Information Theory and coding Research Papers (original) (raw)

Encryption is the process of encoding messages in such a way, that they can only be decoded by the intended receiver. On the other hand, physical-layer (PHY) security exploits channel characteristics, such as noise and multipath fading, in order to ensure confidential transmission. Even though PHY security had initially been considered as an impractical theoretical concept with little application to reality, the continued improvement in the processing power of eavesdroppers’ devices has made encryption methods more vulnerable to cryptanalytic attacks. Therefore, both from an academic and an industrial point of view, PHY security has attracted considerable attention, due to its independence from the computational strength of the eavesdropper.
In this thesis, recent research efforts on PHY security are outlined, and novel mathematical expres- sions for problems related to PHY security are derived. Also, methods and algorithms are proposed, which aim to improve the performance of existing ones. The thesis is divided into three main parts.
The first part examines PHY security from an information-theoretic standpoint, by evaluating mea- sures, such as the secrecy capacity and the secrecy outage probability (SOP). Specifically, the impact of location uncertainty of the eavesdropper on PHY security in wireless systems is evaluated and quantified. A single-antenna downlink system with a single legitimate user and an eavesdropper is considered, and the eavesdropper’s location is modeled as a two-dimensional uniform distribution over a ring-shaped area around the base-station (BS). An exact, closed-form expression for the SOP is derived, as well as a simplified expression for the case of free-space transmission. Moreover, a closed-form expression for the SOP is derived for the case, where the distance between the BS and the eavesdropper is modeled as a one-dimensional uniform distribution from the inner to the outer radius of the ring. Insights are given and conclusions are drawn based on the offered results for the SOP. Next, the effect of interference on the SOP is investigated, in a single-antenna downlink system with a single legitimate user and an eavesdropper. An arbitrary number of broadcasting BSs, whose signals are treated by the legitimate receiver and the eavesdropper as interference, is assumed. Also, all the wireless links in the system are subject to Rayleigh fading. Under these assumptions, an exact, closed-form expression is derived for the SOP. Numerical results for the SOP are provided and conclusions are drawn.
The second part deals with PHY key exchange algorithms, and specifically ones that are based on multipath fading. First, a novel least-square channel thresholding process is presented, so that the transmitter and the legitimate receiver each generate a bit string, based on their respective channel responses. According to the principle of reciprocity, the two bit strings are almost identical. The proposed thresholding method leads to a larger number of series of consecutive ones in the generated bit strings, compared to the case where a constant threshold is used. It is demonstrated that, when this method is used in the context of a PHY key exchange algorithm, this property leads to better protection from eavesdropper attacks. Next, two error reconciliation methods are proposed, in order to correct the discrepancies between the bit strings generated by the transmitter and the legitimate receiver. The first method is based on a neural network, which is constructed and trained by the transmitter, so that inputs similar to its bit string are changed to the correct value. Afterwards, the receiver’s bit string is fed through the neural network, which corrects the bit discrepancies with the transmitter’s bit string. The second method uses block error correction coding, in order to perform error reconciliation. Also, the average number of consecutive ones is used in order to produce a mask, that increases the security of the method against brute-force attacks. The two methods are shown, through simulations, to have higher key agreement rates than other methods proposed in the literature.
The third part focuses on polar codes, and particularly the design of polar codes for the relay channel. An erroneous decoding detection method is proposed, which we refer to as “smart” relaying. This technique can be applied to a polar coding scheme, where successive cancellation decoding is used. Specifically, the log-likelihood ratios (LLRs) used at any point in the decoding process are compared with a threshold parameter, and if a decision is made by taking into consideration an LLR that is too close to 1, the decoded result is discarded. In this case, the relay does not retransmit the message, since it is more likely that the receiver will make the correct decision by only taking into consideration the information received from the direct source-destination channel. Otherwise, part of the information is re-encoded by the relay with a capacity-achieving polar code for the relay-destination channel, and re-transmitted to the destination. A combination of the information received by the source and the relay is used in order to reconstruct the original message. Furthermore, a condition is proven, that shows in which cases “smart” relaying yields a better block error rate, compared to the case where “smart” relaying is not used. An extension of this technique to multiple parallel relay systems is also proposed. Finally, simulation results are presented, in order to illustrate the performance of the proposed method.