Thomas R. Halford

An algorithm for counting short cycles in bipartite graphs

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|).

Spin foam models of Riemannian quantum gravity

Using numerical calculations, we compare three versions of the Barrett–Crane model of four-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov and Rovelli, we show the partition function diverges very rapidly for many triangulated 4-manifolds. In the version with modified face and edge amplitudes given by Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spin-zero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.

Barrage Relay Networks

A receiver-oriented perspective on capacity scaling in mobile ad hoc networks (MANETs) suggests that broadcast and multicast may be more natural traffic models for these systems than the random unicast pairs typically considered. Furthermore, traffic loads for the most promising near-term application for MANET technology — namely, networking at the tactical edge — are largely broadcast. The development of novel MANET approaches targeting broadcast first and foremost, however, has not been reported. Instead, existing system designs largely rely on fundamentally link-based, layered architectures, which are best suited to unicast traffic. In response to the demands of tactical edge communications, TrellisWare Technologies, Inc. developed a MANET system based on Barrage Relay Networks (BRNs). BRNs utilize an autonomous cooperative communication scheme that eliminates the need for link-level collision avoidance. The fundamental physical layer resource in BRNs is not a link, but a portion in space and time of a cooperative, multihop transport fabric. While initial hardware prototypes of BRNs were being refined into products by TrellisWare, a number of concepts similar to those that underlie BRNs were reported independently in the literature. That TrellisWares tactical edge MANET system design and academic research reconsidering the standard networking approach for MANETs arrived at similar design concepts lends credence to the value of these emerging wireless network approaches.

Barrage relay networks for cooperative transport in tactical MANETs

Barrage relay networks (BRNs) are mobile ad-hoc networks (MANETs) based on an autonomous cooperative communication scheme that allows any number of radios to cooperate in sending a given message to one or more receivers without the need for coordination. Messages in a BRN propagate outward in spatial waves wherein the simultaneous reception of a single message from multiple sources results in capture rather than collision, obviating the need for traditional collision avoidance mechanisms. The result is a very low-latency, robust broadcast mechanism. In addition to being valuable on its own (e.g., multi-hop push-to-talk voice), the broadcast capability of BRNs can be leveraged to rapidly establish paths for robust multi-hop unicast and multicast transmission, thereby enabling low-state reactive protocol design. The resulting ldquocontrolled barrage regionsrdquo (CBRs) comprise a set of buffer radio nodes that isolate a set of cooperating BRN radios. The effectiveness of BRN for broadcast and unicast is illustrated via simulations.

Transactions Letters - Random Redundant Iterative Soft-in Soft-out Decoding

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.

Barrage relay networks: System & protocol design

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.

Random Redundant Soft-In Soft-Out Decoding of Linear Block Codes

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 Narayanans algorithm for a number of Bose-Chaudhuri-Hocquenghem (BCH) codes

Which Codes Have

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

4

Scintillation mitigation is an important aspect of free-space optical (FSO) communications link design. While a number of hardware-based mitigation techniques have been proposed in the literature and deployed in experimental systems (e.g., aperture averaging, wavelength diversity, etc.), novel baseband signal processing approaches have the potential to complement - or even supplant - these traditional methods at a much lower cost and with minimal size, weight, and power impact. This paper presents a digital baseband approach to scintillation mitigation that employs multiple stop-and-wait incremental redundancy (IR) hybrid automatic repeat request (HARQ) processes. The proposed IR retransmission scheme provides a bandwidth efficient means of capturing the time diversity that is required to combat millisecond long fades at baseband. Additional gains of improved link margin and link adaptability are afforded by the use of TrellisWares Flexible Low-Density Parity-Check (F-LDPC) code family. The efficacy of the proposed coded protocol is demonstrated via simulation in a number of representative scenarios.

-Cycle-Free Tanner Graphs?

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.