Semidefinite representation of sequential rate-distortion function for stationary Gauss-Markov processes

We consider an information-theoretic performance limitation of zero-delay source coding schemes for multidimensional stationary Gauss-Markov sources. In particular, the sequential rate-distortion (SRD) problem is formulated in which the average rate per stage is minimized subject to a constraint on the average mean-square distortion per stage. We prove that there exists an optimal test channel that is linear and time invariant, which can be efficiently constructed by semidefinite programming (SDP). This result indicates that the exponentiated sequential rate-distortion function admits a semidefinite representation.