Residual reliability of P-threshold graphs

We solve the problem of computing the residual reliability (the RES problem) for all classes of P-threshold graphs for which efficient structural characterizations based on decomposition to indecomposable components have been established. In particular, we give a constructive proof of existence of linear algorithms for computing residual reliability of pseudodomishold, domishold, matrogenic and matroidal graphs. On the other hand, we show that the RES problem is #P-complete on the class of biregular graphs, which implies the #P-completeness of the RES problem on the classes of indecomposable box-threshold and pseudothreshold graph

Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel

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 main channel. In order to circumvent this problem, we numerically optimize the degree distribution of the two edge type LDPC ensemble. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. There are two performance criteria for a coding scheme used over a wiretap channel: reliability and secrecy. The reliability measure corresponds to the probability of decoding error for the intended receiver. This can be easily measured using density evolution recursion. However, it is more challenging to characterize secrecy, corresponding to the equivocation of the message for the wiretapper. M\'easson, Montanari, and Urbanke have shown how the equivocation can be measured for a broad range of standard LDPC ensembles for transmission over the BEC under the point-to-point setup. By generalizing the method of M\'easson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity. However finding explicit sequences of two edge type LDPC ensembles which achieve secrecy capacity is a more difficult problem. We pose it as an interesting open problem.Comment: submitted to IEEE Transactions on Information Theory. Updated versio

Probabilistic Handshake in All-to-all Broadcast Coded Slotted ALOHA

We propose a probabilistic handshake mechanism for all-to-all broadcast coded slotted ALOHA. We consider a fully connected network where each user acts as both transmitter and receiver in a half-duplex mode. Users attempt to exchange messages with each other and to establish one-to-one handshakes, in the sense that each user decides whether its packet was successfully received by the other users: After performing decoding, each user estimates in which slots the resolved users transmitted their packets and, based on that, decides if these users successfully received its packet. The simulation results show that the proposed handshake algorithm allows the users to reliably perform the handshake. The paper also provides some analytical bounds on the performance of the proposed algorithm which are in good agreement with the simulation results

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models

Error Exponents of Low-Density Parity-Check Codes on the Binary Erasure Channel

We introduce a thermodynamic (large deviation) formalism for computing error exponents in error-correcting codes. Within this framework, we apply the heuristic cavity method from statistical mechanics to derive the average and typical error exponents of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) under maximum-likelihood decoding.Comment: 5 pages, 4 figure

An energy scaled and expanded vector-based forwarding scheme for industrial underwater acoustic sensor networks with sink mobility

Industrial Underwater Acoustic Sensor Networks (IUASNs) come with intrinsic challenges like long propagation delay, small bandwidth, large energy consumption, three-dimensional deployment, and high deployment and battery replacement cost. Any routing strategy proposed for IUASN must take into account these constraints. The vector based forwarding schemes in literature forward data packets to sink using holding time and location information of the sender, forwarder, and sink nodes. Holding time suppresses data broadcasts; however, it fails to keep energy and delay fairness in the network. To achieve this, we propose an Energy Scaled and Expanded Vector-Based Forwarding (ESEVBF) scheme. ESEVBF uses the residual energy of the node to scale and vector pipeline distance ratio to expand the holding time. Resulting scaled and expanded holding time of all forwarding nodes has a significant difference to avoid multiple forwarding, which reduces energy consumption and energy balancing in the network. If a node has a minimum holding time among its neighbors, it shrinks the holding time and quickly forwards the data packets upstream. The performance of ESEVBF is analyzed through in network scenario with and without node mobility to ensure its effectiveness. Simulation results show that ESEVBF has low energy consumption, reduces forwarded data copies, and less end-to-end delay

Two-loop corrections to the decay rate of parapositronium

Order $\alpha^2$ corrections to the decay rate of parapositronium are calculated. A QED scattering calculation of the amplitude for electron-positron annihilation into two photons at threshold is combined with the technique of effective field theory to determine an NRQED Hamiltonian, which is then used in a bound state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243(33)$ in units of $(\alpha/\pi)^2$ times the lowest order rate. This is consistent with but more precise than the result $5.1(3)$ of a previous calculation.Comment: 26 pages, 7 figure