Randomized convolutional and concatenated codes for the wiretap channel

Abstract

Wireless networks are vulnerable to various kinds of attacks such as eavesdropping because of their open nature. As a result, security is one of the most important challenges that needs to be addressed for such networks. To address this issue, we utilize information theoretic secrecy approach and develop randomized channel coding techniques akin to the approach proposed by Wyner as a general method for confusing the eavesdropper while making sure that the legitimate receiver is able to recover the transmitted message. We first study the application of convolutional codes to the randomized encoding scheme. We argue how dual of a code plays a major role in this construction and obtain dual of a convolutional code in a systematic manner. We propose optimal and sub-optimal decoders for additive white Gaussian noise (AWGN) and binary symmetric channels and obtain bounds on the decoder performance extending the existing lower and upper bounds on the error rates of coded systems with maximum likelihood (ML) decoding. Furthermore, we apply list decoding to improve the performance of the sub-optimal decoders. We demonstrate via several examples that security gaps achieved by the randomized convolutional codes compete favorably with some of the existing coding methods. In order to improve the security gap hence the system performance further, we develop concatenated coding approaches applied to the randomized encoding scheme as well. These include serial and parallel concatenated convolutional codes and serial concatenation of a low density generator matrix code with a convolutional code. For all of these solutions low-complexity iterative decoders are proposed and their performance in the wiretap channel is evaluated in terms of the security gap. Numerical examples show that for certain levels of confusion at the eavesdropper, randomized serially concatenated convolutional codes oer the best performance.