On achieving capacity on the wire tap channel using LDPC codes

We investigate the use of capacity and near-capacity achieving LPDC codes on the wire tap channel, where the dual conditions of reliable communications and security are required. We show that good codes for conventional channels (like BSC and BEC) also have interesting and useful security properties. In this paper we show the connection between the decoding threshold of the code and its security against eavesdropping. We also give practical code constructions for some special cases of the wire tap channel and show that security (in the Shannon sense) is a function of the decoding threshold. Some of these constructions achieve the secrecy capacity as defined by Wyner. These codes provide secure communications without conventional key distribution and provide a physical-layer approach for either secure communications or key distribution.