We study the problem of two-user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper. In this problem, an eavesdropper receives a signal with a lower signal-to-noise ratio (SNR) compared to the legitimate receiver and all transmitted messages should be kept confidential against the eavesdropper. For this purpose, we propose a secure coding scheme on this channel which utilizes low-density parity-check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC-WT). The puncturing distribution applied to the LDPC code is considered in two cases: random and optimized. We utilize a modified extrinsic information transfer (EXIT) chart analysis to optimize the puncturing distribution for each encoder. The security gap is used as a measure of secrecy for the sent messages over GMAC-WT which should be made as small as possible. We compare the achieved secure rate pair with an achievable secrecy rate region of GMAC-WT to show the effective performance of the proposed scheme. In this paper, equal and unequal power conditions at the transmitters are investigated. For both cases, we attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC-WT.
A coding scheme based on irregular low-density parity-check (LDPC) codes is proposed to send secret messages from a source over the Gaussian wiretap channel to a destination in the presence of a wiretapper, with the restriction that the source can send only binary phase-shift keyed (BPSK) symbols. The secrecy performance of the proposed coding scheme is measured by the secret message rate through the wiretap channel as well as the equivocation rate about the message at the wiretapper. A code search procedure is suggested to obtain irregular LDPC codes that achieve good secrecy performance in s…
We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use convolutional LDPC ensembles based on the coset encoding scheme. More precisely, we consider regular two edge type convolutional LDPC ensembles. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. Convolutional LDPC ensemble were introduced by Felström and Zigangirov and are known to have excellent thresholds. Recently, Kudekar, Richardson, and Urbanke proved that the phenomenon of "Spatial Coupli…
We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction method using two edge type LDPC codes based on the coset encoding scheme. Using a standard LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge type LDPC ensemble with the same threshold. If the given standard LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the m…
For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at least three, we show using density evolution analysis that the expected bit-error probability of these ensembles, when passed through a binary erasure channel with erasure probability $ε$, decays as $\mathcal{O}(\exp(-c_1 n^{c_2}))$ with the block-length $n$ for positive constants $c_1$ and $c_2$, as long as $ε$ is lesser than the erasure threshold $ε_\mathrm{…
This paper presents a scheme named code hopping (CodeHop) for gaussian wiretap channels based on nonsystematic low-density parity-check (LDPC) codes. Different from traditional communications, in the CodeHop scheme, the legitimate receiver (Bob) rapidly switches the parity-check matrix upon each correctly received source message block. Given an authenticated public feedback channel, the transmitter's (Alice) parity-check matrix can also be synchronized with the receiver's. As a result, once an eavesdropper (Eve) erroneously decodes a message block, she may not be able to follow the update of s…
The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination channel; namely, the source can transmit only binary phase shift keyed (BPSK) symbols, and symbol-by-symbol hard-decision quantization is applied to the received symbols of the destination. An error-free public channel is also available for the source and destination to exchange me…
In this work we study the reliability and secrecy performance achievable by practical LDPC codes over the Gaussian wiretap channel. While several works have already addressed this problem in asymptotic conditions, i.e., under the hypothesis of codewords of infinite length, only a few approaches exist for the finite length regime. We propose an approach to measure the performance of practical codes and compare it with that achievable in asymptotic conditions. Moreover, based on the secrecy metrics we adopt to achieve this target, we propose a code optimization algorithm which allows to design i…
We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\geq 2k$, for some $k \geq 2$. We show that if the minimum left degree of the ensemble is $l_\mathrm{min}$, the expected probability of block error is $\calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}})$ when the erasure probability $ε< ε_\mathrm{ef}$, where $ε_\mathrm{ef}$ depends on the degree dist…
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model that corresponds to such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide an…
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.
We design and assess some practical low-density parity-check (LDPC) coded transmission schemes for the Gaussian broadcast channel with confidential messages (BCC). This channel model is different from the classical wiretap channel model as the unauthorized receiver (Eve) must be able to decode some part of the information. Hence, the reliability and security targets are different from those of the wiretap channel. In order to design and assess practical coding schemes, we use the error rate as a metric of the performance achieved by the authorized receiver (Bob) and the unauthorized receiver (…
In this paper, new two-user multiple access wiretap channel models are studied. First, the multiple access wiretap channel II with a discrete memoryless main channel, under three different wiretapping scenarios, is introduced. The wiretapper, as in the classical wiretap channel II model, chooses a fixed-length subset of the channel uses on which she obtains noise-free observations of one of the codewords, a superposition of the two codewords, or each of the two codewords. These thus extend the recently examined wiretap channel II with a noisy main channel to a multiple access setting with a va…
This paper is concerned with the general multiple access wiretap channel and the existence of codes that accomplish reliability and strong secrecy. Information leakage to the eavesdropper is assessed by the variational distance metric, whereas the average error probability is bounded by modifying Feinsteins Lemma. We derive an achievable strong secrecy rate region by utilizing the resolvability theory for the multiple-access channel in terms of information-spectrum methods.
The bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity, if there is a non-zero fraction of degree-two bit nodes. However, the degree-two bit nodes preclude the possibility of a block-error threshold. Interestingly, LDPC codes constructed using protographs allow the possibility of having both degree-two bit nodes and a block-error threshold. In this paper, we analyze density evolution for protograph LDPC codes over the binary erasure channel and show that their bit-error probability decreases double exponentially with the numbe…
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked …
We study deterministic approximations of the Gaussian two-user multiple access wiretap channel (G-MAC-WT) and the Gaussian wiretap channel with a helper (G-WT-H). These approximations enable results beyond the recently shown 2/3 and 1/2 secure degrees of freedom (s.d.o.f.) for the G-MAC-WT and the G-WT-H, respectively. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show achievable schemes which are independent of the rationality of the channel gains. Moreover, our results can differentiate between channel strengths, in particular b…
We study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown $\tfrac{2}{3}$ secure degrees of freedom (s.d.o.f.) for the Gaussian multiple access channel. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show an achievable scheme which is independent of the rationality of the channel gains. Moreover, our result can differentiate between channel strengths, in particular between both users, and establishes a secrecy rate dependent on this difference…
The Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the point-to-point white Gaussian channel with feedback, is secure by itself and also achieves the secrecy capacity of the Gaussian wiretap channel with feedback, i.e., the SK scheme is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel. For the multi-user wiretap channels, recently, it has been shown that Ozarow's capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel …
In this paper, we investigate the effects of an additional trusted relay node on the secrecy of multiple-access wiretap channel (MAC-WT) by considering the model of multiple-access relay wiretap channel (MARC-WT). More specifically, first, we investigate the discrete memoryless MARC-WT. Three inner bounds (with respect to decode-forward (DF), noise-forward (NF) and compress-forward (CF) strategies) on the secrecy capacity region are provided. Second, we investigate the degraded discrete memoryless MARC-WT, and present an outer bound on the secrecy capacity region of this degraded model. Finall…
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matc…
Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state …
We consider a two user multiple-access channel with an eavesdropper at the receiving end. We use previously transmitted messages as a key in the next slot till we achieve the capacity region of the usual Multiple Access Channel (MAC).
We study spatially coupled LDPC codes that allow access to sub-blocks much smaller than the full code block. Sub-block access is realized by a semi-global decoder that decodes a chosen target sub-block by only accessing the target, plus a prescribed number of helper sub-blocks adjacent in the code chain. This paper develops a theoretical methodology for analyzing the semi-global decoding performance of spatially coupled LDPC codes constructed from protographs. The main result shows that semi-global decoding thresholds can be derived from certain thresholds we define for the single-sub-block gr…
This paper deals with the problem of massive random access for Gaussian multiple access channel (MAC). We continue to investigate the coding scheme for Gaussian MAC proposed by A. Vem et al in 2017. The proposed scheme consists of four parts: (i) the data transmission is partitioned into time slots; (ii) the data, transmitted in each slot, is split into two parts, the first one set an interleaver of the low-density parity-check (LDPC) type code and is encoded by spreading sequence or codewords that are designed to be decoded by compressed sensing type decoding; (iii) the another part of transm…
The joint design of input constellation and low-density parity-check (LDPC) codes to approach the symmetric capacity of the two-user Gaussian multiple access channel is studied. More specifically, multilevel coding is employed at each user to construct a high-order input constellation and the constellations of the users are jointly designed so as to maximize the multiuser shaping gain. At the receiver, each layer of the multilevel coding is jointly decoded among users, while successive cancellation is employed across layers. The LDPC code employed by each user in each layer is designed using E…
Security constraint results in \textit{rate-loss} in wiretap channels. In this paper we propose a coding scheme for two user Multiple Access Channel with Wiretap (MAC-WT), where previous messages are used as a key to enhance the secrecy rates of both the users until we achieve the usual capacity region of a Multiple Access Channel (MAC) without the wiretapper (Shannon capacity region). With this scheme all the messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal we introduce secret key buffers at both the user…
We consider a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel with $N$ antennas at each transmitter, $N$ antennas at the legitimate receiver, and $K$ antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of $N$ and $K$. We subdivide our problem into several regimes based on the values of $N$ and $K$, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide …
This paper applies error-exponent and dispersion-style analyses to derive finite-blocklength achievability bounds for low-density parity-check (LDPC) codes over the point-to-point channel (PPC) and multiple access channel (MAC). The error-exponent analysis applies Gallager's error exponent to bound achievable symmetrical and asymmetrical rates in the MAC. The dispersion-style analysis begins with a generalization of the random coding union (RCU) bound from random code ensembles with i.i.d. codewords to random code ensembles in which codewords may be statistically dependent; this generalization…
This article presents a novel enhancement to the random spreading based coding scheme developed by Pradhan et al.\ for the unsourced multiple access channel. The original coding scheme features a polar outer code in conjunction with a successive cancellation list decoder (SCLD) and a hard-input soft-output MMSE estimator. In contrast, the proposed scheme employs a soft-input soft-output MMSE estimator for multi-user detection. This is accomplished by replacing the SCLD based polar code with an LDPC code amenable to belief propagation decoding. This novel framework is leveraged to successfully …
We consider spatially coupled low-density parity-check (SC-LDPC) codes within a non-orthogonal interleave division multiple access (IDMA) scheme to avoid cumbersome degree profile matching of the LDPC code components to the iterative multi-user detector (MUD). Besides excellent decoding thresholds, the approach benefits from the possibility of using rather simple and regular underlying block LDPC codes owing to the universal behavior of the resulting coupled code with respect to the channel front-end, i.e., the iterative MUD. Furthermore, an additional outer repetition code makes the scheme fl…
In this work, we describe an LDPC code design framework for the unequal power two-user Gaussian multiple access channel using EXIT charts. We show that the sum-rate of the LDPC codes designed using our approach can get close to the maximal sum-rate of the two-user Gaussian multiple access channel. Moreover, we provide numerical simulation results that demonstrate the excellent finite-length performance of the designed LDPC codes.
In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted codeword symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by sol…
In this paper, we study a diamond-relay channel where the source is connected to $M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel, but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper's channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretap…
The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode-and-forward …
A joint sparse-regression-code (SPARC) and low-density-parity-check (LDPC) coding scheme for multiple-input multiple-output (MIMO) massive unsourced random access (URA) is proposed in this paper. Different from the state-of-the-art covariance-based maximum likelihood (CB-ML) detection scheme, we first split users' messages into two parts. The former part is encoded by SPARCs and tasked to recover part of the messages, the corresponding channel coefficients as well as the interleaving patterns by compressed sensing. The latter part is coded by LDPC codes and then interleaved by the interleave-d…
In this work, we consider a K-user Gaussian wiretap multiple-access channel (GW-MAC) in which each transmitter has an independent confidential message for the receiver. There is also an external eavesdropper who intercepts the communications. The goal is to transmit the messages reliably while keeping them confidential from the eavesdropper. To accomplish this goal, two different approaches have been proposed in prior works, namely, i.i.d. Gaussian random coding and real alignment. However, the former approach fails at moderate and high SNR regimes as its achievable result does not grow with S…
This paper investigates the secrecy capacity region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can co…
This paper presents a theoretical study of a new type of LDPC codes motivated by practical storage applications. LDPCL codes (suffix L represents locality) are LDPC codes that can be decoded either as usual over the full code block, or locally when a smaller sub-block is accessed (to reduce latency). LDPCL codes are designed to maximize the error-correction performance vs. rate in the usual (global) mode, while at the same time providing a certain performance in the local mode. We develop a theoretical framework for the design of LDPCL codes. Our results include a design tool to construct an L…
A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix 'L' stands for locality) can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus offering flexible access to the coded information alongside the strong reliability of the global full-block decoding. Toward that, we propose constructions of SC-LDPCL codes that allow controlling the trade-off between local and global correction performance. In addition to local and global decoding, the paper develo…
We consider {\it i)} the overhead minimization of maximum-distance separable (MDS) storage codes for the repair of a single failed node and {\it ii)} the total secure degrees-of-freedom (S-DoF) maximization in a multiple-access compound wiretap channel. We show that the two problems are connected. Specifically, the overhead minimization for a single node failure of an {\it optimal} MDS code, i.e. one that can achieve the information theoretic overhead minimum, is equivalent to maximizing the S-DoF in a multiple-access compound wiretap channel. Additionally, we show that maximizing the S-DoF in…
In this paper we investigate the effect of spatial coupling applied to the recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to the bridge between the graphical model describing the iterative interference cancelation process of CSA over the random access frame and the erasure recovery process of low-density parity-check (LDPC) codes over the binary erasure channel (BEC), we propose an access protocol which is inspired by the convolutional LDPC code construction. The proposed protocol exploits the terminations of its graphical model to achieve the spatial coupling effec…
Shannon's secrecy system is studied in a setting, where both the legitimate decoder and the wiretapper have access to side information sequences correlated to the source, but the wiretapper receives both the coded information and the side information via channels that are more noisy than the respective channels of the legitmate decoder, which in turn, also shares a secret key with the encoder. A single--letter characterization is provided for the achievable region in the space of five figures of merit: the equivocation at the wiretapper, the key rate, the distortion of the source reconstructio…
In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we int…
In this paper, we present an extension of the semidefinite programming formulation of the optimal rate code design in single link Binary Erasure Channel (BEC) proposed by the authors to the Binary Erasure Multiple Access Channel (BE-MAC) with two sources correlation. This new way can be easily extended to the multiple access senders. Simulation results show the efficiency and effectiveness of the new approach in practice.
This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density parity-check code designs. The proposed codes are both tested in a setup where the physical layer is abstracted, as well as on a more realistic channel model, where finite-length physical layer simulations of the entire asynchronous random access scheme, including decoding are …
Consider a communication network represented by a directed graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, where $\mathcal{V}$ is the set of nodes and $\mathcal{E}$ is the set of point-to-point channels in the network. On the network a secure message $M$ is transmitted, and there may exist wiretappers who want to obtain information about the message. In secure network coding, we aim to find a network code which can protect the message against the wiretapper whose power is constrained. Cai and Yeung \cite{cai2002secure} studied the model in which the wiretapper can access any one but not more th…
We consider the problem of secure communications over the two-way wiretap channel under a strong secrecy criterion. We improve existing results by developing an achievable region based on strategies that exploit both the interference at the eavesdropper's terminal and cooperation between legitimate users. We leverage the notion of channel resolvability for the multiple-access channel to analyze cooperative jamming and we show that the artificial noise created by cooperative jamming induces a source of common randomness that can be used for secret-key agreement. We illustrate the gain provided …
In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confide…
In this paper, we want to investigate classical-quantum multiple access wiretap channels (CQ-MA-WTC) under one-shot setting. In this regard, we analyze the CQ-MA-WTC using simultaneous position-based decoder for reliable decoding and using a newly introduced technique in order to decode securely. Also, for the sake of comparison, we analyze the CQ-MA-WTC using Sen's one-shot joint typicality lemma for reliable decoding. The simultaneous position-based decoder tends to a multiple hypothesis testing problem. Also, using convex splitting to analyze the privacy criteria in a simultaneous scenario …
In this paper, we investigate the joint design of channel and network coding in bi-directional relaying systems and propose a combined low complexity physical network coding and LDPC decoding scheme. For the same LDPC codes employed at both source nodes, we show that the relay can decodes the network coded codewords from the superimposed signal received from the BPSK-modulated multiple-access channel. Simulation results shown that this novel joint physical network coding and LDPC decoding method outperforms the existing MMSE network coding and LDPC decoding method over AWGN and complex MAC cha…
We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of channels and any given network topology and communication demands, is equivalent to that of a corresponding network where each noisy wiretap channel is replaced by a noiseless wiretap channel. Thus in this case there is a separation between wiretap channel coding on each channel and secure network coding on the resulting noiseless network. We show with an example …
