  In this paper, the problem of spectral-efficient communication and
computation resource allocation for distributed reconfigurable intelligent
surfaces (RISs) assisted probabilistic semantic communication (PSC) in
industrial Internet-of-Things (IIoT) is investigated. In the considered model,
multiple RISs are deployed to serve multiple users, while PSC adopts
compute-then-transmit protocol to reduce the transmission data size. To support
high-rate transmission, the semantic compression ratio, transmit power
allocation, and distributed RISs deployment must be jointly considered. This
joint communication and computation problem is formulated as an optimization
problem whose goal is to maximize the sum semantic-aware transmission rate of
the system under total transmit power, phase shift, RIS-user association, and
semantic compression ratio constraints. To solve this problem, a many-to-many
matching scheme is proposed to solve the RIS-user association subproblem, the
semantic compression ratio subproblem is addressed following greedy policy,
while the phase shift of RIS can be optimized using the tensor based
beamforming. Numerical results verify the superiority of the proposed
algorithm.
