Fault-tolerance and data fusion have been considered as two fundamental functions in wireless sensor networks. In this paper, we propose a novel approach for distributed multiclass classification using a fault-tolerant fusion rule for wireless sensor networks. Binary decisions from local sensors, possibly in the presence of faults, are forwarded to the fusion center that determines the final classification result. Classification fusion in our approach is implemented via error correcting codes to incorporate fault-tolerance capability. This new approach not only provides an improved fault-tolerance capability but also reduces computation time and memory requirements at the fusion center. Code matrix design is essential for the design of such systems. Two efficient code matrix design algorithms are proposed in this paper. The relative merits of both algorithms are also studied. We also develop sufficient conditions for asymptotic detection of the correct hypothesis by the proposed approach. Performance evaluation of the proposed approach in the presence of faults is provided. These results show significant improvement in fault-tolerance capability as compared with conventional parallel fusion networks.

The transmission range that achieves the most economical use of energy in wireless ad hoc networks is studied for uniformly distributed network nodes. By assuming the existence of forwarding neighbors and the knowledge of their locations, the average per-hop packet progress for a transmission range that is universal for all nodes is derived. This progress is then used to identify the optimal per-hop transmission range that gives the maximal energy efficiency. Equipped with this analytical result, the relation between the most energy-economical transmission range and the node density, as well as the path-loss exponent, is numerically investigated. It is observed that when the path-loss exponent is high (such as four), the optimal transmission ranges are almost identical over the range of node densities that we studied. However, when the path-loss exponent is only two, the optimal transmission range decreases noticeably as the node density increases. Simulation results also confirm the optimality of the per-hop transmission range that we found analytically.

Optimal block-codes (in the sense of minimum average error probability, using maximum likelihood decoding) with a small number of codewords are investigated for the binary asymmetric channel (BAC), including the two special cases of the binary symmetric channel (BSC) and the Z-channel (ZC), both with arbitrary cross-over probabilities. For the ZC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two, three, and four codewords and conjectured in the case of five codewords. For the BSC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two and three codewords and conjectured in the case of four codewords. For a general BAC, the best codebooks under the assumption of a threshold decoder are derived for the case of two codewords. The derivation of these optimal codes relies on a new approach of constructing and analyzing the codebook matrix not rowwise (codewords), but columnwise. This new tool leads to an elegant definition of interesting code families that is recursive in the blocklength n and admits their exact analysis of error performance. This allows for a comparison of the average error probability between all possible codebooks.

The performance of a parallel distributed detection system is investigated as the number of sensors tends to infinity. It is assumed that the i.i.d. sensor data are quantized locally into m-ary messages and transmitted to the fusion center for binary hypothesis testing. The boundedness of the second moment of the postquantization log-likelihood ratio is examined in relation to the asymptotic error exponent. It is found that, when that second moment is unbounded, the Neyman-Pearson error exponent can become a function of the test level, whereas the Bayes error exponent remains, as previously conjectured by J.N. Tsitsiklis, (1986), unaffected. Large deviations techniques are also used to show that in Bayes testing the equivalence of absolutely optimal and best identical-quantizer systems is not limited to error exponents, but extends to the actual Bayes error probabilities up to a multiplicative constant