Code Length Research Articles

Hadamard matrices of order 36 formed by codewords in some ternary self-dual codes

In this note, we study the existence of Hadamard matrices of order 36 formed by codewords of weight 36 in some ternary near-extremal self-dual codes of length 36.

MAFH: Multilabel aware framework for bit-scalable cross-modal hashing

Deep hashing techniques have received considerable attention and are widely used in the field of cross-modal retrieval. The training mode of deep cross-modal hashing models has also gradually converged. However, the commonly used training mode ignores noisy labels from different modality original datasets and can only generate fixed-length hash codes, resulting in poor robustness and flexibility of the training generated hash models. Therefore, to effectively optimize the training mode, we propose a multilabel aware framework for bit-scalable deep cross-modal hashing (MAFH) with the following contributions. First, we introduce a label network module to indirectly used the hash representation of multilabels to more accurately supervise the model training process across all modalities. Second, we design a scalable coding strategy to freely manipulate the length of the hash code, which makes the trained model flexible to adapt to different scenarios. Third, we propose a layered multilabel similarity algorithm to preserve more complete feature information, which avoids the loss of discriminative feature information during model training. The training mode of MAFH can effectively enhance model robustness, flexibility and accuracy. We selected thirteen representative hash methods to compare with the proposed method, and experimental results on four public datasets show that the proposed method achieves good performance. https://github.com/x-28/MAFH.git.

SDR implementation and real-time performance evaluation of 5G channel coding techniques

This article presents a study on the real-time performance and practical implementation of several 5G channel coding candidates including low-density parity check (LDPC), polar, turbo, and convolutional channel codes. The experiment was conducted using a wireless communication transceiver system implemented on a software defined radio (SDR) platform called Universal Software Radio Peripheral (USRP). The system was implemented using Matlab software and included scrambling, channel coding, interleaving, and required synchronization and estimation blocks. Various sets of system and channel parameters were tested, including the impact of information block sizes, code lengths, and modulation orders on the performance of each channel coding technique. The study also evaluated the impact of hardware impairments and the required blocks to mitigate them. The results indicated that polar codes had the best performance, while other codes had trade-offs for various system parameters. The study concludes that polar codes with cyclic redundancy check-successive cancellation list (CRC-SCL) are the most reliable 5G channel coding candidates.

A Universal Random Coding Ensemble for Sample-Wise Lossy Compression.

We propose a universal ensemble for the random selection of rate-distortion codes which is asymptotically optimal in a sample-wise sense. According to this ensemble, each reproduction vector, x^, is selected independently at random under the probability distribution that is proportional to 2-LZ(x^), where LZ(x^) is the code length of x^ pertaining to the 1978 version of the Lempel-Ziv (LZ) algorithm. We show that, with high probability, the resulting codebook gives rise to an asymptotically optimal variable-rate lossy compression scheme under an arbitrary distortion measure, in the sense that a matching converse theorem also holds. According to the converse theorem, even if the decoder knew the ℓ-th order type of source vector in advance (ℓ being a large but fixed positive integer), the performance of the above-mentioned code could not have been improved essentially for the vast majority of codewords pertaining to source vectors in the same type. Finally, we present a discussion of our results, which includes among other things, a clear indication that our coding scheme outperforms the one that selects the reproduction vector with the shortest LZ code length among all vectors that are within the allowed distortion from the source vector.

Singleton-optimal LRCs and perfect LRCs via cyclic and constacyclic codes

Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair costs by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have been widely investigated. Optimal LRCs via cyclic and constacyclic codes provide significant benefits of elegant algebraic structure and efficient encoding procedure. In this paper, we continue to consider the constructions of optimal LRCs via cyclic and constacyclic codes with long code lengths. Specifically, we first obtain two classes of q-ary cyclic Singleton-optimal (n,k,d=6;r=2)-LRCs with length n=3(q+1) when 3|(q−1) and q is even, and length n=32(q+1) when 3|(q−1) and q≡1(mod4), respectively. To the best of our knowledge, this is the first construction of q-ary cyclic Singleton-optimal LRCs with length n>q+1 and minimum distance d≥5. On the other hand, an LRC achieving the Hamming-type bound is called a perfect LRC. By using cyclic and constacyclic codes, we construct two new families of q-ary perfect LRCs with length n=qm−1q−1, minimum distance d=5 and locality r=2.

Period Estimation of Spread Spectrum Codes Based on ResNet.

In order to more effectively monitor and interfere with enemy signals, it is particularly important to accurately and efficiently identify the intercepted signals and estimate their parameters in the increasingly complex electromagnetic environment. Therefore, in non-cooperative situations, it is of great practical significance to study how to accurately detect direct sequence spread spectrum (DSSS) signals in real time and estimate their parameters. The traditional time-delay correlation algorithm encounters the challenges such as peak energy leakage and false peak interference. As an alternative, this paper introduces a Pseudo-Noise (PN) code period estimation method utilizing a one-dimensional (1D) convolutional neural network based on the residual network (CNN-ResNet). This method transforms the problem of spread spectrum code period estimation into a multi-classification problem of spread spectrum code length estimation. Firstly, the In-phase/Quadrature(I/Q) two-way of the received DSSS signals is directly input into the CNN-ResNet model, which will automatically learn the characteristics of the DSSS signal with different PN code lengths and then estimate the PN code length. Simulation experiments are conducted using a data set with DSSS signals ranging from -20 to 10 dB in terms of signal-to-noise ratios (SNRs). Upon training and verifying the model using BPSK modulation, it is then put to the test with QPSK-modulated signals, and the estimation performance was analyzed through metrics such as loss function, accuracy rate, recall rate, and confusion matrix. The results demonstrate that the 1D CNN-ResNet proposed in this paper is capable of effectively estimating the PN code period of the non-cooperative DSSS signal, exhibiting robust generalization abilities.

Predictive and Adaptive Deep Coding for Wireless Image Transmission in Semantic Communication

Semantic communication is a newly emerged communication paradigm that exploits deep learning (DL) models to realize communication processes like source coding and channel coding. Recent advances have demonstrated that DL-based joint source-channel coding (DeepJSCC) can achieve exciting data compression and noise-resiliency performances for wireless image transmission tasks, especially in environments with low channel signal-to-noises (SNRs). However, existing DeepJSCC-based semantic communication frameworks still cannot achieve adaptive code rates for different channel SNRs and image contents, which reduces its flexibility and bandwidth efficiency. In this paper, we propose a predictive and adaptive deep coding (PADC) framework for realizing flexible code rate optimization with a given target transmission quality requirement. PADC is realized by a variable code length enabled DeepJSCC (DeepJSCC-V) model for realizing flexible code length adjustment, an Oracle Network (OraNet) model for predicting peak-signal-to-noise (PSNR) value for an image transmission task according to its contents, channel signal to noise ratio (SNR) and the compression ratio (CR) value, and a CR optimizer aims at finding the minimal data-level or instance-level CR with a PSNR quality constraint. By using the above three modules, PADC can transmit the image data with minimal CR, which greatly increases bandwidth efficiency. Simulation results demonstrate that the proposed DeepJSCC-V model can achieve similar PSNR performances compared with the state-of-the-art Attention-based DeepJSCC (ADJSCC) model, and the proposed OraNet model is able to predict high-quality PSNR values with an average error lower than 0.5dB. Results also demonstrate that the proposed PADC can use nearly minimal bandwidth consumption for wireless image transmission tasks with different channel SNR and image contents, at the same time guaranteeing the PSNR constraint for each image data.

Decoding Quantum Tanner Codes

We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density parity-check codes. In this case, our decoders provably correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. The same decoders are easily adapted to the expander lifted product codes of Panteleev and Kalachev. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tighter bound on the minimum distance of quantum Tanner codes.

Research on Evolvable Hardware Based on Improved Evolutionary Strategy

Evolvable hardware (EHW) attracts a lot of researchers because of its excellent adaptive and self-organizing ability. Various of studies have been carried out to improve the evolutionary efficiency. There are mainly two ways: improving the structure of reconfigurable hardware and optimizing evolutionary algorithms. In this paper, we design the reconfigurable circuit based on the systolic array which could reduce the length of circuit coding. And then, an improved evolutionary strategy is proposed, which refers to the yin-yang pair optimization algorithm (YYPO). It can accelerate the evolutionary process and avoid the stalling effect by balancing the relationship between exploration and development. Some experiments were conducted to verify the effect and the results show that the improved method has better searching ability than the traditional evolutionary strategy.

New MDS Self-Dual Codes Over Finite Field F r 2

MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we construct six new classes of MDS self-dual codes by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes. Together with our constructions, the proportion of all known MDS self-dual codes relative to possible MDS self-dual codes generally exceed 57%. As far as we know, this is the largest known ratio. Moreover, some new families of MDS self-orthogonal codes are also constructed.

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

Rate-Diverse Multiple Access Over Gaussian Channels

In this work, we develop a pair of rate-diverse encoder and decoder for a two-user Gaussian multiple access channel (GMAC). The proposed scheme enables the users to transmit with the same codeword length but different coding rates under diverse user channel conditions. First, we propose the row-combining (RC) method and row-extending (RE) method to design practical low-density parity-check (LDPC) channel codes for rate-diverse GMAC. Second, we develop an iterative rate-diverse joint user messages decoding (RDJD) algorithm for GMAC, where all user messages are decoded with a single parity-check matrix. In contrast to the conventional network-coded multiple access (NCMA) and compute-forward multiple access (CFMA) schemes that first recover a linear combination of the transmitted codewords and then decode both user messages, this work can decode both the user messages simultaneously. Extrinsic information transfer (EXIT) chart analysis and simulation results indicate that RDJD can achieve gains up to 1.0 dB over NCMA and CFMA in the two-user GMAC. In particular, we show that there exists an optimal rate allocation for the two users to achieve the best decoding performance given the channel conditions and sum rate.

Performance Analysis of Successive Cancellation Decoder for Polar Codes with Two Stage Channel Estimator

Nowadays polar codes are becoming one of the most favorable capacity achieving Error Correction Codes (ECC) for their simple low encoding and decoding complexity, have received much attention in recent years; they probably achieve the theoretical capacity of discrete memoryless channels using the low complexity successive cancellation (SC) decoding algorithm. However, among the very few prior successive cancellation polar decoder designs, the required long code length makes the decoding latency high. As a new polar decoder, referred to as 2b-SC-Precomputation decoder, reduce the latency from (2n-1) to ((3n/4)-1) without performance loss, which can reduce the hardware complexity by two stage channel estimators. Furthermore, in our method, the decoding latency decreases rapidly with increasing throughput. Significant latency and throughput reductions are shown by simulation results and report synthesis results for ASIC.

Two-Level LDPC-Coded Modulation With Probabilistic Shaping

In this letter, we propose a new coded modulation scheme, namely two-level coding with probabilistic shaping, for transmission with higher spectral efficiency in future 6G communications. At the transmitter, a distribution matcher for probabilistic shaping is concatenated with two-level coding, where the first level is designed based on bit-interleaved coded modulation while the second level is left uncoded. At the receiver, a two-stage decoding is performed prior to shaping decoding. A labeling strategy is optimized to get good performance for the first-level coding. Meanwhile, labels of signal subsets are sign-bit decomposable to accommodate uniform check bits. Numerical results show that, for 256-QAM, performances of the proposed scheme are 0.7~1.4 dB better than uniform BICM at various transmission rates, while the required LDPC code length is shorter by 50%.

Blind Recognition of Reed-Solomon Codes Based on Galois Field Fourier Transform and Reliability Verification

The Galois field Fourier transform (GFFT) method has been widely applied in the blind recognition of Reed-Solomon (RS) codes in recent years. However, as the code length increases, the computational complexity increases rapidly. Also, blind recognition in a poor channel environment remains challenging. To solve the above challenges, a blind recognition algorithm is proposed based on GFFT and reliability verification (RV). Low-complexity GFFT (LC-GFFT) is proposed to calculate the shortened spectrums, reducing the computational complexity and improving the correct codeword utilization rate (CUR). Next, the criteria for parameter estimation (PE) are given. The RV module is designed to verify the correctness of the estimated parameters. The simulations demonstrate that our algorithm can recognize RS(15, 11, 2, 19) and RS(31, 15, 8, 37) with over 95% correct rate when SNR is above 0.8dB and 2.5dB, achieving at least 7dB of signal-to-noise (SNR) defined gain over the existing algorithms. Moreover, the recognition time of our method is reduced by 74.8% compared to that of the GFFT-based method for RS(31, 15, 8, 37) when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> = 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> .

Subject Review: Various Techniques for Image Compression

Due to the quick development of multimedia technology, now can see the increasing amount of multimedia data that is being generated or transmitted over the internet. digital image is one form of multimedia data, that can take different formats and different sizes. And here comes the main objective of image compression in transmitting or storing the data in an effective manner by decreasing the redundant or irrelevant information without significant loss of visual quality in image data. Compression of the images is utilized in various services, including TV broadcasts, satellite imagery, martial communications, webinars, medical imaging, weather reporting, etc. This paper provides a survey of the main techniques in image compression, covering both lossy &amp; lossless approaches. The techniques that depend on lossy compression lose some of the image details during compression, while lossless compression techniques keep the image information without losing. Vector and scalar Quantization, transform coding, block truncation Coding, etc. are all examples of lossy approaches. Run length coding, entropy encoding, statistical coding, etc. are all examples of lossless techniques. This paper will assist the researchers in learning about these techniques and choosing appropriate techniques for their work.

DSSS Signal Detection Based on CNN.

With the wide application of direct sequence spread spectrum (DSSS) signals, the comprehensive performance of DSSS communication systems has been continuously improved, making the electronic reconnaissance link in communication countermeasures more difficult. Electronic reconnaissance technology, as the fundamental means of modern electronic warfare, mainly includes signal detection, recognition, and parameter estimation. At present, research on DSSS detection algorithms is mostly based on the correlation characteristics of DSSS signals, and autocorrelation algorithm is the most mature and widely used method in practical engineering. With the continuous development of deep learning, deep-learning-based methods have gradually been introduced to replace traditional algorithms in the field of signal processing. This paper proposes a spread spectrum signal detection method based on convolutional neural network (CNN). Through experimental analysis, the detection performance of the CNN model proposed in this paper on DSSS signals in various situations has been compared and analyzed with traditional autocorrelation detection methods for different signal-to-noise ratios. The experiments verified the estimation performance of the model in this paper under different signal-to-noise ratios, different spreading code lengths, different spreading code types, and different modulation methods and compared it with the autocorrelation detection algorithm. It was found that the detection performance of the model in this paper was higher than that of the autocorrelation detection method, and the overall performance was improved by 4 dB.

Detection and Correction of Repeated Restricted Burst Errors in Sub-Blocks

In this paper, we present bounds on check symbols required for the codes capable to detect as well as correct the restricted bursts errors that are repeating themselves in a single sub-block. For these codes the whole code length is considered to be subdivided into a certain number of mutually exclusive sub-blocks of equal length.

Approximate NFA universality and related problems motivated by information theory

In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is universal, and this is a hard problem (including the case of whether the NFA accepts all words of a fixed length). On the other hand, it is acceptable to know whether a code is ‘approximately’ maximal, which then boils down to whether a given NFA is ‘approximately’ universal. Here we introduce the notion of a (1−ε)-universal automaton and present polynomial randomized approximation algorithms to test NFA universality and related hard automata problems, for certain natural probability distributions on the set of words. We also conclude that the randomization aspect is necessary, as approximate universality remains hard for any fixed polynomially computable ε.

Exceptional designs in some extended quadratic residue codes

AbstractIn the present paper, we give proofs of the existence of a 3‐design in the extended ternary quadratic residue code of length 14 and the extended quaternary quadratic residue code of length 18.