Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels

Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in two-user Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the two-user multiple access wiretap channel, the two-user interference channel with confidential messages and the two-user interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power. This work was presented in part at Allerton Conference on Communication, Control, and Computing, September 2008 and submitted in part to IEEE Globecom Conference in March, 2009. This work is supported in part by the National Science Foundation with Grants CCR-0237727, CCF-051483, CNS-0716325, CNS-0721445 and the DARPA ITMANET Program with Grant W911NF-07-1-0028.