This paper is a first study on the topic of achieving physical layer security by exploiting non-systematic channel codes. The chance of implementing transmission security at the physical layer is known since many years in information theory, but it is now gaining an increasing interest due to its many possible applications. It has been shown that channel coding techniques can be effectively exploited for designing physical layer security schemes, able to ensure that an unauthorized receiver, experiencing a channel different from that of the the authorized receiver, is not able to gather any information. Recently, it has been proposed to exploit puncturing techniques in order to reduce the security gap between the authorized and unauthorized channels. In this paper, we show that the same target can also be achieved by using non-systematic codes, able to scramble information bits within the transmitted codeword.
Several works have been devoted to the study of what transmission techniques are best suited to reduce the security gap. In particular, in @cite_4 , the authors propose the usage of punctured codes, by associating the secret bits to punctured bits. They consider punctured LDPC codes and prove that such technique, for a fixed secrecy rate, is able to guarantee a considerable reduction in the security gap with respect to non-punctured (systematic) transmission.
@cite_4
1966951829 2139919528 2163096389 2131280424
A coding scheme for the Gaussian wiretap channel based on low-density parity-check (LDPC) codes is presented. The messages are transmitted over punctured bits to hide data from eavesdroppers. It is shown by means of density evolution that the BER of an eavesdropper, who operates below the code's SNR threshold and has the ability to use a bitwise MAP decoder, increases to 0.5 within a few dB. It is shown how asymptotically optimized LDPC codes can be designed with differential evolution where the goal is to achieve high reliability between friendly parties and security against a passive eavesdropper while keeping the security gap as small as possible. The proposed coding scheme is also efficiently encodable in almost linear time. Experimental results show that certain message passing algorithms, namely, survey propagation, are very effective in finding satisfying assignments in random satisfiable 3CNF formulas. In this paper we make a modest step towards providing rigorous analysis that proves the effectiveness of message passing algorithms for random 3SAT. We analyze the performance of Warning Propagation, a popular message passing algorithm that is simpler than survey propagation. We show that for 3CNF formulas generated under the planted assignment distribution, running warning propagation in the standard way works when the clause-to-variable ratio is a sufficiently large constant. We are not aware of previous rigorous analysis of message passing algorithms for satisfiability instances, though such analysis was performed for decoding of Low Density Parity Check (LDPC) Codes. We discuss some of the differences between results for the LDPC setting and our results. This paper describes a methodology for efficient implementation of binning and block-Markov coding for the relay channel using powerful features of low-density parity-check (LDPC) codes. We devise bilayer LDPC codes to approach the theoretically promised rate of the decode-and-forward relaying strategy by incorporating relay-generated random linear paritybits in a specially designed bilayer graphical code structure. Bilayer density evolution is devised as a novel extension of the standard density evolution algorithm to analyze the performance of the proposed bilayer LDPC code. Based on this bilayer density evolution technique, an EXIT-chart-based code design method using linear programming is developed. While conventional LDPC codes are sensitively tuned to operate efficiently at a certain channel parameter, the proposed bilayer LDPC code is capable of working at two different channel parameters, the signal-to-noise ratio (SNR) at the relay and the SNR at the destination. In this paper, for specific channel parameters, it is demonstrated that a bilayer LDPC code can approach the theoretical decode-and-forward rate of the relay channel within a 0.19 dB gap to the source-relay channel capacity and a 0.34 dB gap to the relay-destination channel capacity. We propose Low Density Parity Check (LDPC) code designs for the half-duplex relay channel. Our designs are based on the information theoretic random coding scheme for decode-and-forward relaying. The source transmission is decoded with the help of side information in the form of additional parity bits from the relay. We derive the exact relationships that the component LDPC code profiles in the relay coding scheme must satisfy. These relationships act as constraints for the density evolution algorithm which is used to search for good relay code profiles. To speed up optimization, we outline a Gaussian approximation of density evolution for the relay channel. The asymptotic noise thresholds of the discovered relay code profiles are a fraction of a decibel away from the achievable lower bound for decode-and-forward relaying. With random component LDPC codes, the overall relay coding scheme performs within 1.2 dB of the theoretical limit.