Regular LDPC codes on BMS wiretap channels: Security bounds

We improve the secrecy guarantees for transmission over general binary memoryless symmetric wiretap channels that relies on regular LDPC codes. Previous works showed that LDPC codes achieve secrecy capacity of some classes of wiretap channels while leaking $o(n)$ bits of information over $n$ uses of the channel. In this note, we improve the security component of these results by reducing the leakage parameter to $O(\log^2 n)$. While this result stops short of proving \emph{strong security}, it goes beyond the general secrecy guarantees derived from properties of capacity-approaching code families.