MOTIVATION: DNA storage offers exceptional information density and archival longevity but is constrained by complex biochemical noise inherent to synthesis, storage, and sequencing. Conventional hard-decision error-correction schemes often rely on excessive redundancy to mitigate these imperfections, which significantly compromises storage efficiency and density. RESULTS: We present Polus, a Transformer-based enhancement framework that improves digital reliability through soft-decision decoding (SDD) without requiring encoder modification. At its core is SeqFormer, a Transformer-based channel model that synergizes sequence context with quality signals to generate calibrated per-base confidence scores, effectively transforming uncertain biochemical noise into informative "soft" erasures. In in silico benchmarks, Polus significantly upgrades mainstream DNA storage codecs. It reduces the sequencing coverage required for DNA Fountain by 38.9%-increasing effective physical density by approximately 80%-and eliminates persistent indel-induced errors in the Yin-Yang codec. Furthermore, it enables a targeted resequencing strategy that achieves full recovery with 99.9% less overhead than uniform deepening. Moreover, a nine-metric evaluation suite was employed to provide multi-dimensional quantitative comparisons of DNA storage codecs across reliability, density, and cost. Collectively, Polus provides a reproducible framework for context-aware decoding and system design guidance for DNA storage. AVAILABILITY AND IMPLEMENTATION: All source code of the Polus, including the SeqFormer implementation, codec algorithms, test data used, and the simulation pipeline is available on GitHub (https://github.com/dinglulu/Polus) and Zenodo (https://zenodo.org/communities/bioinfoszu/). A web hosted instance of Polus is available at https://polus.bioailab.net/polls/home. The SeqFormer model is also released as a standalone repository at https://github.com/dinglulu/SeqFormer and https://zenodo.org/communities/bioinfoszu/.

In order to achieve rate-compatible RM codes, two most effective ways are puncturing and shortening. In this paper, puncturing schemes are studied. Different from the existing spherical puncturing, puncturing schemes which do no change the Plotkin structure of RM codes are proposed, enabling existing decoding techniques be readily accessible. The proposed puncturing schemes are based on Hamming weights of column indices of the generator matrix of RM codes. When Hamming weights of column indices (also determining the column weights, CW) are the same, different strategies are proposed, producing four different puncturing strategies, called CW-IV, CW-LSB, CW-MSB, and CW-MSB-Sym, respectively. Analysis is performed to show the union bound on error performance of RM codes with puncturing. Theoretically, it also shows that the punctured first 1st-order subcode can have potentially better performance than the non-puncturing case if puncturing is properly designed. Simulation results show that the proposed puncturing strategies outperform random and quasi-uniform puncturing (QUP) schemes in terms of block error rate (BLER). Union bound results also confirm that the first 1st-order subcode shows better performance than the original non-puncturing case. This fact indicates a more efficient transmission scheme of RM codes: transmitting part of the original codeword to increase the spectrum efficiency while achieving a better BLER performance under recursive list decoding.

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding. The existence of such lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

Recently, Huang and Zhang [1], [2] introduced the derivative as a fundamental structure of cyclic codes, based on which the derivative decoding was further presented. It is well known that some cyclic codes constructed based on finite geometries form a special class of low-density parity-check (LDPC) codes, which perform well under the sum-product algorithm. In this paper, we study the derivative structure of Euclidean geometry (EG) codes, with a special interest in EG-LDPC codes. It is proved that for µ = m −2, the derivative ascendant of the extended (µ,s)th-order EG code of length 2msis the extended (µ+1,s)th-order twofold EG code of length 2ms. As a subcode of EG-LDPC code, the derivative descendant of the extend (1,s)th-order twofold EG code is characterized in terms of the roots of the generator polynomial. The new code relationship suggests that the twofold EG code can leverage the sum-product decoding of the derivative descendant for its derivative decoding.

Polar codes have been proven to be capable of achieving the optimal rate for the lossless compression problem. However, their finite-length performance is not satisfactory due to the insufficient polarization effect. In this work, we combine source polarization with several entropy coding techniques to improve the compression efficiency while keeping the additional complexity negligible. In our framework, the standard encoding of polar codes can be treated as a pre-transform on the source data, and only a small proportion of the transformed data needs further compression thanks to the source polarization. We show that our framework is compatible with the mainstream entropy coding schemes such as Huffman coding, arithmetic coding, and asymmetric number system (ANS). To optimize performance, an iterative algorithm is proposed for the set partitioning of the transformed data. Simulation results show that the improved scheme is superior to the original polar source coding.

Syndrome Trellis Code (STC) stands out as one of the nearly optimal steganographic coding methods to date. Its superior efficiency and performance have garnered significant attention. However, STC has a limitation: it struggles to handle unevenly distributed host signals and messages, preventing it from achieving the theoretical minimum distortion. To address this flaw, we introduce an enhanced STC scheme called Content-Aware STC (CA-STC). In our work, we propose modifying the codebook based on the statistical relationship between host signals and messages. This adjustment aims to reduce overall distortion. Additionally, we introduce a new parameter to strike a balance between complexity and embedding efficiency in the proposed method. Simulation results, including scenarios involving random data, demonstrate that our approach outperforms STC in terms of global distortion, effectively adapting to diverse scenarios. Code available: https://github.com/shx-lyu/CA-STC/.

This paper aims to build a bridge between the probabilistic shaping and the geometric shaping for lattice codes from the perspective of polar lattices. We prove that when performing the lattice Gaussian shaping on polar lattices, a shaping lattice As which is good for the so-called discrete additive white Gaussian noise (AWGN) channel is constructed indeed, and the shaping process is equivalent to the modulo As operation within a multi-level decoding manner. To achieve the power-constraint AWGN channel capacity or the rate distortion bound of the i.i.d. Gaussian source, one classical approach is to construct two nested lattices where the fine lattice takes care of the Gaussian noise or the target distortion, and the coarse lattice is responsible for the boundary of the lattice codewords. Another approach is to construct a single lattice and then perform the lattice Gaussian shaping. The former approach falls into the category of geometric shaping, while the latter one is regarded as a type of probabilistic shaping. This work proposes a unified perspective of these two approaches, and provides new evidence on why they are both able to achieve the optimal performance of Gaussian channel coding and source coding problems.

To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed. Basic properties of the VS structure are presented. With the aid of these properties, existing explicit constructions for column weights from three to five which can be transformed into the VS structure are sorted out. Then two novel explicit constructions with the VS structure which guarantee short codes are presented for column weights of three and six. Moreover, an efficient search-based method is also proposed to find short codes with the VS structure. Compared with the state-of-the-art benchmarks, both the explicit constructions and the search-based method presented in this paper can provide shorter codes for most cases. Simulation results show that the new shorter codes can perform almost the same as or better than the longer existing counterparts. Thus, the new shorter codes can fit better with the low-latency requirement for modern communication systems.

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach$\frac{1}{2\pi e}$as the dimension of lattices increases. It has been predicted by Zamir et al. [1] that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work [2], we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e.$q$bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of$q$bits but only$i$bits,$1 \leq i

The Extremely-large Aperture Reconfigurable In-telligent Surface (RIS) stands out as a promising technology for future 6G communications. However, existing far-field or near-field channel models struggle to adapt effectively to channel estimation in the context of Extremely-large Aperture RIS-assisted wireless communication under a hybrid field. To address this challenge, this paper introduces an efficient hybrid-field channel estimation scheme tailored for Extremely-large Aperture RIS-assisted wireless communication. In this scheme, we initially extend the one-dimensional polar coordinate dictionary to a full-dimensional spherical coordinate dictionary to achieve a more uniform distribution of grid points in the spherical coordinate-domain. Subsequently, we propose a hybrid passive/active RIS architecture, utilizing a limited number of Radio Frequency (RF) chains to acquire channel observations. Finally, we introduce a hybrid-field channel estimation scheme designed to estimate both far-field and near-field components. Simulation results demonstrate that the proposed scheme outperforms purely far-field or near-field schemes.

In this paper, we propose a low-latency probabilistically shaped multilevel polar coded modulation (PS-MLPCM) scheme for 6G called parallel PS-MLPCM. The proposed scheme achieves parallel encoding by disregarding the relationship between different bit levels when profiling shaping bits, while the conventional PS-MLPCM scheme has to perform encoding level by level. Additionally, we have found a suitable mapping scheme for the spiral constellations to ensure that the spiral constellations based parallel PS-MLPCM scheme can approach the capacity of additive white Gaussian noise (AWGN) channels. We perform numerical simulation for 64-Spiral and 64-QAM based schemes under both successive cancellation (SC) decoder and cyclic redundancy check aided SC-list (CA-SCL) decoder. The results show that the 64-Spiral based scheme achieves more than 0.8dB shaping gain at high signal-to-noise ratio (SNR). Meanwhile, the 64-Spiral based scheme can outperform the 64- QAM based scheme, especially when SNR is high or CA-SCL decoder is used.

Abstract We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

Multitask optimization aims to solve two or more optimization tasks simultaneously by leveraging intertask knowledge transfer. However, as the number of tasks increases to the extent of many-task optimization, the knowledge transfer between tasks encounters more uncertainty and challenges, thereby resulting in degradation of optimization performance. To give full play to the many-task optimization framework and minimize the potential negative transfer, this article proposes an evolutionary many-task optimization algorithm based on a multisource knowledge transfer mechanism, namely, EMaTO-MKT. Particularly, in each iteration, EMaTO-MKT determines the probability of using knowledge transfer adaptively according to the evolution experience, and balances the self-evolution within each task and the knowledge transfer among tasks. To perform knowledge transfer, EMaTO-MKT selects multiple highly similar tasks in terms of maximum mean discrepancy as the learning sources for each task. Afterward, a knowledge transfer strategy based on local distribution estimation is applied to enable the learning from multiple sources. Compared with the other state-of-the-art evolutionary many-task algorithms on benchmark test suites, EMaTO-MKT shows competitiveness in solving many-task optimization problems.

Multitasking optimization can achieve better performance than traditional single-tasking optimization by leveraging knowledge transfer between tasks. However, the current multitasking optimization algorithms suffer from some deficiencies. Particularly, on high similar problems, the existing algorithms might fail to take full advantage of knowledge transfer to accelerate the convergence of the search, or easily get trapped in the local optima. Whereas, on low similar problems, they tend to suffer from negative transfer, resulting in performance degradation. To solve these issues, this article proposes an evolutionary multitasking optimization algorithm for multiobjective/many-objective optimization with two-stage adaptive knowledge transfer based on population distribution. The resultant algorithm named EMT-PD can improve the convergence performance of the target optimization tasks based on the knowledge extracted from the probability model that reflects the search trend of the whole population. At the first stage of knowledge transfer, an adaptive weight is used to adjust the search step size of each individual, which can reduce the impact of negative transfer. At the second stage of knowledge transfer, the search range of each individual is further adjusted dynamically, which can improve the population diversity and be beneficial for jumping out of the local optima. Experimental results on multitasking multiobjective optimization test suites show that EMT-PD is superior to other state-of-the-art evolutionary multitasking/single-tasking algorithms. To further investigate the effectiveness of EMT-PD on many-objective optimization problems, a multitasking many-objective optimization test suite is also designed in this article. The experimental results on the new test suite also demonstrate the competitiveness of EMT-PD.

This paper investigates the application of physical-layer network coding (PNC) to Industrial Internet of Things (IIoT) in which a controller and a robot are out of each other’s transmission range, and they exchange messages with the assistance of a relay. We particularly focus on a scenario where 1) the controller has more information to transmit than the robot; 2) the channel of the controller is stronger than that of the robot, and both users have nearly the same transmit power. To reduce the communication latency, we put forth an asymmetric PNC transmission scheme in which the controller transmits more information than the robot by exploiting its stronger channel gain in the uplink of PNC. However, the current channel-coded PNC requires the two users to transmit the same amount of source information in order to preserve the linearity of the two users’ channel codes at the relay for successful decoding. Therefore, a challenge in the asymmetric PNC transmission scheme is how to construct a channel decoder at the relay, considering that a superimposed symbol at the relay contains different amounts of source information from the controller and robot. To fill this gap, we propose a lattice-based encoding and decoding scheme in which the robot and controller encode and modulate their information in lattices with different lattice construction levels. The network-coded messages are decoded level-by-level in the lattice. Our design is versatile on that the controller and the robot can freely choose their modulation orders based on their channel power, and the design is applicable for arbitrary channel codes, not just for one particular channel code. The simulation results demonstrate the effectiveness of the proposed channel-coded asymmetric PNC transmission scheme.

Mobile edge computing (MEC) can supplement cloud computing by helping to overcome the limitations of long physical transmission distances and accelerating the responsiveness of edge computing servers. In 5G (fifth generation) cellular networks, adopting MEC can guarantee ultralow latency. To enhance the MEC quality, optimization of the user service profile migration according to the user mobility is essential. However, this optimization establishes an NP-hard problem. Moreover, high-speed 5G base stations with MEC servers often experience high energy consumption. As conventional service migration algorithms such as those based on profile tracking and game theory tend to fall in local optima and neglect energy consumption constraints, we propose a memetic algorithm based on community detection local search (MA-CDLS) to continuously optimize the service migration in 5G MEC scenarios. During busy periods or in crowded areas, MA-CDLS adopts a single-objective optimization of user-perceived latency to achieve high-performance 5G services. During light-load periods or in uncrowded areas, MA-CDLS uses two measures, namely the user-perceived latency and energy consumption, to realize energy-efficient 5G services. MA-CDLS effectively reduces the search space and speeds up the elite selection in the meme operator. Experiments in simulated scenarios show that MA-CDLS achieves a lower user-perceived latency and energy consumption, than the traditional profile tracking and game theory methods, especially during congestion.

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and decoding while Markov chain Monte Carlo (MCMC) methods from statistics offer an effective way to solve it. In this paper, the sliced lattice Gaussian sampling algorithm is proposed to further improve the convergence performance of the Markov chain targeting at lattice Gaussian sampling. We demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Meanwhile, the convergence rate of the underlying Markov chain is also investigated, and we show the proposed sliced sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. On the other hand, the decoding performance based on the proposed sampling algorithm is analyzed, where the optimization with respect to the standard deviation σ > 0 of the target lattice Gaussian distribution is given. After that, a judicious mechanism based on distance judgement and dynamic updating for choosing σ is proposed for a better decoding performance. Finally, simulation results based on multiple-input multiple-output (MIMO) detection are presented to confirm the performance gain by the convergence enhancement and the parameter optimization.

In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound of a memoryless Gaussian source. The structure of the proposed polar lattices allows to integrate entropy coding into the lattice quantizer, which greatly simplifies the compression process. The overall complexity of encoding and decoding is O(N log2N) for any target distortion and fixed rate larger than the rate-distortion bound. Moreover, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems. The Wyner-Ziv coding problem for a Gaussian source can be solved by using a capacity-achieving polar lattice for the Gaussian channel, nested with a rate-distortion bound achieving lattice, while the Gelfand-Pinsker problem can be solved in a reversed manner. The polar lattice quantizer is further extended to extract Wyner's common information of a pair of Gaussian sources or multiple Gaussian sources.

In this letter, a random sampling strategy is proposed for the non-cooperative spectrum sensing to improve its performance and efficiency in cognitive radio (CR) networks. The proposed refined Metropolis-Hastings (RMH) algorithm generates the desired channel sequence for fine sensing by sampling from the approximated channel availability distributions in an Markov chain Monte Carlo (MCMC) way. The proposal distribution during the sampling is fully exploited and the convergence of the Markov chain is studied in detail, which theoretically demonstrate the superiorities of the proposed RMH sampling algorithm in both sensing performance and efficiency.

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend polarization theories to a more general information measure, namely, the Rényi entropy. Our study shows that under conditional Rényi entropies of different orders, the same synthetic sub-channel may exhibit opposite extremal states. This result reveals more insights into the polarization phenomenon on the micro scale (probability pairs) rather than on the average scale (entropy, mutual information, etc.).

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity (1/2) log(1+SNR) of the additive white Gaussiannoise (AWGN) channel. Our construction follows the multilevel approach of Forney et al., where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby, fulfilling the requirement of the multilevel lattice construction. We prove that the polar lattices are AWGN-good. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is O(N log N) for any fixed target error probability.

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doubly symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel.

In this paper, an explicit scheme of wiretap coding based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. First, polar lattices are used to construct secrecy-good lattices for the mod-ΛsGaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mod-Λsfront end and extend polar lattices to the genuine GWC. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both O(N log N log (log N)) . The proposed scheme is proven to be semantically secure.

We consider explicit constructions of multi-level lattice codes that universally approach the capacity of the compound block-fading channel. Specifically, building on algebraic partitions of lattices, we show how to construct codes with negligible probability of error for any channel realization and normalized log-density approaching the Poltyrev limit. Capacity analyses and numerical results on the achievable rates for each partition level are provided. The proposed codes have several enjoyable properties such as constructiveness and good decoding complexity, as compared to random one-level codes. Numerical results for finite-dimensional multi-level lattices based on polar codes are exhibited.

In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the egodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log2N).

In this paper, we design polar codes and polar lattices for independent identically distributed fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the ergodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the ergodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log2N).

Polar lattices have been proved to be able to achieve the strong secrecy capacity of the Mod-Λsadditive white Gaussian noise (AWGN) wiretap channel. In this work, we propose an explicit shaping scheme and extend polar lattice coding to the genuine Gaussian wiretap channel. This shaping technique is based on discrete lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. The construction of polar codes for an asymmetric channel can be converted to that for a related symmetrized channel, and it turns out that this symmetrized channel is equivalent to a scaled Λ/Λ' channel in lattice coding in terms of polarization. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously.

Polar lattices, which are constructed from polar codes, are provably good for the additive white Gaussian noise (AWGN) channel. In this work, we propose a new polar lattice construction that achieves the secrecy capacity under the strong secrecy criterion over the mod-Λ Gaussian wiretap channel. This construction leads to an AWGN-good lattice and a secrecy-good lattice simultaneously. The design methodology is mainly based on the equivalence in terms of polarization between the Λ/Λ' channel in lattice coding and the equivalent channel derived from the chain rule of mutual information in multilevel coding.