We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper's channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.
This paper presents a new technique for providing the analysis and comparison of wiretap codes in the small blocklength regime over the binary erasure wiretap channel. A major result is the development of Monte Carlo strategies for quantifying a code's equivocation, which mirrors techniques used to analyze normal error correcting codes. For this paper, we limit our analysis to coset-based wiretap codes, and make several comparisons of different code families at small and medium blocklengths. Our results indicate that there are security advantages to using specific codes when using small to med…
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.
In this paper, we consider a semi-deterministic wiretap channel where the main channel is noiseless and the eavesdropper's channel is a binary erasure channel (BEC). We provide a lower bound for the achievable secrecy rates of polar and Reed Muller codes and compare it to the second order coding rate for the semi-deterministic wiretap channel. To the best of our knowledge, this is the first work which demonstrates the secrecy performance of polar and Reed-Muller codes in short blocklengths. The results show that under a total variation secrecy metric, Reed Muller codes can achieve secrecy rate…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievabili…
The secrecy capacity of the type II wiretap channel (WTC II) with a noisy main channel is currently an open problem. Herein its secrecy-capacity is derived and shown to be equal to its semantic-security (SS) capacity. In this setting, the legitimate users communicate via a discrete-memoryless (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the blocklength. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. The SS criterion demands neglig…
In this paper we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid …
We consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously while a passive eavesdropper overhears a combination of their exchanged signals. The legitimate users wish to design a cooperative jamming code such that the interference between their codewords can jam the eavesdropper. In this paper, we design a polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion. The chaining method is u…
We propose multi-dimensional short blocklength probabilistic shaping to increase the nonlinear tolerance gain in digital subcarrier multiplexing transmission systems and demonstrate an improvement in performance compared to lower dimensional formats.
In this paper we develop a finite blocklength version of the Output Statistics of Random Binning (OSRB) framework. The framework is shown to be optimal in the point-to-point case. New second order regions for broadcast channel and wiretap channel with strong secrecy criterion are derived.
Two-Way Wiretap Channel under Mixed Secrecy Constraint
Volkswagen Infotainment GmbH（大众车载娱乐有限公司）；School of Data Science, The Chinese University of Hong Kong Shenzhen（香港中文大学深圳校区数据科学学院）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）
Rate-Splitting Multiple Access (RSMA) is an emerging flexible and powerful multiple access for downlink multiantenna networks. In this paper, we introduce the concept of RSMA into short-packet downlink communications. We design optimal linear precoders that maximize the sum rate with Finite Blocklength (FBL) constraints. The relations between the sum rate and blocklength of RSMA are investigated for a wide range of network loads and user deployments. Numerical results demonstrate that RSMA can achieve the same transmission rate as Non-Orthogonal Multiple Access (NOMA) and Space Division Multip…
Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengths and requires long blocklengths to achieve high shaping gain, which makes its implementation very challenging. In this paper, we propose to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same shaping rate, which makes it a suitable candidate to…
Recently, rate-$1/ω$ zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths. This paper designs CRCs for rate-$(ω-1)/ω$ CCs with short blocklengths, considering both the ZT and TB cases. The CRC design seeks to optimize the frame error rate (FER) performance of the code resulting from the concatenation of the CRC and the CC. Utilization of the dual trellis proposed by Yamada \emph{et al.} lowers the complexity of CRC-aided serial l…
In this letter, we investigate Rate-Splitting Multiple Access (RSMA) for an uplink communication system with finite blocklength. Considering a two-user Single-Input Single-Output (SISO) Multiple Access Channel (MAC), we study the impact of Signal-to-Noise Ratio (SNR), blocklength, power allocation and target rate on the error probability performance of RSMA where one user message is split. We demonstrate that RSMA can improve the error probability performance significantly compared to Non-Orthogonal Multiple Access (NOMA) and RSMA can have a larger rate region than NOMA.
This paper presents a variable-length decision-feedback scheme that uses tail-biting convolutional codes and the tail-biting Reliability-Output Viterbi Algoritm (ROVA). Comparing with recent results in finite-blocklength information theory, simulation results for both the BSC and the AWGN channel show that the decision-feedback scheme using ROVA can surpass the random-coding lower bound on throughput for feedback codes at average blocklengths less than 100 symbols. This paper explores ROVA-based decision feedback both with decoding after every symbol and with decoding limited to a small number…
In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achi…
In this letter, we explore the performance limits of short polar codes and find that the maximum likelihood (ML) performance of a simple CRC-polar concatenated scheme can approach the finite blocklength capacity. Then, in order to approach the ML performance with a low average complexity, a CRC-aided hybrid decoding (CA-HD) algorithm is proposed and its decoding process is divided into two steps. In the first step, the received sequence is decoded by the adaptive successive cancellation list (ADSCL) decoding. In the second step, CRC-aided sphere decoding with a reasonable initial radius is use…
We construct a modular scheme which extends codes for wiretap channels of type I for use in wiretap channels of type II. This is done by using a concatenate and permute strategy, wherein multiple uses of the wiretap type I code are concatenated and then the joint sequence of symbols permuted. The choice of permutation is then encoded with a short code and appended to the transmitted sequence. Analysis shows essentially no degradation in operational parameters (rate, error rate, leakage) for the new code over the wiretap type II channel when compared to those of multiple uses of the original co…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach …
We show that on an $n=24m+8k$-dimensional even unimodular lattice, if the shortest vector length is $\geq 2m$, then as the number of vectors of length $2m$ decreases, the secrecy gain increases. We will also prove a similar result on general unimodular lattices. Furthermore, assuming the conjecture by Belfiore and Solé, we will calculate the difference between inverses of secrecy gains as the number of vectors varies. Finally, we will show by an example that there exist two lattices in the same dimension with the same shortest vector length and the same kissing number, but different secrecy ga…
Wirelessly powered communications will entail short packets due to naturally small payloads, low-latency requirements and/or insufficient energy resources to support longer transmissions. In this paper, a wirelessly powered communication system is investigated where an energy harvesting transmitter, charged by one or more power beacons via wireless energy transfer, attempts to communicate with a receiver over a noisy channel. Under a save-then-transmit protocol, the system performance is characterized using metrics such as the energy supply probability at the transmitter, and the achievable ra…
Recently, a secrecy measure based on list-reconstruction has been proposed [2], in which a wiretapper is allowed to produce a list of $2^{mR_{L}}$ reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity \emph{lossy-equivocation}, which is proven to be the minimum optimistic 1-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for \emph{infinitely…
In this paper, a multi-objective optimization problem (MOOP) is proposed for maximizing the achievable finite blocklength (FBL) rate while minimizing the utilized channel blocklengths (CBLs) in a reconfigurable intelligent surface (RIS)-assisted short packet communication system. The formulated MOOP has two objective functions namely maximizing the total FBL rate with a target error probability, and minimizing the total utilized CBLs which is directly proportional to the transmission duration. The considered MOOP variables are the base station (BS) transmit power, number of CBLs, and passive b…
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use of serial list Viterbi decoding (SLVD) to achieve maximum-likelihood decoding. The convolutional encoder of interest is of rate-$1/ω$ and the convolutional code is either zero-terminated (ZT) or tail-biting (TB). The resulting CRC-aided convolutional code is called a CRC-ZTCC or a CRC-TBCC. To design a good CRC-aided convolutional code, we propose the distanc…
We show that a 0.9 dB SNR improvement can be obtained via short-blocklength enumerative sphere shaping for single-span transmission at 56 GBd. This gain vanishes for higher symbol rates and a larger number of spans.
Polar codes have been gaining a lot of interest due to it being the first coding scheme to provably achieve the symmetric capacity of a binary memoryless channel with an explicit construction. However, the main drawback of polar codes is the low throughput of its successive cancellation (SC) decoding. Simplified SC decoding algorithms of polar codes can be used to reduce the latency of the polar decode by faster processing of specific sub-codes in the polar code. By combining simplified SC with a list decoding technique, such as SC list (SCL) decoding, polar codes can cater to the two conflict…
This paper applies probabilistic amplitude shaping (PAS) to a cyclic redundancy check (CRC) aided trellis coded modulation (TCM) to achieve the short-blocklength random coding union (RCU) bound. In the transmitter, the equally likely message bits are first encoded by distribution matcher to generate amplitude symbols with the desired distribution. The binary representations of the distribution matcher outputs are then encoded by a CRC. Finally, the CRC-encoded bits are encoded and modulated by Ungerboeck's TCM scheme, which consists of a $\frac{k_0}{k_0+1}$ systematic tail-biting convolutional…
Building on the work of Horstein, Shayevitz and Feder, and Naghshvar \emph{et al.}, this paper presents algorithms for low-complexity sequential transmission of a $k$-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial $k$ binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in $k$ to linear in $k$. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approa…
In this paper, we study a quantized feedback scheme to maximize the goodput of a finite blocklength communication scenario over a quasi-static fading channel. It is assumed that the receiver has perfect channel state information (CSI) and sends back the CSI to the transmitter over a resolution-limited error-free feedback channel. With this partial CSI, the transmitter is supposed to select the optimum transmission rate, such that it maximizes the overall goodput of the communication system. This problem has been studied for the asymptotic blocklength regime, however, no solution has so far bee…
This work introduces downlink non-orthogonal multiple access (NOMA) into short-packet communications. NOMA has great potential to improve fairness and spectral efficiency with respect to orthogonal multiple access (OMA) for low-latency downlink transmission, thus making it attractive for the emerging Internet of Things. We consider a two-user downlink NOMA system with finite blocklength constraints, in which the transmission rates and power allocation are optimized. To this end, we investigate the trade-off among the transmission rate, decoding error probability, and the transmission latency m…
We investigate novel inner and outer bounds on the rate region of a 2-user Gaussian broadcast channel with finite, heterogeneous blocklength constraints (HB-GBC). In particular, we introduce a new, modified Sato-type outer bound that can be applied in the finite blocklength regime and which does not require the same marginal property. We then develop and analyze composite shell codes, which are suitable for the HB-GBC. Especially, to achieve a lower decoding latency for the user with a shorter blocklength constraint when successive interference cancellation is used, we derive the number of sym…
Wireless-powered communications will entail short packets due to naturally small payloads, low latency requirements and/or insufficient energy resources to support longer transmissions. In this paper, a wireless-powered communication system is investigated where an energy harvesting transmitter, charged by a power beacon via wireless energy transfer, attempts to communicate with a receiver over a noisy channel. Leveraging the framework of finite-length information theory, the system performance is analyzed using metrics such as the energy supply probability at the transmitter, and the achievab…
Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data transmission and the other fraction becomes near useless for this task. Mahdavifar and Vardy have recently exploited this phenomenon to construct codes that achieve the symmetric private capacity for private data transmission over a degraded wiretap channel. In the current paper, we build on their work and demonstrate how to construct quantum wiretap polar c…
