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.

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.

In this paper, we use 2 check digits to construct systematic polynomial codes over FP, where p is an odd prime, that correct all the singleand adjacent transposition errors (which are typographic errors often made by human operators). As a result, we give constructions of several classes of codes with code length n = ½ (p + 1) and ½ (p -1). In particular, the classes of codes with n = ½ (p + 1) are new to our knowledge; while for the class of codes with n = ½ (p -1), our construction provides a larger set of code candidates compared with the previous work.

Single- and adjacent transposition errors are the typographic errors often made by human operators. In this paper, we use 2 check digits to construct systematic polynomial codes over FP, where p is an odd prime, that correct all the single- and adjacent transposition errors. As a result, we give constructions of some classes of codes with code length n = 1/2 (p + 1). To our knowledge, these codes are new in the literature. Interestingly, they are in general not cyclic, although they consist of a cyclic sub-class for p ≡ 1 mod 4.

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 $\mathcal {S}\subseteq \mathcal {K}=\{1,2,\ldots, K\}$ , is made vanishing). Since secrecy is of concern only to transmitters $\{i|i\in \mathcal {S}\}$ but not to transmitters $\{i|i\in \mathcal {S}^{c}\}$ , where $\mathcal {S}^{c}=\mathcal {K}\backslash \mathcal {S}$ , different transmission strategies could be employed at transmitters $\{i|i\in \mathcal {S}^{c}\}$ . Consider the following two scenarios: 1) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use deterministic encoders (which are conventionally used for MAC without secrecy), competing for the channel resource (i.e., being competitive) and 2) transmitters $\{i|i\in \mathcal {S}^{c}\}$ use stochastic encoders, helping to hide other transmitters’ messages from the eavesdropper (i.e., being cooperative). As a result, we establish the respective $\mathcal {S}$ -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 problem of secure communication over the broadcast channel with receiver-side information under the lens of individual secrecy constraints, that is, the transmitter wants to send two independent messages to two receivers, which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user.

This paper studies the problem of secure communications over broadcast channels under theindividualsecrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant ofeachmessage (i.e., the information leakage rate fromeachmessage to the eavesdropper is made vanishing). Building upon Carleial–Hellman’s secrecy coding, Wyner’s secrecy coding, and the framework of Marton’s coding together with techniques, such as rate splitting and indirect decoding, an achievable individual secrecy rate region is established with the characterization of capacity regions for some special cases. In particular, the individual secrecy capacity region for the linear deterministic model is fully characterized, and for the Gaussian model, a constant gap (i.e., 0.5 b within the individual secrecy capacity region) result is obtained. To illustrate the impact of different secrecy constraints on the corresponding capacity regions, comparisons are made with those satisfying joint secrecy and without secrecy constraints. Overall, when compared with the joint secrecy constraint, the results allow for trading off secrecy level and throughput in the system.

Bufferless network operation is favorable in many application domains such as industrial networks, on-chip networks and optical packet switching (OPS). The main challenge with zero buffers is the avoidance or handling of contention; indeed, many domain-specific contention resolution techniques have been proposed in the literature. In this paper, we propose a generic combined forward error correction (FEC) and network coding (NC) scheme, which mitigates the negative impact of contentions at the network layer. Specifically, we present a case study for OPS utilizing FEC at the ingress node and NC at an intermediary optical packet switch to reduce packet loss due to contention. Our analysis shows that if used in a smart way, our mechanism can reduce decoding error and packet loss with multiple orders of magnitude while adhering to buffering limitations and meeting delay requirements. We believe that such a combined coding scheme has the potential to be utilized both in OPS (data center and core networks) and other networks where (near-)zero buffers are required.

This paper studies the problem of secure communication over broadcast channels under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). It is known that, for the communication over the degraded broadcast channels, the stronger receiver is able to decode the message of the weaker receiver. In the individual secrecy setting, the message for the weaker receiver can be further utilized to secure the partial message that is intended to the stronger receiver. With such a coding spirit, it is shown that more secret bits can be conveyed to the stronger receiver. In particular, for the corresponding Gaussian model, a constant gap (i.e., 0.5 bits within the individual secrecy capacity region) result is obtained. Overall, when compared with the joint secrecy constraint, the results allow for trading-off secrecy level and throughput in the system.

This paper studies the problem of secret-message transmission over a wiretap channel with correlated sources in the presence of an eavesdropper who has no source observation. A coding scheme is proposed based on a careful combination of 1) Wyner-Ziv's source coding to generate secret key from correlated sources based on a certain cost on the channel, 2) one-time pad to secure messages without additional cost, and 3) Wyner's secrecy coding to achieve secrecy based on the advantage of legitimate receiver's channel over the eavesdropper's. The work sheds light on optimal strategies for practical code design for secure communication/storage systems.

In this paper, we study the problem of secure communication over the broadcast channel with receiver side information, under the lens of individual secrecy constraints (i.e., information leakage from each message to an eavesdropper is made vanishing). Several coding schemes are proposed by extending known results in broadcast channels to this secrecy setting. In particular, individual secrecy provided via one-time pad signal is utilized in the coding schemes. As a result, we obtain an achievable rate region together with a characterization of the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers). Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a square with missing corners; a phenomenon occurring due to the coupling between user's rates. At the expense of having a weaker notion of security, positive secure transmission rates are always guaranteed, unlike the case of the joint secrecy constraint.

In this paper, we study a check digit system which is based on the use of elementary abelian p-groups of order pk. This paper is inspired by a recently introduced check digit system for hexadecimal numbers. By interpreting its check equation in terminology of matrix algebra, we generalize the idea to build systems over a group of order pk, while keeping the ability to detect all the: 1) single errors; 2) adjacent transpositions; 3) twin errors; 4) jump transpositions; and 5) jump twin errors. Besides, we consider two categories of jump errors: 1) t-jump transpositions and 2) t-jump twin errors, which include and further extend the double error types of 2)-5). In particular, we explore Rc, the maximum detection radius of the system on detecting these two kinds of generalized jump errors, and show that it is 2k-2 for p=2 and (pk-1)/2-1 for an odd prime p. Also, we show how to build such a system that detects all the single errors and these two kinds of double jump-errors within Rc.

In this paper, we consider check digit systems which are based on the use of elementary abelian p-groups of order pk. The work is inspired by a recently introduced check digit system for hexadecimal numbers. By interpreting its check equation in terminology of matrix algebra, we generalize the idea to build systems over a group of order pk, while keeping the ability to detect all the 1) single errors, 2) adjacent transpositions, 3) twin errors, 4) jump transpositions and 5) jump twin errors. Besides, we consider two categories of jump errors: t-jump transpositions and t-jump twin errors, which include and further extend the double error types of 2)-5). In particular, we explore the capacity range of the system to detect these two kinds of generalized jump errors, and demonstrate that it is 2k- 3 for p = 2 and (pk-1)/2-2 for an odd prime p. Also, we show how to build such a system that detects all the single errors and these two kinds of double jump-errors within the capacity range.

In this paper we describe two methods for constructing Multivariate Quadratic Quasigroups (MQQ) in Galois fields of any characteristic and order. Our constructions extend the previously known constructions defined for operations over the prime field of characteristic 2. Application of these new constructions can reduce the public key size of the recently introduced family of public key schemes based on MQQs up to 58 times.

Abstract In this paper, we investigate the binary symmetric wiretap channel. We show that the secrecy capacitycan be achieved by using random linear codes. The random coding scheme gives insight into the structure of secrecy capacity achieving code but unfortunately involves a rather impractical decoder. We further explore the coset‐coding schemeconstructed by linear codes. As a result, we give an upper bound on the total information loss, which sheds light on the design of the applicable coset codes for the secure transmission with limited information leakage. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed–Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed–Muller codes of length${\leq}256$. We show that the bound is tight in both orders for the codes of length${\leq}128$.

In this paper, for some linear block codes, two kinds of optimum distance profiles (ODPs) are introduced to consider how to construct and then exclude (or include) the basis codewords one by one while keeping a distance profile as large as possible in a dictionary order (or in an inverse dictionary order, respectively). The aim is to improve fault-tolerant capability by selecting subcodes in communications and storage systems. One application is to serve a suitable code for the realization of the transport format combination indicators (TFCIs) of code-division multiple-access (CDMA) systems. Another application is in the field of address retrieval on optical media.

In this paper, we give a lower bound for the optimum distance profiles of the second order Reed-Muller code in the dictionary order and in the inverse dictionary order. In addition, we investigate the second order Reed-Muller codes of length les 256. We show that the bound is tight, in the dictionary order for the code of length les 32 and in the inverse dictionary order for the code of length les 128.

This correspondence gives an achievable rate equivocation region for the discrete memoryless wiretap channel with side information. We extend our results to the Gaussian case. The main contribution of this correspondence is that, for the Gaussian wiretap channel, the side information helps to get a largersecrecy capacityand a largerrate equivocationregion.

We have proved a coding theorem for the discrete memoryless wiretap channel with side information. Extending the result to the Gaussian case, an achievable rate equivocation region is given by using a strategy similar to Costa's method on dirty paper channel. In this paper, we propose an extended region for the Gaussian wiretap channel with side information. On the other hand, it is well known that, to yield the optimal rate, Costa only considers the situation when the codeword sent by the encoder is independent of side information. Here we will show that, for the wiretap channel, to yield higher rate with the same equivocation, it might be a better choice to send a codeword dependent of side information in some cases.

This paper gives a rate equivocation achievable region for the discrete memoryless wiretap channel with side information. The secrecy capacities in some special cases are also determined. We extend our result to the Gaussian case. It is very interesting to find that, for the wiretap channel, unlike the dirty paper channel, the side information helps to get larger secrecy capacity. Moreover, the rate equivocation region is also larger than that of the Gaussian wiretap channel where the side information is absent