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.

中文翻译：

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窃听通道的有限关键信息的近乎完美的代码扰乱


在本文中，我们提出了一种实用的代码加扰方案，用于通过窃听信道进行信道编码的安全传输。我们开发了显式加扰和解扰矩阵生成算法，可以使用每次消息传输的有限长度密钥来执行该算法。我们证明了所提出的方案通过二元运算避免了大型加扰和解扰矩阵的直接逆运算。因此，在不会产生巨大的复杂性负载和反馈开销的情况下，发送器和合法接收器处的加扰和解扰矩阵可以通过每一侧的一些二进制操作同时更新为新的对。我们还证明，当提供具有均匀伯努利分布的足够长的独立密钥时，所提出的方案接近最大化解码错误扩散的完美加扰条件，其中实际应用中的密钥长度条件可以通过传输过程中的密钥累积来克服。此外，当窃听者对密钥的估计不完善时，所提出的方案还受益于解扰矩阵不匹配。数值结果证实了我们的分析，并表明所提出的方案显着提高了窃听通道中代码加扰的保密性能。