Index coding is concerned with efficient broadcast of a set of messages to receivers in the presence of receiver side information. In this paper, we study the secure index coding problem with security constraints on the receivers themselves. That is, for each receiver there is a single legitimate message it needs to decode and a prohibited message list, none of which should be decoded by that receiver. To this end, our contributions are threefold. We first introduce a secure linear coding scheme, which is an extended version of the fractional local partial clique covering scheme that was originally devised for non-secure index coding. We then develop two information-theoretic bounds on the performance of any valid secure index code, namely secure polymatroidal outer bound (on the capacity region) and secure maximum acyclic induced subgraph lower bound (on the broadcast rate). The structure of these bounds leads us to further develop two necessary conditions for a given index coding problem to be securely feasible (i.e., to have nonzero rates).
This letter investigates the role of index coding in the capacity of AWGN broadcast channels with receiver message side information. We first show that index coding is unnecessary where there are two receivers; multiplexing coding and superposition coding are sufficient to achieve the capacity region. We next show that, for more than two receivers, multiplexing coding and superposition coding alone can be suboptimal. We give an example where these two coding schemes alone cannot achieve the capacity region, but adding index coding can. This demonstrates that, in contrast to the two-receiver ca…
This paper studies the problem of secure communcation over the two-receiver discrete memoryless broadcast channel with one-sided receiver side information and with a passive eavesdropper. We proposed a coding scheme which is based upon the superposition-Marton framework. Secrecy techniques such as the one-time pad, Carleial-Hellman secrecy coding and Wyner serecy coding are applied to ensure individual secrecy. This scheme is shown to be capacity achieving for some cases of the degraded broadcast channel. We also notice that one-sided receiver side information provides the advantage of rate re…
The problem of characterizing the capacity region for Gaussian broadcast channels with receiver message side information appears difficult and remains open for N >= 3 receivers. This paper proposes a joint network and Gelfand-Pinsker coding method for 3-receiver cases. Using the method, we establish a unified inner bound on the capacity region of 3-receiver Gaussian broadcast channels under general message side information configuration. The achievability proof of the inner bound uses an idea of joint interference cancelation, where interference is canceled by using both dirty-paper coding at …
We extend the equivalence between network coding and index coding by Effros, El Rouayheb, and Langberg to the secure communication setting in the presence of an eavesdropper. Specifically, we show that the most general versions of secure network-coding setup by Chan and Grant and the secure index-coding setup by Dau, Skachek, and Chee, which also include the randomised encoding setting, are equivalent.
The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established usin…
We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index co…
This paper simplifies an existing coding scheme for the two-receiver discrete memoryless broadcast channel with complementary receiver side information where there is a passive eavesdropper and individual secrecy is required. The existing coding scheme is simplified in two steps by replacing Wyner secrecy coding with Carleial-Hellman secrecy coding. The resulting simplified scheme is free from redundant message splits and random components. Not least, the simplified scheme retains the existing achievable individual secrecy rate region. Finally, its construction simplicity helps us gain additio…
We consider achieving the rates in the capacity region of a multi-level 3-receiver broadcast channel, in which the second receiver is degraded with respect to the first receiver, with degraded message sets. We propose a two-level chaining strategy based on polar codes that achieves the capacity region of the considered setting without time-sharing. We also look at a slight variation of this problem, where the first receiver only requires to decode its own private message and the other two receivers require to decode another private message common to them. We observe that the capacity region do…
This paper studies pliable index coding, in which a sender broadcasts information to multiple receivers through a shared broadcast medium, and the receivers each have some message a priori and want any message they do not have. An approach, based on receivers that are absent from the problem, was previously proposed to find lower bounds on the optimal broadcast rate. In this paper, we introduce new techniques to obtained better lower bounds, and derive the optimal broadcast rates for new classes of the problems, including all problems with up to four absent receivers.
In this paper, we consider the problem of secure and reliable communication with uncertain channel state information (CSI) and present a new solution named active secure coding which combines the machine learning methods with the traditional physical layer secure coding scheme. First, we build a detectable wiretap channel model by combining the hidden Markov model with the compound wiretap channel model, in which the varying of channel block CSI is a Markov process and the detected information is a stochastic emission from the current CSI. Next, we present a CSI learning scheme to learn the CS…
A code equivalence between index coding and network coding was established, which shows that any index-coding instance can be mapped to a network-coding instance, for which any index code can be translated to a network code with the same decoding-error performance, and vice versa. Also, any network-coding instance can be mapped to an index-coding instance with a similar code translation. In this paper, we extend the equivalence to secure index coding and secure network coding, where eavesdroppers are present in the networks, and any code construction needs to guarantee security constraints in …
We consider the problem of source coding with receiver side information for the simple network proposed by R. Gray and A. Wyner in 1974. In this network, a transmitter must reliably transport the output of two correlated information sources to two receivers using three noiseless channels: a public channel which connects the transmitter to both receivers, and two private channels which connect the transmitter directly to each receiver. We extend Gray and Wyner's original problem by permitting side information to be present at each receiver. We derive inner and outer bounds for the achievable ra…
In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information available at the intended receiver is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR, compared to the intended receiver. The objective is to minimize the distortion of source reconstruction at the intended receiver. In this work, it is shown that the source-channel separation coding scheme is optimum in the sense of achieving minimum distortion. Two hybrid digita…
In this work, we study the secure index coding problem where there are security constraints on both legitimate receivers and eavesdroppers. We develop two performance bounds (i.e., converse results) on the symmetric secure capacity. The first one is an extended version of the basic acyclic chain bound (Liu and Sadeghi, 2019) that takes security constraints into account. The second converse result is a novel information-theoretic lower bound on the symmetric secure capacity, which is interesting as all the existing converse results in the literature for secure index coding give upper bounds on …
We characterise the optimal broadcast rate for a few classes of pliable-index-coding problems. This is achieved by devising new lower bounds that utilise the set of absent receivers to construct decoding chains with skipped messages. This work complements existing works by considering problems that are not complete-S, i.e., problems considered in this work do not require that all receivers with a certain side-information cardinality to be either present or absent from the problem. We show that for a certain class, the set of receivers is critical in the sense that adding any receiver strictly …
In network coding, information transmission often encounters wiretapping attacks. Secure network coding is introduced to prevent information from being leaked to adversaries. For secure linear network codes (SLNCs), the required field size is a very important index, because it largely determines the computational and space complexities of a SLNC, and it is also very important for the process of secure network coding from theoretical research to practical application. In this letter, we further discuss the required field size of SLNCs, and obtain a new lower bound. This bound shows that the fie…
We study the secure decentralized Pliable Index CODing (PICOD) problem with circular side information sets at the users. The security constraint forbids every user to decode more than one message while a decentralized setting means there is no central transmitter in the system. Compared to the secure but centralized version of the problem, a converse bound from one of our previous works showed a factor of three difference in optimal code length under the constraint of linear encoding. In this paper, we first list the linearly infeasible cases, that is, problems where no linear code can simulta…
We investigate the construction of weakly-secure index codes for a sender to send messages to multiple receivers with side information in the presence of an eavesdropper. We derive a sufficient and necessary condition for the existence of index codes that are secure against an eavesdropper with access to any subset of messages of cardinality $t$, for any fixed $t$. In contrast to the benefits of using random keys in secure network coding, we prove that random keys do not promote security in three classes of index-coding instances.
It is common in the study of secure multicast network coding in the presence of an eavesdropper that has access to $z$ network links, to assume that the source node is the only node that generates random keys. In this setting, the secure multicast rate is well understood. Computing the secure multicast rate, or even the secure unicast rate, in the more general setting in which all network nodes may generate (independent) random keys is known to be as difficult as computing the (non-secure) capacity of multiple-unicast network coding instances --- a well known open problem. This work treats an …
It is known that, as opposed to point-to-point channel, separate source and channel coding is not optimal in general for sending correlated sources over multiuser channels. In some works joint source-channel coding has been investigated for some certain multiuser channels; i.g., multiple access channel (MAC) and broadcast channel (BC). In this paper, we obtain a sufficient condition for transmitting arbitrarily correlated sources over a discrete memoryless BC with cooperating receivers, where the receivers are allowed to exchange messages via a pair of noisy cooperative links. It is seen that …
We study zero-error unicast index-coding instances, where each receiver must perfectly decode its requested message set, and the message sets requested by any two receivers do not overlap. We show that for all these instances with up to five receivers, linear index codes are optimal. Although this class contains 9847 non-isomorphic instances, by using our recent results and by properly categorizing the instances based on their graphical representations, we need to consider only 13 non-trivial instances to solve the entire class. This work complements the result by Arbabjolfaei et al. (ISIT 201…
The two-sender unicast index coding problem is the most fundamental multi-sender index coding problem. The two senders collectively cater to the demands of all the receivers, by taking advantage of the knowledge of their side-information. Each receiver demands a unique message and has some side-information. Weakly secure index coding problem is a practical version of the index coding problem in the presence of an eavesdropper. The eavesdropper can not gain any information about the messages he does not have, by listening to the senders' transmissions. We provide constructions of weakly secure …
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of communication and secret key. This tradeoff is the result of a mutual information optimization under Markov constraints. As a corollary, we deduce a general formula for Wyner's Common Information in the Gaussian setting.
For a packet erasure broadcast channel with three receivers, we propose a new coding algorithm that makes use of feedback to dynamically adapt the code. Our algorithm is throughput optimal, and we conjecture that it also achieves an asymptotically optimal average decoding delay at the receivers. We consider heavy traffic asymptotics, where the load factor ρapproaches 1 from below with either the arrival rate (λ) or the channel parameter (μ) being fixed at a number less than 1. We verify through simulations that our algorithm achieves an asymptotically optimal decoding delay of O(1/(1-ρ)).
This paper addresses lossy transmission of a common source over a broadcast channel when there is correlated side information at the receivers, with emphasis on the quadratic Gaussian and binary Hamming cases. A digital scheme that combines ideas from the lossless version of the problem, i.e., Slepian-Wolf coding over broadcast channels, and dirty paper coding, is presented and analyzed. This scheme uses layered coding where the common layer information is intended for both receivers and the refinement information is destined only for one receiver. For the quadratic Gaussian case, a quantity c…
We study index-coding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of index-coding problems can be fully described by directed graphs. The aim is to find the minimum codelength that the sender needs to transmit in order to simultaneously satisfy all receivers' requests. For any directed graph, we show that if a maximum acyclic induced subgraph (MAIS) is obtained by removing two or fewer vertices from the graph, then the minimum codelength (i.e., the solution to the…
In this paper, we propose a polar coding scheme for secure communication over the multiple-input, single-output, single-antenna eavesdropper (MISOSE) fading channel. We consider the case of block fading channels with known eavesdropper channel state information (CSI) and the case of fading channels with known eavesdropper channel distribution information (CDI). We use the artificial noise assisted secure precoding method to maximize the secrecy capacity in the first case, and to overcome the unawareness of the eavesdropper CSI in the second case. We show that our proposed scheme can provide bo…
Index coding models broadcast networks in which a sender sends different messages to different receivers simultaneously, where each receiver may know some of the messages a priori. The aim is to find the minimum (normalised) index codelength that the sender sends. This paper considers unicast index coding, where each receiver requests exactly one message, and each message is requested by exactly one receiver. Each unicast index-coding instances can be fully described by a directed graph and vice versa, where each vertex corresponds to one receiver. For any directed graph representing a unicast…
We investigate two source coding problems with secrecy constraints. In the first problem we consider real--time fully secure transmission of a memoryless source. We show that although classical variable--rate coding is not an option since the lengths of the codewords leak information on the source, the key rate can be as low as the average Huffman codeword length of the source. In the second problem we consider causal source coding with a fidelity criterion and side information at the decoder and the eavesdropper. We show that when the eavesdropper has degraded side information, it is optimal …
Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition co…
In this work, the problem of transmitting an i.i.d Gaussian source over an i.i.d Gaussian wiretap channel with an i.i.d Gaussian side information is considered. The intended receiver is assumed to have a certain minimum SNR and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. The objective is minimizing the distortion of source reconstruction at the intended receiver. In this work, it is shown that unlike the Gaussian wiretap channel without side information, Shannon's source-channel separation coding scheme is not optimum in the sense of achieving th…
This paper shows determining the secrecy capacity of a unicast network with uniform wiretap sets is at least as difficult as the k-unicast problem. In particular, we show that a general k-unicast problem can be reduced to the problem of finding the secrecy capacity of a corresponding single unicast network with uniform link capacities and one arbitrary wiretap link.
The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a $ρ$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability al…
We consider secure multi-terminal source coding problems in the presence of a public helper. Two main scenarios are studied: 1) source coding with a helper where the coded side information from the helper is eavesdropped by an external eavesdropper; 2) triangular source coding with a helper where the helper is considered as a public terminal. We are interested in how the helper can support the source transmission subject to a constraint on the amount of information leaked due to its public nature. We characterize the tradeoff between transmission rate, incurred distortion, and information leak…
Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem introduced by Roche (1992) and Yeung (1995). In this setting, a simple separate coding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate (Roche, Yeung, and Hau, 1997) and the entire admissible rate region (Yeung and Zhang, 1999) of the problem. This paper considers a natural generalization of SMDC to the secure communication setting with an additional eavesdropper. It is required that all sources need to be kept perfectly secret from the eavesdropper as long a…
In this paper, we investigate the secure coding issue for a wiretap channel model with fixed main channel and varying wiretap channel, by assuming that legitimate parties can obtain the wiretapping channel state information (CSI) after some time delay. For the symmetric degraded delay CSI case, we present an explicit weak security scheme by constructing secure polar codes on a one-time pad chaining structure, and prove its weak security, reliability and capability of approaching the secrecy capacity of perfect CSI case with delay CSI assumption. Further for the symmetric no-degraded delay CSI …
In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network…
In the secure network coding for multicasting, there is loss of information rate due to inclusion of random bits at the source node. We show a method to eliminate that loss of information rate by using multiple statistically independent messages to be kept secret from an eavesdropper. The proposed scheme is an adaptation of Yamamoto et al.'s secure multiplex coding to the secure network coding.
This paper studies a special class of multicast index coding problems where a sender transmits messages to multiple receivers, each with some side information. Here, each receiver knows a unique message a priori, and there is no restriction on how many messages each receiver requests from the sender. For this class of multicast index coding problems, we obtain the optimal index code, which has the shortest codelength for which the sender needs to send in order for all receivers to obtain their (respective) requested messages. This is the first class of index coding problems where the optimal i…
We consider the problem of secure communication over a network in the presence of wiretappers. We give a new cut-set bound on secrecy capacity which takes into account the contribution of both forward and backward edges crossing the cut, and the connectivity between their endpoints in the rest of the network. We show the bound is tight on a class of networks, which demonstrates that it is not possible to find a tighter bound by considering only cut set edges and their connectivity.
This paper addresses the performance of space-time coding over fading channels with impulsive noise which is known to accurately capture network interference. We use the symmetric alpha stable noise distribution and adopt two models which assume dependent and independent noise components across receive antennas. We derive pairwise error probability (PEP) of orthogonal space-time block codes (STBC) with a benchmark genie-aided receiver (GAR), or the minimum distance receiver (MDR) which is optimal in the Gaussian case. For general space-time codes we propose a maximum-likelihood (ML) receiver, …
We consider the three-receiver Gaussian multiple-input multiple-output (MIMO) broadcast channel with an arbitrary number of antennas at each of the transmitter and the receivers. We investigate the degrees-of-freedom (DoF) region of the channel when each receiver requests a private message, and may know some of the messages requested by the other receivers as receiver message side information (RMSI). We establish the DoF region of the channel for all 16 possible non-isomorphic RMSI configurations by deriving tight inner and outer bounds on the region. To derive the inner bounds, we first propo…
We consider the problem of securing a multicast network against a wiretapper that can intercept the packets on a limited number of arbitrary network edges of its choice. We assume that the network employs the network coding technique to simultaneously deliver the packets available at the source to all the receivers. We show that this problem can be looked at as a network generalization of the wiretap channel of type II introduced in a seminal paper by Ozarow and Wyner. In particular, we show that the transmitted information can be secured by using the Ozarow-Wyner approach of coset coding at t…
In a single hop broadcast packet erasure network, we demonstrate that it is possible to provide multirate packet delivery outside of what is given by the network min-cut. This is achieved by using a deterministic non-block-based network coding scheme, which allows us to sidestep some of the limitations put in place by the block coding model used to determine the network capacity. Under the network coding scheme we outline, the sender is able to transmit network coded packets above the channel rate of some receivers, while ensuring that they still experience nonzero delivery rates. Interestingl…
We consider a transmitter and $K$ receivers, each of which shares a key variable with the transmitter. Through a noiseless broadcast channel, the transmitter wishes to send a common message $W$ securely to $N$ out of the $K$ receivers while the remaining $K-N$ receivers learn no information about $W$. We are interested in the maximum message rate, i.e., the maximum number of bits of $W$ that can be securely groupcast to the legitimate receivers per key block and the minimum broadcast bandwidth, i.e., the minimum number of bits of the broadcast information required to securely groupcast the mes…
In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set. We study the minimum key lengths for zero-error and perfectly secure index coding problem. On one hand, this problem is a generalization of the index coding problem (and thus a difficult one). On the ot…
This paper considers the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) know some of the messages requested by other receivers as side information. For this setup, all possible side information configurations have been recently classified into eight groups and the capacity of the channel has been established for six groups (Asadi et al., ISIT 2014). We propose inner and outer bounds for the two remaining groups, groups 4 and 7. A distinguishing feature of these two groups is that the weakest receiver knows the requested message of the stron…
We investigate the combination between causal/zero-delay source coding and information-theoretic secrecy. Two source coding models with secrecy constraints are considered. We start by considering zero-delay perfectly secret lossless transmission of a memoryless source. We derive bounds on the key rate and coding rate needed for perfect zero-delay secrecy. In this setting, we consider two models which differ by the ability of the eavesdropper to parse the bit-stream passing from the encoder to the legitimate decoder into separate messages. We also consider causal source coding with a fidelity c…
In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at receiver and low-complexity decoding. With an unquantized receiver, coding based on algebraic rotations is known to achieve modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum mo…
In this letter, we extend the sparse Kronecker-product (SKP) coding scheme, originally designed for the additive white Gaussian noise (AWGN) channel, to multiple input multiple output (MIMO) unsourced random access (URA). With the SKP coding adopted for MIMO transmission, we develop an efficient Bayesian iterative receiver design to solve the intended challenging trilinear factorization problem. Numerical results show that the proposed design outperforms the existing counterparts, and that it performs well in all simulated settings with various antenna sizes and active-user numbers.
We consider a cache-aided communications system in which a transmitter communicates with many receivers over an erasure broadcast channel. The system serves as a basic model for communicating on-demand content during periods of high network congestion, where some content can be pre-placed in local caches near the receivers. We formulate the cache-aided communications problem as a joint cache-channel coding problem, and characterise some information-theoretic tradeoffs between reliable communications rates and cache sizes. We show that if the receivers experience different channel qualities, th…
Silva et al. proposed a universal secure network coding scheme based on MRD codes, which can be applied to any underlying network code. This paper considers a stronger eavesdropping model where the eavesdroppers possess the ability to re-select the tapping links during the transmission. We give a proof for the impossibility of attaining universal security against such adversaries using Silva et al.'s code for all choices of code parameters, even with restricted number of tapped links. We also consider the cases with restricted tapping duration and derive some conditions for this code to be sec…
In this paper, we aim to identify the strategies that can maximize and monotonically increase the density of the coding opportunities in instantly decodable network coding (IDNC).Using the well-known graph representation of IDNC, first derive an expression for the exact evolution of the edge set size after the transmission of any arbitrary coded packet. From the derived expressions, we show that sending commonly wanted packets for all the receivers can maximize the number of coding opportunities. Since guaranteeing such property in IDNC is usually impossible, this strategy does not guarantee t…
This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers (i) have private-message requests and (ii) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our te…
In the paradigm of network coding, the information-theoretic security problem is encountered in the presence of a wiretapper, who has capability of accessing an unknown channel-subset in communication networks. In order to combat this eavesdropping attack, secure network coding is introduced to prevent information from being leaked to adversaries. For any construction of secure linear network codes (SLNCs) over a wiretap network, the based field size is a very important index, because it largely determines the computational and space complexities, and further the efficiency of network transmis…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability can be a beneficial feature in some communication scenarios, such as when the receivers can afford to listen to only a part of the transmissions because of limited availability of power. The locality of an index code is the ratio of the maximum number of codeword symbols queried by a receiver to the message length. In this paper we analyze the optimum localit…
