A random access scheme is a fundamental scenario in which the users transmit through a shared channel and cannot coordinate with each other. Recently, successive interference cancellation (SIC) is introduced into the random access scheme. The SIC decodes the transmitted packets using collided packets. The coded slotted ALOHA (CSA) is a random access scheme using the SIC. The CSA encodes each packet by a local code prior to transmission. It is known that the CSA achieves excellent throughput. On the other hand, it is reported that shift operation improves the decoding performance for packet-oriented erasure correcting coding systems. In this paper, we propose a protocol which applies the shift operation to the CSA. Numerical simulations show that the proposed protocol achieves better throughput and packet loss rate than the CSA. Moreover, we analyze the asymptotic behavior of the throughput and the decoding erasure rate for the proposed protocol by the density evolution.