An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (dmc) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second dmc). Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire-tapper. The designer attempts to build the encoder-decoder in such a way as to maximize the transmission rate R, and the equivocation d of the data as seen by the wire-tapper. In this paper, we find the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission. In particular, if d is equal to Hs, the entropy of the data source, then we consider that the transmission is accomplished in perfect secrecy. Our results imply that there exists a C s > 0, such that reliable transmission at rates up to C s is possible in approximately perfect secrecy. <s> BIB001 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> Wyner's results for discrete memoryless wire-tap channels are extended to the Gaussian wire-tap channel. It is shown that the secrecy capacity Cs is the difference between the capacities of the main and wire.tap channels. It is further shown that Rd= Cs is the upper boundary of the achievable rate-equivocation region. <s> BIB002 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> Consider the following situation. K data bits are to be encoded into N> K bits and transmitted over a noiseless channel. An intruder can observe a subset of his choice of size μ < N. The encoder is to be designed to maximize the intruder's uncertainty about the data given his μ intercepted channel bits, subject to the condition that the intended receiver can recover the K data bits perfectly from the N channel bits. The optimal trade-offs among the parameters K, N, and μ and the intruder's uncertainty H (H is the "conditional entropy" of the data given the μ intercepted channel bits) were found. In particular, it was shown that for μ = N − K, a system exists with H ≈ K − l. Thus, for example, when N = 2K and μ = K, it is possible to encode the K data bits into 2K channel bits, so that by looking at any K channel bits, the intruder obtains no more than one bit of the data. <s> BIB003 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> To communicate an r-bit secret s through a wire-tap channel, the syndrome coding strategy consists of choosing a linear transformation h and transmitting an n-bit vector x such that h(x) = s. The receiver obtains a corrupted version of x and the eavesdropper an even more corrupted version of x: the (syndrome) function h should be chosen in such a way as to minimize both the length n of the transmitted vector and the information leakage to the eavesdropper. We give a refined analysis of the information leakage that involves m-th moment methods. <s> BIB004 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> This paper presents a coding scheme for the Gaussian wiretap channel based on low-density parity-check (LDPC) codes. The messages are transmitted over punctured bits to hide data from eavesdroppers. The proposed coding scheme is asymptotically effective in the sense that it yields a bit-error rate (BER) very close to 0.5 for an eavesdropper whose signal-to-noise ratio (SNR) is lower than the threshold SNRE, even if the eavesdropper has the ability to use a bitwise maximum a posteriori (MAP) decoder. Such codes also achieve high reliability for the friendly parties provided they have an SNR above a second threshold SNRB . It is shown how asymptotically optimized LDPC codes are designed with differential evolution where the goal is to achieve high reliability between friendly parties while keeping the security gap SNRB/SNRE as small as possible to protect against passive eavesdroppers. The proposed coding scheme is encodable in linear time, applicable at finite block lengths, and can be combined with existing cryptographic schemes to deliver improved data security by taking advantage of the stochastic nature of many communication channels. <s> BIB005 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> 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. <s> BIB006 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> A coding scheme based on irregular low-density parity-check (LDPC) codes is proposed to send secret messages from a source over the Gaussian wiretap channel to a destination in the presence of a wiretapper, with the restriction that the source can send only binary phase-shift keyed (BPSK) symbols. The secrecy performance of the proposed coding scheme is measured by the secret message rate through the wiretap channel as well as the equivocation rate about the message at the wiretapper. A code search procedure is suggested to obtain irregular LDPC codes that achieve good secrecy performance in such context. <s> BIB007 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes. <s> BIB008 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> This paper examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise 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 and low-density parity-check 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 to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request 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. <s> BIB009 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> The book focuses on a recently emerging topic in security. Specifically, the book focuses on physical layer security. Whereas conventional security mechanisms involve cryptography that operates at higher layers of the protocol stack, the methods described in this book secure communications at the physical layer. The area of physical layer security is an emerging field of research that has seen an explosion of research in the past few years. This trend is only expected to continue as there is a growing need to secure wireless communications without conventional cryptographic network security protocols. The proposed book will consist of contributions from roughly a dozen of the leading research groups in this emerging area. For the first time, important results will be collected together. Important topics will include the secrecy rate of MIMO wireless systems, practical codes for the dissemination of secrets, and authentication of wireless transmitters using waveform-level properties. <s> BIB010 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> In this paper, a concatenated coding scheme based on polar codes and LDPC codes is proposed for the additive white Gaussian noise (AWGN) wiretap channel. We first analyze the bit error rate (BER) performance of the proposed coding scheme through the density evolution (DE). Then, the security gap that our coding scheme can achieve is investigated. Finally, to adapt to the dynamic environments, we present a transmission scheme using rate compatible Polar-LDPC codes. Numerical results suggest that the proposed coding scheme is more effective and flexible than other existing secure coding schemes. <s> BIB011 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We extend the Bellare-Tessaro coding scheme for a discrete, degraded, symmetric wiretap channel to a Gaussian wiretap channel. Denoting by SNR the signal-to-noise ratio of the eavesdropper’s channel, the proposed scheme converts a transmission code of rate R for the channel of the legitimate receiver into a code of rate R−0.5 log(1+SNR) for the Gaussian wiretap channel. The conversion has a polynomial complexity in the codeword length and the proposed scheme achieves strong security. In particular, when the underlying transmission code is capacity achieving, this scheme achieves the secrecy capacity of the Gaussian wiretap channel. <s> BIB012 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> In this paper, we propose a polar coding scheme for secure communication over the multiple-input, single-output, single-antenna eavesdropper (MISOSE) fading channel. We consider the case of block fading channels with known eavesdropper channel state information (CSI) and the case of fading channels with known eavesdropper channel distribution information (CDI). We use the artificial noise assisted secure precoding method to maximize the secrecy capacity in the first case, and to overcome the unawareness of the eavesdropper CSI in the second case. We show that our proposed scheme can provide both reliable and secure communication over the MISOSE channel with low encoding and decoding complexity. <s> BIB013 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> The renewed interest for physical-layer security techniques has put forward a new role for error-control codes. In addition to ensuring reliability, carefully designed codes have been shown to provide a level of information-theoretic secrecy, by which the amount of information leaked to an adversary may be controlled. The ability to achieve information-theoretic secrecy relies on the study of alternative coding mechanisms, such as channel resolvability and privacy amplification, in which error-control codes are exploited as a means to shape the distribution of stochastic processes. This use of error-control codes, which goes much beyond that of correcting errors, creates numerous new design challenges. The objective of this paper is threefold. First, the paper aims at providing system engineers with explicit tools to build simple secrecy codes in order to stimulate interest and foster their integration in communication system prototypes. Second, it aims at providing coding and information theorists with a synthetic overview of the theoretical concepts and techniques for secrecy. Finally, it aims at highlighting the open challenges and opportunities faced for the integration of these codes in practical systems. <s> BIB014 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> In this work we study the reliability and secrecy performance achievable by practical low-density parity-check (LDPC) codes over the Gaussian wiretap channel. While several works have already addressed this problem in asymptotic conditions, i.e., under the hypothesis of codewords of infinite length, only a few approaches exist for the finite length regime. We propose an approach to measure the performance of practical codes and compare it with that achievable in asymptotic conditions. Moreover, based on the secrecy metrics we adopt to achieve this target, we propose a code optimization algorithm which allows to design irregular LDPC codes able to approach the ultimate performance limits even at moderately small codeword lengths (in the order of 10000 bits). <s> BIB015 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> A bit error rate (BER)-based physical layer security approach is proposed for finite blocklength. For secure communication in the sense of high BER, the information-theoretic strong converse is combined with cryptographic error amplification achieved by substitution permutation networks (SPNs) based on confusion and diffusion. For discrete memoryless channels (DMCs), an analytical framework is provided showing the tradeoffs among finite blocklength, maximum/minimum possible transmission rates, and BER requirements for the legitimate receiver and the eavesdropper. Also, the security gap is analytically studied for Gaussian channels and the concept is extended to other DMCs including binary symmetric channels (BSCs) and binary erasure channels (BECs). For fading channels, the transmit power is optimized to minimize the outage probability of the legitimate receiver subject to a BER threshold for the eavesdropper. <s> BIB016 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We consider the Gaussian wiretap channel, where two legitimate players Alice and Bob communicate over an additive white Gaussian noise (AWGN) channel, while Eve is eavesdropping, also through an AWGN channel. We propose a coding strategy based on lattice coset encoding. We define the secrecy gain as a design criterion for wiretap lattice codes, expressed in terms of the lattice theta series, which characterizes Eve’s confusion as a function of the channel parameters. The secrecy gain is studied for even unimodular lattices, and an asymptotic analysis shows that it grows exponentially in the dimension of the lattice. Examples of wiretap lattice codes are given. <s> BIB017 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> This paper investigates the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are shown to be tighter than existing bounds. The bounds also lead to the tightest second-order coding rate for discrete memoryless and Gaussian wiretap channels. <s> BIB018 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that hierarchically utilizes polar codes is presented. In particular, on the polarization of different binary symmetric channels over different fading blocks, each channel use is modeled as an appropriate binary erasure channel over fading blocks. Polar codes are constructed for both coding over channel uses for each fading block and coding over fading blocks for certain channel uses. In order to guarantee security, random bits are introduced at appropriate places to exhaust the observations of the eavesdropper. It is shown that this coding scheme, without instantaneous CSI at the transmitter, is secrecy capacity achieving for the simultaneous fading scenario. For the independent fading case, the capacity is achieved when the fading realizations for the eavesdropper channel are always degraded with respect to the receiver. For the remaining cases, the gap between lower and upper bounds is analyzed. Remarkably, for the scenarios where the secrecy capacity is achieved, the results imply that the instantaneous CSI does not increase the secrecy capacity. <s> BIB019 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models. <s> BIB020 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> Transmissions over the wiretap channel have been studied for a long time from the information theory standpoint. This has allowed to assess the secrecy performance against eavesdropping while ensuring reliable transmission towards the legitimate receiver. However, most previous studies rely on a number of assumptions which are far from practical wireless communications, like infinite length codewords, random coding, discrete channels or continuous channels with Gaussian signaling. In this paper, we show how the level of security at the physical layer can be assessed from the information theoretic standpoint while taking into account the constraints of practical transmissions over realistic wireless wiretap channels, i.e., by considering practical codes with finite length, discrete modulation formats and continuous channels with fading. For this purpose, we consider the notion of mutual information security, which is provably equivalent to semantic security. Our target is to show that classical and already implemented coding and modulation schemes can be used to achieve some level of security at the physical layer, opposed to approaches resorting to completely new designs tailored to secure transmissions. To corroborate this thesis, we consider some coding and modulation schemes compliant with the IEEE 802.16e (WiMax) standard and show how they can be used to achieve some given security level. <s> BIB021 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We study application of convolutional codes to the randomized encoding scheme introduced by Wyner as a way of confusing the eavesdropper over a wiretap channel. We describe optimal and practical sub-optimal decoders for the main and the eavesdropper’s channels, and estimate the security gap, which is used as the main metric. The sub-optimal decoder works based on the trellis of the code generated by a convolutional code and its dual, where one encodes the data bits and the other encodes the random bits. By developing a code design metric, we describe how these two generators should be selected for optimal performance over a Gaussian wiretap channel. We also propose application of serially concatenated convolutional codes to this setup so as to reduce the resulting security gaps. Furthermore, we provide an analytical characterization of the system performance by extending existing lower and upper bounds for coded systems to the current randomized convolutional coding scenario. We illustrate our findings via extensive simulations and numerical examples, which show that the newly proposed coding scheme can outperform the other existing methods in the literature in terms of security gap. <s> BIB022 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We study application of parallel and serially concatenated convolutional codes known as turbo codes to the randomized encoding scheme introduced by Wyner for physical layer security. For this purpose, we first study how randomized convolutional codes can be constructed. Then, we use them as building blocks for developing randomized turbo codes. We also develop iterative low-complexity decoders corresponding to the randomized schemes introduced and evaluate the code performance. We demonstrate via several examples that the newly designed schemes can outperform other existing coding methods in the literature (e.g., punctured low density parity check (LDPC) and scrambled BCH codes) in terms of the resulting security gap. <s> BIB023 </s> An Overview of Physical Layer Security With Finite-Alphabet Signaling <s> IX. PRACTICAL WIRETAP CODE CONSTRUCTIONS <s> We study the application of a special class of low-density parity-check codes to the wiretap channel. We construct a randomized coding scheme based on serially concatenated low-density generator matrix codes and their duals extending the approach used for convolutional and turbo codes. Furthermore, we propose an efficient iterative decoder for this scheme utilizing a joint iterative message passing algorithm. We demonstrate via numerical examples that this approach outperforms other available practical coding alternatives for the Gaussian wiretap channel in terms of the resulting security gap. <s> BIB024
The achievability of the secrecy rates described in the previous sections is proved with the aid of random coding arguments, i.e., from an information theoretic point of view. However, in practice, one needs to realize secure communications with the aid of practical codes. In this regard, explicit and implementable code design for secrecy has also been a topic of recent interest in the literature. In particular, errorcorrecting codes have found a new role since the emergence of physical layer security. Aside from providing reliable transmission, carefully designed codes are also capable of securing the transmitted messages against an eavesdropper. On the other hand, it is challenging to design these codes because they are required to meet two conflicting requirements: 1) they need to add redundancy in order to counter the randomness of the channel and provide reliable communication, and 2) in order to offer a secure transmission, they need to maximize the randomness perceived at the eavesdropper. An important step towards designing codes for the wiretap channel is choosing a metric for measuring security. In contrast to measuring reliability where probability of error is being used as a universally accepted metric, there are multiple metrics for quantifying secrecy for this scenario as listed in Table I . Computation of these metrics for explicit finite length coding schemes, however, has been limited to some specific channels. BIB010 One example is BIB014 in which the authors apply semantic secrecy to a finite length Reed-Muller code used over a binary erasure channel (BEC). For AWGN channels, a BER based metric called security gap (as mentioned in Section II-D2) is widely used by the research community, which is easily applicable to all practical coding schemes, however, its relation to the information theoretic notions is not established in a rigorous manner. An analytical definition of security gap, which is nothing but the difference between the qualities (SNRs) of the main and the eavesdropper's channels, can be given as follows. Let us fix two threshold values for the maximum desired BER over the main channel (denoted by P max B ≤ 1 2 ) and the minimum desired BER at the eavesdropper (denoted by P min E > 0). Then, the security gap equals to the difference between the SNR values corresponding to these two, i.e., SNR B − SNR E measured in dBs. For AWGN channels without feedback, this value must be greater than zero in order to result in a positive secrecy capacity (which equals to the difference between the capacities of the main and the eavesdropper's channels BIB002 ). Small security gaps are desirable because they provide secrecy even with a small degradation of the eavesdropper's channel with respect to the main one. The major shortcoming of the above BER-based analysis is that it assumes that if P min eve ≈ 0.5, then Eve cannot extract any information about the secret message. However, if there exists a statistical correlation between the bit errors or between the Eve's observation and the transmitted message, the amount of leaked information will not be zero. Kim et al. BIB016 employ tools from cryptography literature to eliminate such correlations. Specifically, they propose the use of substitution permutation networks (SPNs) without any secret key to satisfy the strict avalanche criterion (SAC) and the bit independence criterion (BIC). The required SPNs can be implemented efficiently BIB016 , hence they can be applied to the message bits before the encoding stage. Therefore, one can design practical coding schemes, which result in BERs very close to 0.5 with no (or, small) correlation at Eve. The general coding scheme for physical layer security is the randomized encoding proposed by Wyner BIB001 to prove that there exists a code that achieves the secrecy capacity of the degraded wiretap channel. This method is also known as coset-coding studied further in BIB003 and BIB004 . In this method, the all-zero message is mapped to a linear block code C, with the generator matrix G, and a non-zero message s = [s 1 , s 2 , . . . , s k ] is mapped to the coset obtained by adding the n-tuple s 1 h 1 + s 2 h 2 + · · · + s k h k to all the codewords in C where h i 's are linearly independent n-tuples outside C. Assuming h i 's form a matrix H of size k × n, the transmitted codeword through the channel is where v = [v 1 , v 2 , . . . , v r ] denotes the random bit vector used for choosing a codeword in the corresponding coset uniformly randomly. Fig. 11 illustrates this method where the small code is denoted by C and c ij denotes the i th codeword in the j th coset. We note that in conventional (non-stochastic) encoding, the leakage of information about the secret message to Eve, H (S K |Z n ), is equal to the leakage of the codewords H (c n |Z n ) BIB014 since there is a one-to-one mapping between the messages and the codewords. In the randomized encoding scheme, however, this is not true anymore since different codewords may represent the same message. Application of lattice codes to the Gaussian wiretap channel is studied in BIB017 where the authors define an alternative security metric (called secrecy gain), which is related to the theta series of lattices and shows the amount of confusion at the eavesdropper. Without introducing a decoding method, they evaluate the performance of different lattices based on the secrecy gain. The confusion at the eavesdropper in BIB017 is the result of using a random lattice in addition to the lattice that is responsible for transmitting the original message. As a further development, Ling et al. BIB008 prove the existence of lattices that are semantically secure over the Gaussian wiretap channel. Wong et al. BIB007 and Baldi et al. BIB015 provide a lower bound on the mutual information between the secret message and the Eve's observation. They utilize this lower bound to quantify the equivocation for finite length codes for Gaussian wiretap channels. Specifically, they use finite length LDPC codes and demonstrate certain achievable points in the equivocation-rate region. In BIB021 , the level of security at the physical layer is assessed from an information theoretic perspective while taking into account the constraints of practical transmissions over realistic wireless wiretap channels, i.e., by considering practical codes with finite length, discrete modulation formats and channels with fading. Several practical coding schemes aiming directly at reducing the security gap are also proposed in the literature. Specifically, Fig. 12 . The resulting security gaps from different coding schemes. The parameters n, k and r denote length of a code, number of data bits and number of random bits, respectively. S means scrambling has been applied. The results are taken from BIB022 , BIB024 , and  . punctured LDPC codes are exploited for physical layer security in BIB005 . Reference BIB006 demonstrates how non-systematic codes can be effective to reduce the resulting security gap, while BIB009 applies different techniques including scrambling, concatenation, and hybrid automatic repeat-request to LDPC and BCH codes in order to further reduce the security gap. Concatenation of polar and LDPC codes are proposed in BIB011 . Coset codes based on convolutional and turbo codes are constructed in BIB022 and BIB023 for physical layer security. Moreover, application of serially concatenated low density generator matrix (SCLDGM) codes to the randomized scheme is studied in BIB024 . Tyagi and Vardy BIB012 introduce a method which provides strong secrecy for the Gaussian wiretap channel by means of hash functions and capacity approaching channel codes of infinite length. Using this scheme, it is also possible to quantify the level of leakage obtained for a fixed block length. Finally, BIB018 provides the maximal secrecy rate over a wiretap channel subject to reliability and secrecy constraints at a given block length. Table IX summarizes the existing practical coding schemes for Gaussian wiretap channel along with their main contributions. Furthermore, Fig. 12 demonstrates several representative security gaps from some of these practical coding schemes.  One can see that when a BER of 0.5 is desired at Eve, security gaps as small as 1 dB can be obtained using carefully designed codes of length 10 4 or longer. In addition to the Gaussian wiretap channels, some efforts are also made to develop practical coding schemes for fading wiretap channels. Zheng et al. BIB013 and Si et al. BIB019 propose polar coding schemes for achieving secrecy over block fading wiretap channels. In BIB013 , a secure coding scheme is designed with the aid of instantaneous MCSI and ECSI, while the polar coding approach proposed in BIB019 relies on statistical CSI of BIB022 both channels. Application of algebraic lattice codes is also proposed over block fading wiretap channels. For instance, a sequence of non-random lattice codes is developed in BIB020 that achieve strong secrecy and semantic security over ergodic fading channels. We emphasize that the easy-to-compute property of security gap makes it a widely used metric in majority of the aforementioned code designs, which try to avoid potential complexities associated with computing the original information-theoretic metrics for finite-length scenarios. Despite some limited efforts such as BIB015 in providing a lower bound for informationtheoretic metrics (Table I) , the literature of physical layer security still lacks a comprehensive and satisfactory finite length analysis of different metrics especially for AWGN and fading wiretap channels.