Abstract-This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding stored information. Second, the paper focuses on coding schemes that enable optimal local repairs. It further brings these two concepts together, to develop locally repairable coding schemes for DSS that are secure against eavesdroppers.The main results of this paper include: a. An improved bound on the secrecy capacity for minimum storage regenerating codes, b. secure coding schemes that achieve the bound for some special cases, c. a new bound on minimum distance for locally repairable codes, d. code construction for locally repairable codes that attain the minimum distance bound, and e. repair-bandwidth-efficient locally repairable codes with and without security constraints.

Abstract-This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number of node failures. This construction, based on maximum rank distance (MRD) Gabidulin codes, provides new optimal vector and scalar LRCs. In addition, the paper also discusses mechanisms by which codes obtained using this construction can be used to construct LRCs with efficient repair of failed nodes by combination of LRC with regenerating codes.

Abstract-We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λe = O (log n)−2 , almost all of the nodes achieve a perfectly secure rate of Ω 1 √ n . The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.

This paper studies the frequency/time selective K-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the one with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) about the external eavesdropper. Using interference alignment along with secrecy pre-coding, it is shown that each user can achieve non-zero secure Degrees of Freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves2K−2 secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve K−2 2K secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks. I. INTRODUCTIONThe wiretap channel was introduced by Wyner [1], in which the eavesdropper is assumed to have access to a degraded version of the intended receiver's signal. This pioneering work was later generalized to cover the non-degraded scenario [2] and the Gaussian channel [3]. However, these results show that the secrecy capacity saturates in the high signal-to-noise ratio (SNR) regime implying a vanishing value for the secure degrees of freedom (DoF).Recently, there has been a growing interest in the analysis and design of secure wireless communication networks based on information theoretic principles. For example, the secrecy capacity of relay networks was studied in [4], [5], while the fundamental limits of the wiretap channel with feedback were analyzed by [6]. On the other hand, the multiple access and broadcast channels with secrecy constraints were investigated in [7], [8], [9]. Finally, the role of multiple antennas in enhancing the secrecy capacity was established in [10], [11] and the positive impact of fading on secrecy capacity was revealed in [12], [13].Here, the frequency/time selective K-user Gaussian interference channel with secrecy constraints is considered. Without the secrecy constraints, it has been recently shown that a

Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt is to overcome this elusive task by employing the polar coding technique of Arıkan. It is shown that polar codes achieve nontrivial perfect secrecy rates for binary-input degraded wiretap channels while enjoying their low encoding-decoding complexity. In the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy capacity. Next, fading erasure wiretap channels are considered and a secret key agreement scheme is proposed, which requires only the statistical knowledge of the eavesdropper channel state information (CSI). The enabling factor is the creation of advantage over Eve, by blindly using the proposed scheme over each fading block, which is then exploited with privacy amplification techniques to generate secret keys.

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously. I. BACKGROUND A. Vector CodesAn [n, K, d min , α] vector code over a field F q is a code C of block length n, having a symbol alphabet F α q for some α > 1, satisfying the additional property that given c, c ∈ C and a, b ∈ F q , ac + bc also belongs to C. As a vector space over F q , C has dimension K, termed the scalar dimension (equivalently, the file size) of the code and as a code over the alphabet F α q , the code has minimum distance d min . Associated with the vector code C is an F q -linear scalar code C (s) of length N = nα, where C (s) is obtained by expanding each vector symbol within a codeword into α scalar symbols (in some prescribed order). Given a generator matrix G for the scalar code C (s) , the first code symbol in the vector code is naturally associated with the first α columns of G etc. We will refer to the collection of α columns of G associated with the i th code symbol c i as the i th thick column and to avoid confusion, the columns of G themselves as thin columns. B. Locality in Vector CodesLet C be an [n, K, d min , α] vector code over a field F q , possessing a (K × nα) generator matrix G. The i th code symbol, c i , is said to have (r, δ) locality, δ ≥ 2, if there exists a punctured code C i := C| Si of C (called a local code) with support S i ⊆ {1, 2, · · · , n} such thatThe code C is said to have (r, δ) information locality if there exists l code symbols with (r, δ) locality and respective support setsThe code C is said to have (r, δ) all-symbol locality if all code symbols have (r, δ) locality. A code with (r, δ) information (respectively, all-symbol) locality is said to have full (r, δ) information (respectively, all-symbol) locality, if all local codes have parameters given by |S i | = r + δ − 1 and d min (C i ) = δ, for i = 1, · · · , l.The concept of locality for scalar codes, with δ = 2, was introduced in [1] and extended in [2] and [3] to scalar codes with arbitrary δ, and vector codes with δ = 2, respectively. This was further extended to vector codes with arbitrary δ in [4] and [5], where, in addition to constructions of vector codes with locality, authors derive minimum distance upper bounds and also consider settings in which the local codes have regeneration properti...

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This paper considers a distributed storage system, where multiple storage nodes can be reconstructed simultaneously at a centralized location. This centralized multi-node repair (CMR) model is a generalization of regenerating codes that allow for bandwidth-efficient repair of a single failed node. This work focuses on the trade-off between the amount of data stored and repair bandwidth in this CMR model. In particular, repair bandwidth bounds are derived for the minimum storage multi-node repair (MSMR) and the minimum bandwidth multi-node repair (MBMR) operating points. The tightness of these bounds are analyzed via code constructions. The MSMR point is characterized through codes achieving this point under functional repair for general set of CMR parameters, as well as with codes enabling exact repair for certain CMR parameters. The MBMR point, on the other hand, is characterized with exact repair codes for all CMR parameters for systems that satisfy a certain entropy accumulation property. Finally, the model proposed here is utilized for the secret sharing problem, where the codes for the multi-node repair problem is used to construct communication efficient secret sharing schemes with the property of bandwidth efficient share repair.• Finally, we focus on the secret sharing problem, and show that the codes for the multi-node repair problem can be transformed into communication efficient secret sharing schemes that posses not only 1 This eavesdropping model is important for non-MBR codes, as for MBR codes, the amount of downloaded content for a node repair is same as the data stored in the node. March 16, 2016 DRAFT