For ordinary circuits with a xed upper bound on the fanin of its gates it has been shown that logarithmic redundancy is necessary and suucient to overcome random hardware faults (noise). Here, we consider the same question for unbounded fanin circuits which in the fault-free case can compute Boolean functions in sublogarithmic depth. Now the details of the fault model become more important. One...

We study the detection error probability associated with balanced binary relay trees, in which sensor nodes fail with some probability. We consider N identical and independent crummy sensors, represented by leaf nodes of the tree. The root of the tree represents the fusion center, which makes the final decision between two hypotheses. Every other node is a relay node, which fuses at most two bi...

Background In clinical chemistry, a number of studies shows that the probability of very large errors is much greater than expected from the Gaussian distribution. In addition, it has been empirically found that the behavior of nonlin-ear complex systems is often asymptotically exponential. Consequently, we may assume that the error of some analytical systems may be approximated by the sum of a...

Generalizing the maximum and the average error criteria for channel coding, we introduce the α-decodability, defined as the α-norm of the probabilities of correctly decoding the messages. Several aspects, such as the exponent, the existence of a strong Fano’s inequality, and the achievability of the channel capacity by random coding are investigated, and it is revealed that α “ 0 (corresponding...

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses composite, there an inherent difficulty in defining optimality criterion both informative and well-justified. For simple normal location (that is, for mean multivariate Gaussians), we overcome as follows. In this exists a natural “hardness” order between parameters different error-probabiliti...

applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

In this study, we propose an effective data-decoding method for holographic data storage (HDS) by combining convolutional neural network (CNN) and spatially coupled low-density parity-check (SC-LDPC) code. The trained CNN provides output class probabilities accurately demodulates the reproduced from HDS. We focus on these probabilities, wherein only untrainable noise components such as white Ga...