On the analysis of multiplicative-repetition code and polar code over binary erasure channels

It was recently shown that the multiplicative-repetition codes can achieve surprising excellent performance when concatenated with non-binary LDPC codes. However, the role of multiplicative-repetition codes is not well understood. In this paper, we provide important insights into the performance of the multiplicative-repetition codes under the maximum-likelihood decoding over binary erasure channels (BECs). It is shown that the design of good multiplicative-repetition code with repetition degree of T under ML decoding is equivalent to optimizing the distance profile of the minimal codewords for the code of the rate T-1/T Furthermore, we also provide important insights into the design of polar codes, as it can be viewed as a special class of multiplicative-repetition codes.