Coding with Scrambling, Concatenation, and HARQ for the AWGN Wire-Tap Channel: A Security Gap Analysis

This study examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise (AWGN) wire-tap channel. Unlike the previous approaches, we propose to implement nonsystematic coded transmission by scrambling the information bits, and characterize the bit error rate of scrambled transmissions through theoretical arguments and numerical simulations. We have focused on some examples of Bose-Chaudhuri-Hocquenghem (BCH) and low-density parity-check (LDPC) codes to estimate the security gap, which we have used as a measure of physical layer security, in addition to the bit error rate. Based on a number of numerical examples, we found that such a transmission technique can outperform alternative solutions. In fact, when an eavesdropper (Eve) has a worse channel than the authorized user (Bob), the security gap required to reach a given level of security is very small. The amount of degradation of Eve's channel with respect to Bob's that is needed to achieve sufficient security can be further reduced by implementing scrambling and descrambling operations on blocks of frames, rather than on single frames. While Eve's channel has a quality equal to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request (HARQ) protocol with authentication still allows achieving a sufficient level of security. Finally, the secrecy performance of some practical schemes has also been measured in terms of the equivocation rate about the message at the eavesdropper and compared with that of ideal codes.Comment: 29 pages, 10 figure

Increasing Physical Layer Security through Scrambled Codes and ARQ

We develop the proposal of non-systematic channel codes on the AWGN wire-tap channel. Such coding technique, based on scrambling, achieves high transmission security with a small degradation of the eavesdropper's channel with respect to the legitimate receiver's channel. In this paper, we show that, by implementing scrambling and descrambling on blocks of concatenated frames, rather than on single frames, the channel degradation needed is further reduced. The usage of concatenated scrambling allows to achieve security also when both receivers experience the same channel quality. However, in this case, the introduction of an ARQ protocol with authentication is needed.Comment: 5 pages, 4 figures; Proc. IEEE ICC 2011, Kyoto, Japan, 5-9 June 201

A Physical Layer Secured Key Distribution Technique for IEEE 802.11g Wireless Networks

Key distribution and renewing in wireless local area networks is a crucial issue to guarantee that unauthorized users are prevented from accessing the network. In this paper, we propose a technique for allowing an automatic bootstrap and periodic renewing of the network key by exploiting physical layer security principles, that is, the inherent differences among transmission channels. The proposed technique is based on scrambling of groups of consecutive packets and does not need the use of an initial authentication nor automatic repeat request protocols. We present a modification of the scrambling circuits included in the IEEE 802.11g standard which allows for a suitable error propagation at the unauthorized receiver, thus achieving physical layer security.Comment: 9 pages, 7 figures. Accepted for publication in IEEE Wireless Communications Letters. Copyright transferred to IEE

Improving the efficiency of the LDPC code-based McEliece cryptosystem through irregular codes

We consider the framework of the McEliece cryptosystem based on LDPC codes, which is a promising post-quantum alternative to classical public key cryptosystems. The use of LDPC codes in this context allows to achieve good security levels with very compact keys, which is an important advantage over the classical McEliece cryptosystem based on Goppa codes. However, only regular LDPC codes have been considered up to now, while some further improvement can be achieved by using irregular LDPC codes, which are known to achieve better error correction performance than regular LDPC codes. This is shown in this paper, for the first time at our knowledge. The possible use of irregular transformation matrices is also investigated, which further increases the efficiency of the system, especially in regard to the public key size.Comment: 6 pages, 3 figures, presented at ISCC 201

Progressive Differences Convolutional Low-Density Parity-Check Codes

We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable features, such as fixed minimum distance and Tanner graphs without short cycles. The design approach we propose ensures that these properties are guaranteed independently of the code rate. This makes these codes of interest in many practical applications, particularly when high rate codes are needed for saving bandwidth. We provide some examples of coded transmission schemes exploiting this new class of codes.Comment: 8 pages, 2 figures. Accepted for publication in IEEE Communications Letters. Copyright transferred to IEE

A class of punctured simplex codes which are proper for error detection

Binary linear [n,k] codes that are proper for error detection are known for many combinations of n and k. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied in detail. In particular, it is shown that these codes are proper for many combinations of n and k which were previously unsettled

Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy

We use ideas of the geometry of bihamiltonian manifolds, developed by Gel'fand and Zakharevich, to study the KP equations. In this approach they have the form of local conservation laws, and can be traded for a system of ordinary differential equations of Riccati type, which we call the Central System. We show that the latter can be linearized by means of a Darboux covering, and we use this procedure as an alternative technique to construct rational solutions of the KP equations.Comment: Latex, 27 pages. To appear in Commun. Math. Phy

Exact and Approximate Expressions for the Probability of Undetected Error of Varshamov-Tenengol'ts Codes

Computation of the undetected error probability for error correcting codes over the Z-channel is an important issue, explored only in part in previous literature. In this paper we consider the case of Varshamov-Tenengol'ts codes, by presenting some analytical, numerical, and heuristic methods for unveiling this additional feature. Possible comparisons with Hamming codes are also shown and discussed.Comment: 33 pages, 9 figures, 1 table. Submitted to the IEEE Transactions on Information Theor

A normal form analysis in a finite neighborhood of a hopf bifurcation: on the center manifold dimension

The problem of determining the bounds of applicability of perturbation expansions in terms both of the system parameters and the state-space variable amplitude is a key point in the perturbation analysis of nonlinear systems. In the present paper an analysis in a finite neighborhood of a Hopf bifurcation is presented in order to analyze the conditions under which a Normal Form zero-divisors-based approach fails to describe the local dynamics and, therefore, a small divisor approach is required. The condition of “smallness” referred to the divisors is analyzed from both a qualitative and a quantitative point of view. Finally, a simple but effective analytical and numerical example is introduced to illustrate the theoretical issues along with an interpretation within a codimension-two framework

Array Convolutional Low-Density Parity-Check Codes

This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density parity-check (LDPC) block code into an RTI-LDPCC code, and we obtain a new method to design RTI-LDPCC codes with better performance and shorter constraint length. Differently from previous techniques, we start the design from an array LDPC block code. We show that, for codes with high rate, a performance gain and a reduction in the constraint length are achieved with respect to previous proposals. Additionally, an increase in the minimum distance is observed.Comment: 4 pages, 2 figures, accepted for publication in IEEE Communications Letter