Application of LDGM-LDPC codes to secrecy coding for the type-II binary symmetric wiretap channel

This paper studies the problem of secrecy coding for the type-II binary symmetric memoryless wiretap channel. In this model, the main channel is binary-input and noiseless and the eavesdropper channel is binary-symmetric memoryless. A coding strategy based on secure nested codes is proposed. A capacity achieving length-n code for the eavesdropper channel bins the space {0, 1} <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> into co-sets which are used for secret messaging. The resulting co-set scheme achieves secrecy capacity of the type-II binary symmetric memoryless channel. As an example, the ensemble of capacity-achieving regular low-density generator-matrix/low-density parity-check (LDGM-LDPC) codes is studied as a basis for binning.