We consider a coded cooperative data exchange problem with the goal of generating a secret key. In particular, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with the fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in the traditional cooperative data exchange setting can be solved in polynomial time. In doing this, we completely characterize the best possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal. Finally, we extend the single-key results to characterize the minimum number of public transmissions required to generate a desired integer number of statistically independent secret keys.

Advances in lattice-based cryptography are enabling the use of public key algorithms (PKAs) in power-constrained ad hoc and sensor network devices. Unfortunately, while many wireless networks are dominated by group communications, PKAs are inherently unicast—i.e., public/private key pairs are generated by data destinations. To fully realize public key cryptography in these networks, lightweight PKAs should be augmented with energy-efficient mechanisms for group key agreement. We consider a setting where master keys are loaded on clients according to an arbitrary distribution. We present a protocol that uses session keys derived from those master keys to establish a group key that is information-theoretically secure. When master keys are distributed randomly, our protocol requires$O(\log_b t)$multicasts, where$1-1/b$is the probability that a given client possesses a given master key. The minimum number of public multicast transmissions required for a set of clients to agree on a secret key in our setting was recently characterized. The proposed protocol achieves the best possible approximation to that optimum that is computable in polynomial time. Moreover, the computational requirements of our protocol compare favorably to multi-party extensions of Diffie-Hellman key exchange.

We consider a cooperative data exchange problem with the goal of generating a secret key. Specifically, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with fewest linear transmissions is NP-hard, while it is known that the analogous problem in traditional cooperative data exchange can be solved in polynomial time. In doing this, we completely characterize the best-possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal.

Conditionally cycle-free graphical models (i.e., cyclic graphical models which become cycle-free after conditioning on a subset of the hidden variables) are constructed for coset codes. Following the description of a general construction procedure, examples of a number of families of codes-including first-order Reed-Muller (RM) and the Delsarte-Goethals codes - are provided for which the proposed procedure yields optimal soft-in soft-out (SISO) decoding algorithms that are less complex than the best known trellis-based algorithms. In the case of the first-order RM codes, which have a recursive coset construction, the optimal SISO decoding algorithm that results when the proposed construction is applied repeatedly is denoted recursive coset representation (RCR) decoding. Connections are made between RCR decoding and existing algorithms that exploit fast Hadamard transforms. Finally, the utility of the proposed decoding algorithms are supported by a practically motivated application: the construction of serially concatenated codes that have high rates and low error floors. Extended Hamming codes are proposed as outer codes in such constructions with efficient decoding employing the SISO algorithms developed herein.

Barrage relay networks (BRNs) are mobile ad hoc networks designed from the ground up to meet the demands of tactical edge communications. The fundamental building block of BRNs is not a point-to-point wireless link, but rather a rapid and robust broadcast mechanism that employs an autonomous cooperative communications scheme. Following a summary of basic BRN concepts, this paper demonstrates how the efficient barrage broadcast mechanism can be contained for unicast traffic via controlled barrage regions (CBRs). In particular, a protocol for CBR establishment is defined and formally verified.

This letter presents an iterative soft-in soft-out (SISO) decoding algorithm based on redundant Tanner graphs that is applicable to arbitrary linear block codes. The proposed algorithm utilizes the permutation group of a code in order to efficiently and randomly generate redundant parity-checks.

Two broad classes of graphical modeling problems for codes can be identified in the literature: constructive and extractive problems. The former class of problems concern the construction of a graphical model in order to define a new code. The latter class of problems concern the extraction of a graphical model for a (fixed) given code. The design of a new low-density parity-check code for some given criteria (e.g., target block length and code rate) is an example of a constructive problem. The determination of a graphical model for a classical linear block code that implies a decoding algorithm with desired performance and complexity characteristics is an example of an extractive problem. This work focuses on extractive graphical model problems and aims to lay out some of the foundations of the theory of such problems for linear codes. The primary focus of this work is a study of the space of all graphical models for a (fixed) given code. The tradeoff between cyclic topology and complexity in this space is characterized via the introduction of a new bound: the forest-inducing cut-set bound (FI-CSB). The proposed bound provides a more precise characterization of this tradeoff than that which can be obtained using existing tools (e.g., the CSB) and can be viewed as a generalization of the square-root bound for tail-biting trellises to graphical models with arbitrary cyclic topologies. Searching the space of graphical models for a given code is then enabled by introducing a set of basic graphical model transformation operations that are shown to span this space. Finally, heuristics for extracting novel graphical models for linear block codes using these transformations are investigated.

Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized parity-check matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles and thus derive optimal soft-in soft-out (SISO) decoding algorithms. Conditionally cycle-free generalized Tanner graphs are shown to imply optimal SISO decoding algorithms for the first order Reed-Muller codes and their duals - the extended Hamming codes - which are substantially less complex than conventional bit-level trellis decoding. The study of low-complexity optimal SISO decoding algorithms for the family of extended Hamming codes is practically motivated. Specifically, it is shown that exended Hamming codes offer an attractive alternative to high- rate convolutional codes in terms of both performance and complexity for use in very high-rate, very low-floor, serially concatenated coding schemes.

A number of authors have recently considered iterative soft-in soft-out (SISO) decoding algorithms for classical linear block codes that utilize redundant Tanner graphs. Jiang and Narayanan presented a practically realizable algorithm that applies only to cyclic codes while Kothiyal et al. presented an algorithm that, while applicable to arbitrary linear block codes, does not imply a low-complexity implementation. This work first presents the aforementioned algorithms in a common framework and then presents a related algorithm - random redundant iterative decoding - that is both practically realizable and applicable to arbitrary linear block codes. Simulation results illustrate the successful application of the random redundant iterative decoding algorithm to the extended binary Golay code. Additionally, the proposed algorithm is shown to outperform Jiang and Narayanan's algorithm for a number of Bose-Chaudhuri-Hocquenghem (BCH) codes

Let C be an [n, k, d] binary linear code with rate R = k/n and dual Cperp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperples lfloorradicnp(p-1)+n2/4+n/2rfloor where p = n - k and dperpis the minimum distance of Cperp. By applying this result, it is shown that 4-cycle-free Tanner graphs do not exist for many classical binary linear block codes

Let G=(U/spl cup/W, E) be a bipartite graph with disjoint vertex sets U and W, edge set E, and girth g. This correspondence presents an algorithm for counting the number of cycles of length g, g+2, and g+4 incident upon every vertex in U/spl cup/W. The proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as O(gn/sup 3/) where n=max(|U|,|W|).

Let C be an [n,k,d] binary linear code with rate R=k/n and dual Cperp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperples lfloorradicnp(p-1)+n2/4+n/2 rfloorwhere p=n-k and dperpis the minimum distance of Cperp. By applying this result, it is shown that 4-cycle- free Tanner graphs do not exist for many classical binary linear block codes

This correspondence presents an optimal soft-in soft-out (SISO) decoding algorithm for the binary image of Reed-Solomon (RS) codes that is based on Vardy and Be'ery's optimal soft-in hard-out algorithm. A novel suboptimal list-based SISO decoder that exploits Vardy and Be'ery's decomposition is also presented. For those codes with very high rate, which allows practical decoding with the proposed algorithms, the proposed suboptimal SISO significantly outperforms standard list-based decoding techniques in iteratively decoded systems.