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where ds,i denotes the distance between the source S and the node ni . The observation noise Ni of each node ni is modeled as i.i.d. Gaussian random variable with zero mean 2 2 and variance N , that is, Ni N(0, N ). As each sensor node ni observes an event information Xi , this information is encoded and then sent to the sink through the WSN. In traditional point-to-point communication, the optimum performance is obtained by compressing the information according to the source statistics and then adding redundant information to accommodate the errors introduced in the wireless channel. This technique is known as the separation principle. In WSNs, where multiple nodes try to send information about the same event, however, it is known that joint source-channel coding outperforms separate coding [10, 13]. In addition, for Gaussian sources, if the source is Gaussian and the cost on the channel is the encoding power, then uncoded transmission is optimal for point-to-point transmission [14]. Furthermore, for sensor networks with nite number of nodes, uncoded transmission outperforms any approach based on the separation paradigm leading to the optimal solution for in nite number of nodes [10]. Hence, we adopt uncoded transmission for the sensor observations in this model. Each node ni sends to the sink, a scaled version, Yi , of the observed sample Xi according to encoding power constraint PE . Yi = PE X, 2 i + N i = 1, ..., N (5.6)

static const TArmContextElement* const* NThread::UserContextTables();

; de Noronha, C; Yonemoto, W; Greene, W C HIV-1 Vif blocks the antiviral activity of APOBEC3G by impairing both its translation and intracellular stability Mol Cell 2003, 12, 591 601 47 Marin, M; Rose, K M; Kozak, S L; Kabat, D HIV-1 Vif protein binds the editing enzyme APOBEC3G and induces its degradation Nat Med 2003, 9, 1398 1403 Epub 2003 Oct 1395 48 Sheehy, A M; Gaddis, N C; Malim, M H The antiretroviral enzyme APOBEC3G is degraded by the proteasome in response to HIV-1 Vif Nat Med 2003, 9, 1404 1407 Epub 2003 Oct 1405 49 Mehle, A; Strack, B; Ancuta, P; Zhang, C; McPike, M; et al Vif overcomes the innate antiviral activity of APOBEC3G by promoting its degradation in the ubiquitin-proteasome pathway J Biol Chem 2004, 279, 7792 7798 Epub 2003 Dec 7713.

2 S

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const TArmContextElement* const ThreadUserContextTables[] = { ContextTableUndefined, // EContextNone ContextTableException, ContextTableUndefined, ContextTableUserInterrupt, ContextTableUserInterruptDied, ContextTableSvsrInterrupt1, ContextTableSvsrInterrupt1Died, ContextTableSvsrInterrupt2, ContextTableSvsrInterrupt2Died, ContextTableWFAR, ContextTableWFARDied, ContextTableExec, ContextTableKernel, 0 // Null terminated };

2 2 where S and N are the variances of the event information Si and the observation noise Ni , respectively. The sink needs to calculate the estimation of each event information, Si , in order to estimate the event source S. Since uncoded transmission is used, it is well known that minimum mean square error (MMSE) estimation is the optimum decoding technique [15]. Hence, the estimation, Zi , of the event information Si is simply the MMSE estimation of Yi , which is given by

50 Mangeat, B; Turelli, P; Caron, G; Friedli, M; Perrin, L; et al Broad antiretroviral defence by human APOBEC3G through lethal editing of nascent reverse transcripts Nature 2003, 424, 99 103 51 Turelli, P; Mangeat, B; Jost, S; Vianin, S; Trono, D Inhibition of hepatitis B virus replication by APOBEC3G Science 2004, 303, 1829 52 Bass, B L RNA editing by adenosine deaminases that act on RNA Annu Rev Biochem 2002, 71, 817 846 53 Wong, S K; Sato, S; Lazinski, D W Elevated activity of the large form of ADAR1 in vivo: very ef cient RNA editing occurs in the cytoplasm RNA 2003, 9, 586 598 54 Moriyama, K; Otsuka, C; Loakes, D; Negishi, K.

This structure holds 18 pointers to tables (one for each thread context type). Each item is an array of TArmContextElement objects, one per ARM CPU register, in the order de ned in TArmRegisters:

E[Si Yi ] Yi E[Yi2 ]

Highly ef cient random mutagenesis in transcription reverse-transcription cycles by a hydrogen bond ambivalent nucleoside 50 -triphosphate analogue: potential candidates for a selective anti-retroviral therapy Nucleosides Nucleotides Nucleic Acids 2001, 20, 1473 1483 55 Moriyama, K; Negishi, K; Briggs, M S; Smith, C L; Hill, F; et al Synthesis and RNA polymerase incorporation of the degenerate ribonucleotide analogue rPTP Nucleic Acids Res 1998, 26, 2105 2111 56 Harki, D A; Graci, J D; Korneeva, V S; Ghosh, S K; Hong, Z; et al Synthesis and antiviral evaluation of a mutagenic and non-hydrogen bonding ribonucleoside analogue: 1-beta-D-Ribofuranosyl-3-nitropyrrole Biochemistry 2002, 41, 9026 9033 57 Carroll, S S; Tomassini, J E; Bosserman, M; Getty, K; Stahlhut, M W; et al Inhibition of hepatitis C virus RNA replication by 20 -modi ed nucleoside analogs J Biol Chem.

(5.7)

// Structure storing where a given // register is saved on the supervisor stack. class TArmContextElement { public: enum TType { // register is not available

Note that the estimated values of Zi s are spatially correlated since the actual event information Si s are spatially correlated. This spatial correlation results in redundancy in each event information sent to the sink. Although the sink is interested in estimating the event source, S, with a distortion constraint, intuitively, this constraint can still be met by using a smaller number of sensor nodes rather than all the nodes in the event area. In order to investigate the distortion achieved with a smaller number of nodes sending information, we assume that only M out of N packets are received by the sink, where N is the total number of sensor nodes in the event area. Since the sink decodes each Yi using the MMSE estimator, the event source can simply be computed by taking the average of all the event information received at the sink. Then, S, the estimate of S, is given as 1 S(M) = M

2003, 278, 11979 11984..

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