Secret Sharing LDPC Codes for the Constrained Gaussian Wiretap Channel

The problem of secret sharing over the Gaussian wiretap channel is considered. A source and a destination intend to share secret information over a Gaussian channel in the presence of a wiretapper who observes the transmission through another Gaussian channel. Two constraints are imposed on the source-to-destination Gaussian channel, namely, the source can transmit only binary phase shift keyed symbols and symbol-by-symbol hard-decision quantization is applied to the destination's received symbols. An error-free public channel is also available for the source and destination to exchange messages in order to help the secret sharing process. The wiretapper can perfectly observe all messages in the public channel. It is shown that a secret sharing scheme that employs a random ensemble of regular low density parity check (LDPC) codes can achieve key capacity of the constrained Gaussian wiretap channel asymptotically with increasing block length. Fixed irregular LDPC codes are also designed to replace the regular LDPC code ensemble in the secret sharing scheme when the practical constraints of finite block length and limited decoding complexity are considered.