Near-Perfect Code Scrambling With Limited Key Information for Wiretap Channels.

In this paper, we propose a practical code scrambling scheme for secure transmissions with channel coding over wiretap channels. We develop explicit scrambling and descrambling matrix generation algorithms that can be performed with a key of limited length for each message transmission. We demonstrate that the proposed scheme avoids the direct inverse operation for large scrambling and descrambling matrices through binary operations. Therefore, without huge complexity loads and feedback overheads being incurred, the scrambling and descrambling matrices at the transmitter and legitimate receiver, respectively, can be simultaneously updated to the new pair through a few binary operations on each side. We also demonstrate that the proposed scheme approaches the perfect scrambling condition for maximizing the decoding error spreading when a sufficiently long independent key with a uniform Bernoulli distribution is provided, where the key length condition in practical applications can be overcome via key accumulation over transmissions. In addition, the proposed scheme also benefits from the descrambling matrix mismatch when the estimation for the key at the eavesdropper is imperfect. Numerical results confirm our analysis and indicate that the proposed scheme significantly improves the secrecy performance of code scrambling in wiretap channels. [ABSTRACT FROM AUTHOR]