In this paper, we establish the partial order (POs) for both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC) under any block rate-matched polar codes. Firstly, we define the POs in the sense of rate-matched polar codes as a sequential block version. Furthermore, we demonstrate the persistence of POs after block rate matching in the BEC. Finally, leveraging the existing POs in the BEC, we obtain more POs in the BMSC under block rate matching. Simulations show that the PW sequence constructed from \beta-expansion can be improved by the tool of POs. Actually, any fixed reliable sequence in the mother polar codes can be improved by POs for rate matching.

翻译：本文针对任意分块速率匹配的极化码，建立了二进制擦除信道（BEC）和二进制无记忆对称信道（BMSC）下的部分序（POs）理论。首先，我们将速率匹配极化码中的部分序定义为一种顺序分块版本。进一步地，我们证明了在BEC中分块速率匹配后部分序的持久性。最后，借助BEC中已有的部分序，我们得到了BMSC在分块速率匹配条件下的更多部分序。仿真结果表明，通过部分序工具可以改进基于β展开构建的PW序列。事实上，对于速率匹配场景，母极化码中的任意固定可靠序列均可通过部分序进行优化。