Achieving the secrecy capacity on strong security using LT code with polar code pre-coding

Abstract

Coset coding is often used in the study of the physical layer security based on wiretap channel model. As almost every secure coding schemes using coset codes need a precise prediction of the channel state information (CSI), they are much more difficult to implement. To solve this problem, we propose a concatenated coding scheme combined of polar code and fountain code in wiretap channel model on binary memoryless erasure channels, achieving the strong security condition without the need for CSI. Unlike ordinary secure coding, we add fountain code after the coset encoding, making the code become a rateless code. Firstly, we illustrate the details of our scheme, and prove its security using information theory analysis method. Then, we give the result of our coding scheme against finite code length with limited security in practice. It shows our scheme works well when the code length is big enough. At last, two possible main reasons are discussed for the loss of coding rate.