exponent could be regarded as a generalization of Gallager's error exponent.
This paper investigates the information-theoretic secrecy problem for a K-user discrete memoryless (DM) multiple-access wiretap (MAC-WT) channel. Instead of using the weak secrecy criterion characterized by information leakage rate, we adopt the strong secrecy metric defined by information leakage to better protect the confidential information. We provide an achievable rate region and prove its achievability by providing a coding scheme and analyzing the output statistics in terms of (average) variational distance. We show that the rate region obtained in previous works on the subject is a special case of ours. We also show that the achievability proof in such works is incomplete, because it is assumed that certain inequalities hold while they may not in some cases. We solve this problem by constructing an inequality structure for the rates of all users’ secret and redundant messages, and analyzing the conditions required to maintain this structure.
This paper studies the problem of secure communication over a
K -transmitter multiple access channel (MAC) in the presence of an external eavesdropper, subject to a collective secrecy constraint (i.e., information leakage rate to an eavesdropper on a collection of messages that are from a pre-specified subset of the
K transmitters, say
S⊆K={1,2,…,K} , is made vanishing). Since secrecy is of concern only to transmitters
{i∣i∈S} but not to transmitters
{i∣i∈Sc} , where
Sc=K\S , different transmission strategies could be employed at transmitters
{i∣i∈Sc} . Consider the following two scenarios: 1) transmitters
{i∣i∈Sc} use deterministic encoders (which are conventionally used for MAC without secrecy), competing for the channel resource (i.e., being competitive) and 2) transmitters
{i∣i∈Sc} use stochastic encoders, helping to hide other transmitters’ messages from the eavesdropper (i.e., being cooperative). As a result, we establish the respective
S -collective secrecy achievable rate regions and demonstrate the advantage of being cooperative theoretically and numerically. To this end, in addition to the standard techniques, our results build upon two techniques. The first is a generalization of Chia-El Gamal’s lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with submodular properties of mutual information functions involved, leads to an efficient Fourier-Motzkin elimination. These two approaches allow us to derive achievable regions in this work, and could also be of independent interest in other context.
This paper studies the problem of secure communication over a K-transmitter multiple access channel in the presence of an external eavesdropper, subject to a joint secrecy constraint (i.e., information leakage rate from the collection of K messages to an eavesdropper is made vanishing). As a result, we establish the joint secrecy achievable rate region. To this end, our results build upon two techniques in addition to the standard information-theoretic methods. The first is a generalization of Chia-El Gamal's lemma on entropy bound for a set of codewords given partial information. The second is to utilize a compact representation of a list of sets that, together with properties of mutual information, leads to an efficient Fourier-Motzkin elimination. These two approaches could also be of independent interests in other contexts.
This paper studies the secrecy results for the two-way wiretap channel (TW-WC) with an external eavesdropper under a strong secrecy metric. Employing non-adaptive coding, we analyze theinformation leakageand the decoding error probability, and derive inner bounds on the secrecy capacity regions for the TW-WC under strong joint and individual secrecy constraints. For the TW-WC without cost constraint, both the secrecy and error exponents could be characterized by theconditional Rényi mutual informationin a concise and compact form. And, some special cases secrecy capacity region and sum-rate capacity results are established, demonstrating that adaption is useless in some cases or the maximum sum-rate that could be achieved by non-adaptive coding. For the TW-WC with cost constraint, we consider the peak cost constraint and extend our secrecy results by using the constant composition codes. Accordingly, we characterize both the secrecy and error exponents bya modification of Rényi mutual information, which yields inner bounds on the secrecy capacity regions for the general discrete memoryless TW-WC with cost constraint. Our method works even when a pre-noisy processing is employed based on a conditional distribution in the encoder and can be easily extended to other multi-user communication scenarios.
The problem of secure communication over a multiple access wiretap channel (MAWC) is studied. Here, two transmitters send confidential messages to a legitimate receiver while keeping a non-legitimate eavesdropper ignorant of them. In this paper, this communication scenario is studied for compound channels, for which it is only known to the users that the actual channel realization is fixed and belongs to a known set of possible channels. The criterion of strong secrecy is analyzed and its impact on the decoding performance of the eavesdropper is specified. It is shown that the average decoding error at the eavesdropper approaches one exponentially fast regardless of the applied decoding strategy. Furthermore, an achievable strong secrecy rate region is presented and a multi-letter outer bound is derived. Both together establish a multi-letter description of the strong secrecy capacity region.