Coding With Scrambling, Concatenation, and HARQ for the AWGN Wire-Tap Channel: A Security Gap Analysis

Abstract

This study examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise (AWGN) wire-tap channel. Unlike the previous approaches, we propose to implement nonsystematic coded transmission by scrambling the information bits, and characterize the bit error rate of scrambled transmissions through theoretical arguments and numerical simulations.We have focused on some examples of Bose-Chaudhuri-Hocquenghem (BCH) and low-density paritycheck (LDPC) codes to estimate the security gap, which we have used as a measure of physical layer security, in addition to the bit error rate. Based on a number of numerical examples, we found that such a transmission technique can outperform alternative solutions. In fact, when an eavesdropper (Eve) has a worse channel than the authorized user (Bob), the security gap required to reach a given level of security is very small. The amount of degradation of Eve's channel with respect to Bob's that is needed to achieve sufficient security can be further reduced by implementing scrambling and descrambling operations on blocks of frames, rather than on single frames. While Eve's channel has a quality equal in Ricerca 2010" funding program. to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request (HARQ) protocol with authentication still allows achieving a sufficient level of security. Finally, the secrecy performance of some practical schemes has also been measured in terms of the equivocation rate about the message at the eavesdropper and compared with that of ideal codes.

Security gap analysis of some LDPC coded transmission schemes over the flat and fast fading Gaussian wire-tap channels

“…In particular, scrambling is defined perfect when even a single error at the descrambler input produces about half of the information bits in error at the output and with randomly distributed error positions. In our previous papers [14,15], we have verified that perfect scrambling is rather easy to approach in practice.…”

“…On the other hand, the use of punctured codes brings the disadvantage of an increase in the power consumption. In some of our previous papers [12][13][14], we have demonstrated that similar, and even larger, reductions in the security gap can be achieved by using scrambled transmissions, and with considerable power saving with respect to punctured codes. A similar approach can also be used in the context of IEEE 802.11 wireless networks, where less powerful convolutional codes are used in the place of LDPC codes [15].…”

Randomized Convolutional Codes for the Wiretap Channel

“…Bit error probability of the eavesdropper versus the security gap (for P max main = 10 −5 ) when the convolutional code [657 435] encodes the data bits for 3 different codeword lengths and two different random bit encoders in (26) and (28). Results corresponding to the optimized punctured LDPC codes reported in [8] and [9] are also included for comparison. data bits and a subset of its dual for random bits.…”

“…Specifically, punctured LDPC codes are exploited for physical layer security in [7]. Furthermore, [8] demonstrates that using nonsystematic codes obtained from scrambling information bits of a systematic code are quite effective to reduce the security gap, while [9] applies different techniques including scrambling, concatenation, and hybrid automatic repeat-request to LDPC and BCH codes in order to further reduce the security gap.…”

Secret message transmission by HARQ with multiple encoding

“…A suboptimal strategy of power allocation and scheduling to maximize the overall network utility is then derived. The HARQ secrecy scenario is also considered in [9] with a rather different approach, where standard codes are used with the addition of scrambling, but secrecy is expressed in terms of the bit error probability at the eavesdropper. Lastly, the throughput of HARQ without secrecy constraints has been studied in [10], but the analysis does not fit immediately the different scenario where a secret message must be transmitted.…”