Various aspects of the present disclosure generally relate to wireless communication. In some aspects, a user equipment (UE) may receive, configuration information indicating that the UE is to compress a precoding matrix indicator in connection with channel state information reporting, wherein the precoding matrix indicator is to be compressed based at least in part on a quantization dependency between transmission layers or an orthogonality relationship between the transmission layers, and wherein the configuration information is associated with a type II, higher rank codebook for multiple input multiple output configuration. The UE may transmit, to a base station (BS), the compressed precoding matrix indicator to the base station based at least in part on receiving the configuration information. The UE and BS may use a communication configuration based at least in part on a precoding matrix indicator recovered from the compressed precoding matrix indicator. Numerous other aspects are provided.