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Pointing at the vexed question of blind recognition in the convolutional code class, this paper proposes a convolutional code blind identification method via convolutional neural networks (CNNs). First, this algorithm uses the traditional method to generate different convolutional codes, and the feature extraction algorithm adopts the theorem of Euclid’s algorithm. Then, the input signal is loaded to the CNN; next, the feature is extracted by convolutional kernel. Finally, the Softmax activation function is applied to full‐connection layer network. After the input signals pass through the above layers, the system classifies the signals. The research results indicate that the presented algorithm has improved the recognition performance of code length and rate. For different convolutional codes with parameters of (5, 7), (15, 17), (23, 35), (53, 75), and (133, 171) and similar convolutional codes with parameters of (3, 1, 6), (3, 1, 7), (2, 1, 7), (2, 1, 6), and (2, 1, 5), the recognition rate of parameter classification can reach 100% at signal‐to‐noise ratio (SNR) of 3 dB.

In this paper, some optimized encoding and decoding schemes are proposed for the generalized LDPC convolutional codes (GLDPC–CCs). In terms of the encoding scheme, a flexible doping method is proposed, which replaces multiple single parity check (SPC) nodes with one generalized check (GC) node. Different types of BCH codes can be selected as the GC node by adjusting the number of SPC nodes to be replaced. Moreover, by fine-tuning the truncated bits and the extended parity check bits, or by reasonably adjusting the GC node distribution, the performance of GLDPC–CCs can be further improved. In terms of the decoding scheme, a hybrid layered normalized min-sum (HLNMS) decoding algorithm is proposed, where the layered normalized min-sum (LNMS) decoding is used for SPC nodes, and the Chase–Pyndiah decoding is adopted for GC nodes. Based on analysis of the decoding convergence of GC node and SPC node, an adaptive weight factor is designed for GC nodes that changes as the decoding iterations, aiming to further improve the decoding performance. In addition, an early stop decoding strategy is also proposed based on the minimum amplitude threshold of mutual information in order to reduce the decoding complexity. The simulation results have verified the superiority of the proposed scheme for GLDPC–CCs over the prior art, which has great application potential in optical communication systems.

Quantum convolutional codes, which are the correct generalization to quantum domain of their classical analogs, were introduced to overcome decoherence during long distance quantum communications. In this paper, we construct some classes of quantum convolutional codes via classical constacyclic codes. These codes are maximum-distance-separable (MDS) codes in the sense that they achieve the Singleton bound for pure convolutional stabilizer codes. Furthermore, compared with some of the codes available in the literature, our codes have better parameters and are more general.

A trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero. In the area of Coding Theory, superregular matrices over finite fields are connected with codes with optimum error correcting capabilities. There are two types of superregular matrices that yield two different types of codes. One has in all of its entries a nonzero element, and these are called full superregular matrices. The second interesting class of superregular matrices is formed by lower triangular Toeplitz matrices. In contrast to full superregular matrices, all general constructions of these matrices require very large field sizes. In this work, we investigate the construction of lower triangular Toeplitz superregular matrices over small finite prime fields. Instead of computing all possible minors, we study the structure of finite fields in order to reduce the possible nonzero minors. This allows us to restrict the huge number of possibilities that one needs to check and come up with novel constructions of superregular matrices over relatively small fields. Finally, we present concrete examples of lower triangular Toeplitz superregular matrices of sizes up to 10.

It is shown how the decoding algorithms of Pellikaan and Rosenthal can be coupled to produce a decoding algorithm for convolutional codes. Bounds for the computational cost per decoded codeword are also computed. As a case study, our results are applied to a family of convolutional codes constructed by Rosenthal–Schumacher–York and, in this situation, the previous bounds turn out to be polynomial on the degree of the code.

Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a machine learning approach to improve the state-of-the-art decoding of tail-biting codes, focusing on the widely employed short length regime as in the LTE standard. This standard also includes a CRC code. First, we parameterize the circular Viterbi algorithm, a baseline decoder that exploits the circular nature of the underlying trellis. An ensemble combines multiple such weighted decoders, and each decoder specializes in decoding words from a specific region of the channel words’ distribution. A region corresponds to a subset of termination states; the ensemble covers the entire states space. A non-learnable gating satisfies two goals: it filters easily decoded words and mitigates the overhead of executing multiple weighted decoders. The CRC criterion is employed to choose only a subset of experts for decoding purpose. Our method achieves FER improvement of up to 0.75 dB over the CVA in the waterfall region for multiple code lengths, adding negligible computational complexity compared to the circular Viterbi algorithm in high signal-to-noise ratios (SNRs).

In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.

The reliable transmission of multimedia information that is coded through highly compression efficient encoders is a challenging task. This article presents the iterative convergence performance of IrRegular Convolutional Codes (IRCCs) with the aid of the multidimensional Sphere Packing (SP) modulation assisted Differential Space Time Spreading Codes (IRCC-SP-DSTS) scheme for the transmission of H.264/Advanced Video Coding (AVC) compressed video coded stream. In this article, three different regular and irregular error protection schemes are presented. In the presented Regular Error Protection (REP) scheme, all of the partitions of the video sequence are regular error protected with a rate of 3/4 IRCC. In Irregular Error Protection scheme-1 (IREP-1) the H.264/AVC partitions are prioritized as A, B & C, respectively. Whereas, in Irregular Error Protection scheme-2 (IREP-2), the H.264/AVC partitions are prioritized as B, A, and C, respectively. The performance of the iterative paradigm of an inner IRCC and outer Rate-1 Precoder is analyzed by the EXtrinsic Information Transfer (EXIT) Chart and the Quality of Experience (QoE) performance of the proposed mechanism is evaluated using the Bit Error Rate (BER) metric and Peak Signal to Noise Ratio (PSNR)-based objective quality metric. More specifically, it is concluded that the proposed IREP-2 scheme exhibits a gain of 1 dB Eb/N0 with reference to the IREP-1 and Eb/N0 gain of 0.6 dB with reference to the REP scheme over the PSNR degradation of 1 dB.

Wireless body area networks (WBANs) are attracting attention as a very important technology for realizing an Internet of Medical Things (IoMT). IEEE 802.15.6 is well known as one of the international standards for WBANs for the IoMT. This article proposes the combination of the IEEE 802.15.6 ultra-wideband (UWB) physical layer (PHY) with a super orthogonal convolutional code (SOOC) and evaluates its performance as a dependable WBAN. Numerical results show that sufficient dependability cannot be obtained with the error-correcting code specified in IEEE 802.15.6 when applying the single pulse option, while both high energy efficiency and dependability can be obtained by applying an SOCC. In addition, it is confirmed that higher dependability can be obtained by combining an SOCC with a Reed–Solomon (RS) code with a coding rate that is almost the same as the error correction code specified in the standard. Furthermore, the results indicate that high dependability and energy efficiency can be obtained by adjusting the SOCC coding rate and UWB PHY parameters, even in the burst pulse option. The SOCC-applied UWB PHY of this research satisfies the high requirements of the IoMT.

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.