The long-haul communication systems can offer ultra high-speed data transfer rates but suffer from burst errors. The high-rate and high-performance staircase codes provide an efficient way for long-haul transmission. The staircase coding scheme is a concatenation structure, which provides the opportunity to improve the performance of high-rate polar codes. At the same time, the polar codes make the staircase structure more reliable. Thus, a high-rate polar-staircase coding scheme is proposed, where the systematic polar codes are applied as the component codes. The soft cancellation decoding of the systematic polar codes is proposed as a basic ingredient. The encoding of the polar-staircase codes is designed with the help of density evolution, where the unreliable parts of the polar codes are enhanced. The corresponding decoding is proposed with low complexity, and is also optimized for burst error channels. With the well designed encoding and decoding algorithms, the polar-staircase codes perform well on both AWGN channels and burst error channels.