  Semantic communication (SemCom) aims to achieve high fidelity information
delivery under low communication consumption by only guaranteeing semantic
accuracy. Nevertheless, semantic communication still suffers from unexpected
channel volatility and thus developing a re-transmission mechanism (e.g.,
hybrid automatic repeat request [HARQ]) is indispensable. In that regard,
instead of discarding previously transmitted information, the incremental
knowledge-based HARQ (IK-HARQ) is deemed as a more effective mechanism that
could sufficiently utilize the information semantics. However, considering the
possible existence of semantic ambiguity in image transmission, a simple
bit-level cyclic redundancy check (CRC) might compromise the performance of
IK-HARQ. Therefore, it emerges a strong incentive to revolutionize the CRC
mechanism, so as to reap the benefits of both SemCom and HARQ. In this paper,
built on top of swin transformer-based joint source-channel coding (JSCC) and
IK-HARQ, we propose a semantic image transmission framework SC-TDA-HARQ. In
particular, different from the conventional CRC, we introduce a topological
data analysis (TDA)-based error detection method, which capably digs out the
inner topological and geometric information of images, so as to capture
semantic information and determine the necessity for re-transmission. Extensive
numerical results validate the effectiveness and efficiency of the proposed
SC-TDA-HARQ framework, especially under the limited bandwidth condition, and
manifest the superiority of TDA-based error detection method in image
transmission.
