  In this paper, the problem of joint transmission and computation resource
allocation for a multi-user probabilistic semantic communication (PSC) network
is investigated. In the considered model, users employ semantic information
extraction techniques to compress their large-sized data before transmitting
them to a multi-antenna base station (BS). Our model represents large-sized
data through substantial knowledge graphs, utilizing shared probability graphs
between the users and the BS for efficient semantic compression. The resource
allocation problem is formulated as an optimization problem with the objective
of maximizing the sum of equivalent rate of all users, considering total power
budget and semantic resource limit constraints. The computation load considered
in the PSC network is formulated as a non-smooth piecewise function with
respect to the semantic compression ratio. To tackle this non-convex non-smooth
optimization challenge, a three-stage algorithm is proposed where the solutions
for the receive beamforming matrix of the BS, transmit power of each user, and
semantic compression ratio of each user are obtained stage by stage. Numerical
results validate the effectiveness of our proposed scheme.
