Noisy Pooled PCR for Virus Testing

Junan Zhu; Kristina Rivera; Dror Baron

Conventional RT-PCR. RT-PCR has a binary outcome. That is, once the sample is amplified, there is plenty of genetic material available for identification. Prior to amplification, there can be problems during pre-processing to isolate purified RNA. Either genetic material can be damaged, in which case all further tests with this material are negative, or the sample is contaminated, in which case further tests are positive. However, such pre-processing problems essentially flip the sample's condition permanently from negative to positive or Fig. 1 . System model. A Bernoulli process with probability ρ of sickness generates an input vector x ∈ {0, 1} N , which reflects patient illness status. The input is multiplied by a measurement matrix, A ∈ {0, 1} M ×N , resulting in noiseless measurements, w = Ax ∈ N M (1), which are processed by an RT-PCR channel, resulting in noisy measurements, y ∈ {0, 1} M (2). GAMP [7] processes the input channel relating ρ and x with g in (·) (4), and the output channel relating w and x with gout(·) (5) (details in Sec. III).