In this paper, we have proposed a causal logging protocol for LRC based DSM systems. The notable points of the proposed protocol is to utilize the data structures and operations inherited from the LRC memory model. As a result, causal logging can be achieved by inserting some information to recreate the vector clock value for each interval, and the message overhead can be much smaller than the earlier causal logging schemes. To evaluate the performance of the proposed protocol, the logging protocol has been implemented on top of CVM distributed shared memory system. The experimental results show that the proposed scheme requires 35%-66% less log size compared to the earlier causal logging schemes.