Tail-biting Convolutional Codes Research Articles

Design of Serially Concatenated Tail-Biting Convolutional Code With Index Modulation

Design of Serially Concatenated Tail-Biting Convolutional Code With Index Modulation

Advanced hybrid algorithms for precise multipath channel estimation in next-generation wireless networks

Multipath channels continue to present challenges in wireless communication for both 5G and 6G networks. A multipath channel is a phenomenon in wireless communications where signals traverse from the sender to the receiver along various paths. This end occurs due to the reflection, diffraction, and refraction of signals of various objects and structures in the environment. Such pathways can cause symbol interference in the transmitted signal, leading to communication issues. To this end, our paper proposes the integration of three algorithms: teaching-learning-based optimization (TLBO), particle swarm optimization (PSO), and artificial neural networks (ANN). This combination effectively analyzes and stabilizes the transmission channel, minimizing symbol interference. We have developed, simulated, and evaluated this hybrid approach for multipath fading channels. We apply it to various coding schemes, including tail-biting convolutional code, turbo codes, low-density parity-check, and polar code. Additionally, we have explored various decoding methods such as Viterbi, maximum logarithmic maximum a posteriori, minimum sum, and cyclic redundancy check soft cancellation list. Our study encompasses new channel equalization schemes and coding gains derived from simulations and mathematical analysis. Our proposed method significantly enhances channel equalization, reducing interference and improving error correction in wireless communication systems.

Noncoherent Demodulation and Decoding via Polynomial Zeros Modulation for Pilot-Free Short Packet Transmissions over Multipath Fading Channels

With the advent of the Internet of Things (IoT), short packet transmissions will dominate the future wireless communication. However, traditional coherent demodulation and channel estimation schemes require large pilot overhead, which may be highly inefficient for short packets in multipath fading scenarios. This paper proposes a novel pilot-free short packet structure based on the association of modulation on conjugate-reciprocal zeros (MOCZ) and tail-biting convolutional codes (TBCC), where a noncoherent demodulation and decoding scheme is designed without the channel state information (CSI) at the transceivers. We provide a construction method of constellation sets and demodulation rule for M-ary MOCZ. By deriving low complexity log-likelihood ratios (LLR) for M-ary MOCZ, we offer a reasonable balance between energy and bandwidth efficiency for joint coding and modulation scheme. Simulation results show that our proposed scheme can attain significant performance and throughput gains compared to the pilot-based coherent modulation scheme over multipath fading channels.

Hyper-Dimensional Modulation for Robust Short Packets in Massive Machine-Type Communications

In this paper, we introduce Hyper-Dimensional Modulation (HDM) for massive machine-type communications (mMTC). HDM enables robust communication of short packets by spreading information bits across many elements in a hyper-dimensional vector and superimposing a set of such non-orthogonal vectors. The proposed CRC-aided K-best decoding algorithm for HDM can achieve a very low packet error rate (PER) in additive white Gaussian noise (AWGN) channels for short packets. Furthermore, extended decoding algorithms are proposed to combat overwhelming interference in an mMTC network. Comprehensive simulation and real-world experiment results show that HDM outperforms sparse superposition codes in AWGN channels and state-of-the-art short codes such as polar and tail-biting convolutional codes in interference-heavy channels for short packet transmissions.

Performance Analysis of Resource Hopping-Based Grant-Free Multiple Access for Massive IoT Networks

In this letter, we mathematically analyze the bit-error-rate (BER) and frame-error-rate (FER) performance of the resource hopping-based grant-free multiple access (RH-GFMA) systems that were recently proposed for 6G massive Internet-of-Things (mIoT) networks. In the RH-GFMA systems, each IoT device intermittently sends a short-packet to the access point (AP) based on a predetermined resource hopping pattern (HP). Each IoT device may experience HP collisions within the packet, but the effect of HP collisions on error performance can be reduced to be collision-friendly by exploiting multi-antenna-based signal detection and error-correction capability of channel codes. In this letter, hence, we rigorously analyze the effect of HP collisions on the error performance in the RH-GFMA system where repetition codes (RC) and tail-biting convolutional codes (TB-CC) are considered channel coding schemes for satisfying low-complexity and low-latency requirements of mIoT networks. Through computer simulations, we validate that our mathematical analysis is well-matched with the simulation results.

Construction D’ Lattices for Power-Constrained Communications

Designs and methods for nested lattice codes using Construction D&#x2019; lattices for coding and convolutional code lattices for shaping are described. Two encoding methods and a decoding algorithm for Construction D&#x2019; coding lattices that can be used with shaping lattices for power-constrained channels are given. We construct nested lattice codes with good coding properties, high shaping gain, and low-complexity encoding and decoding. Convolutional code generator polynomials for Construction A lattices with the greatest shaping gain are given, as a result of an extensive search. It is shown that rate 1/3 convolutional codes provide a more favorable performance-complexity trade-off than rate 1/2 convolutional codes. Tail-biting convolutional codes have higher shaping gain than that of zero-tailed convolutional codes. A design for quasi-cyclic low-density parity-check (QC-LDPC) codes to form Construction D&#x2019; lattices which have efficient encoding and indexing is presented. The resulting QC-LDPC Construction D&#x2019; lattices are evaluated using four shaping lattices: the <inline-formula> <tex-math notation="LaTeX">$E_{8}$ </tex-math></inline-formula> lattice, the <inline-formula> <tex-math notation="LaTeX">$BW_{16}$ </tex-math></inline-formula> lattice, the Leech lattice and our best-found convolutional code lattice, showing a shaping gain of approximately 0.65 dB, 0.86 dB, 1.03 dB and 1.25 dB at dimension 2304.

Sequential Decoding of Short Length Binary Codes: Performance Versus Complexity

Sequential decoding of short length binary codes for the additive white Gaussian noise channel is considered. A variant of the variable-bias term (VBT) metric is introduced, producing useful trade-offs between performance and computational complexity. Comparisons are made with tail-biting convolutional codes decoded with a wrap-around Viterbi algorithm (WAVA) and with polar codes under successive-cancellation list (SCL) decoding. It is found that sequential decoding with the improved VBT metric has a better performance&#x2013;complexity tradeoff than tail-biting codes under WAVA decoding (except at low complexities) but a worse performance&#x2013;complexity tradeoff than polar codes under SCL decoding (except at high complexities).

Nested Tail-Biting Convolutional Codes Construction for Short Packet Communications

Nested Tail-Biting Convolutional Codes Construction for Short Packet Communications

Nested Tail-Biting Convolutional Codes Construction for Short Packet Communications

Nested Tail-Biting Convolutional Codes Construction for Short Packet Communications

Twisted-Pair Superposition Transmission

We propose in this paper a new coding scheme called twisted-pair superposition transmission (TPST). The encoding is to “mix together” a pair of basic codes by superposition, while the decoding can be implemented as a successive cancellation list decoding algorithm. The most significant features of the TPST code are its predictable performance that can be estimated numerically from the basic codes and its flexible construction in the sense that it can be easily adapted to different coding rates. To construct good TPST codes in the finite length regime, we propose two design approaches – rate allocation and partial superposition. By taking tail-biting convolutional codes (TBCC) as basic codes, we show by numerical results that the constructed TPST-TBCCs have performance close to the random coding union bound in the short length regime.

Performance comparison of channel coding schemes for 5G massive machine type communications

&lt;p&gt;&lt;span&gt;Channel coding for the fifth generation (5G) mobile communication is currently facing new challenges as it needs to uphold diverse emerging applications and scenarios. Massive machine-type communication (mMTC) constitute one of the main usage scenarios in 5G systems, which promise to provide low data rate services to a large number of low power and low complexity devices. Research on efficient coding schemes for such use case is still ongoing and no decision has been made yet. Therefore, This paper compares the performance of different coding schemes, namely: tail-biting convolutional code (TBCC), low density parity check codes (LDPC), Turbo code and Polar codes, in order to select the appropriate channel coding technique for 5G-mMTC scenario. The considered codes are evaluated in terms of bit error rate (BER) and block error rate (BLER) for short information block lengths (K ≤ 256). We further investigate their Algorithmic complexity in terms of the number of basic operations. The Simulation results indicate that polar code with CRC-aided successive cancelation list decoder has better performance compared with other coding schemes for 5G-mMTC scenario.&lt;/span&gt;&lt;/p&gt;

Latency and Reliability Trade-Off With Computational Complexity Constraints: OS Decoders and Generalizations

In this article, we study the problem of latency and reliability trade-off in ultra-reliable low-latency communication (URLLC) in the presence of decoding complexity constraints. We consider linear block encoded codewords transmitted over a binary-input AWGN channel and decoded with order-statistic (OS) decoder. We first investigate the performance of OS decoders as a function of decoding complexity and propose an empirical model that accurately quantifies the corresponding trade-off. Next, a consistent way to compute the aggregate latency for complexity constrained receivers is presented, where the latency due to decoding is also included. It is shown that, with strict latency requirements, decoding latency cannot be neglected in complexity constrained receivers. Next, based on the proposed model, several optimization problems, relevant to the design of URLLC systems, are introduced and solved. It is shown that the decoding time has a drastic effect on the design of URLLC systems when constraints on decoding complexity are considered. Finally, it is also illustrated that the proposed model can closely describe the performance versus complexity trade-off for other candidate coding solutions for URLLC such as tail-biting convolutional codes, polar codes, and low-density parity-check codes.

Deep Ensemble of Weighted Viterbi Decoders for Tail-Biting Convolutional Codes.

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).

LEARN Codes: Inventing Low-Latency Codes via Recurrent Neural Networks

Designing channel codes under low-latency constraints is one of the most demanding requirements in 5G standards. However, a sharp characterization of the performance of traditional codes is available only in the large block-length limit. Guided by such asymptotic analysis, code designs require large block lengths as well as latency to achieve the desired error rate. Tail-biting convolutional codes and other recent state-of-the-art short block codes, while promising reduced latency, are neither robust to channel-mismatch nor adaptive to varying channel conditions. When the codes designed for one channel (e.g., Additive White Gaussian Noise (AWGN) channel) are used for another (e.g., non-AWGN channels), heuristics are necessary to achieve non-trivial performance. In this paper, we first propose an end-to-end learned neural code, obtained by jointly designing a Recurrent Neural Network (RNN) based encoder and decoder. This code outperforms canonical convolutional code under block settings. We then leverage this experience to propose a new class of codes under low-latency constraints, which we call Low-latency Efficient Adaptive Robust Neural (LEARN) codes . These codes outperform state-of-the-art low-latency codes and exhibit robustness and adaptivity properties. LEARN codes show the potential to design new versatile and universal codes for future communications via tools of modern deep learning coupled with communication engineering insights.

Approximate ML Decoding of Short Convolutional Codes Over Phase Noise Channels

We propose a decoding algorithm for tail-biting convolutional codes over phase noise channels. It can be seen as a reduced complexity approximation of maximum likelihood decoding. We target short blocks and extend the wrap-around Viterbi algorithm to trellises describing the random evolution of the phase impairment, for which we adopt two different models: a blockwise non-coherent and a blockwise Wiener channel model. Numerical results show that the performance of the proposed algorithm is within a few tenths of dB or less from maximum likelihood decoding for the setup studied in this letter.

A Low-Complexity Maximum-Likelihood Decoder for Tail-Biting Convolutional Codes

Due to the growing interest in applying tail-biting convolutional coding techniques in real-time communication systems, fast decoding of tail-biting convolutional codes has become an important research direction. In this paper, a new maximum-likelihood decoder for tail-biting convolutional codes is proposed. It is named bidirectional priority-first search algorithm (BiPFSA) because priority-first search algorithm has been used both in forward and backward directions during decoding. Simulations involving the antipodal transmission of (2, 1, 6) and (2, 1, 12) tail-biting convolutional codes over additive white Gaussian noise channels shows that BiPFSA not only has the least average decoding complexity among the state-of-the-art decoding algorithms for tail-biting convolutional codes but can also provide a highly stable decoding complexity with respect to growing information length and code constraint length. More strikingly, at high SNR, its average decoding complexity can even approach the ideal benchmark complexity, obtained under a perfect noise-free scenario by any sequential-type decoding. This demonstrates the superiority of BiPFSA in terms of decoding efficiency.

Rate-Compatible Tail-Biting Convolutional Codes for M2M Communications

We propose an algorithm to construct a group of rate-compatible tail-biting convolutional codes (RC-TBCCs) with consistently good frame error rate performance for both short and long information lengths. The algorithm considers the free distance property and the minimum distance profile of a TBCC jointly. We construct a group of RC-TBCCs with code rates $1/n$ , $3\leq n\leq 12$ . Numerical results show that the constructed RC-TBCCs have better frame error rate performance than the TBCCs used in LTE standards for various information lengths and code rates.

A New List Decoding Algorithm for Short-Length TBCCs With CRC

In this paper, a new list decoding algorithm for tail-biting convolutional codes (TBCCs) with a cyclic redundancy check (CRC) is proposed, where the CRC is considered as a concatenated outer code. The main idea of the proposed algorithm is to modify the list decoding procedure of the TBCC by using the CRC. Two algorithms are proposed for the list decoding of the TBCC with the CRC. The first proposed algorithm is a new initial state estimating algorithm using re-encoded CRC bits and having the low computational complexity. The other proposed algorithm is a modified list Viterbi algorithm, where trellis paths are fixed by re-encoded CRC bits and some CRC bits are used for the error correction. For the TBCC concatenated with the CRC code defined in the long-term evolution standard, the proposed decoding scheme by partially using CRC bits outperforms the conventional list decoding algorithms for the list size $L=4$ even though the proposed algorithm has the lower decoding complexity.

Non-binary Tail-Biting LDPC Convolutional Code Encoding for Image Transmission

In current image transmission, data channel encoding is needed to consider noise and bit-error protection in order to enhance and guarantee image-data quality. This paper focuses on a problem of image transmission with high bit error rate (BER) and additive white Gaussian noise (AWGN) channel, and proposes a method of non-binary tail-biting low-density parity-check convolutional (NB TB-LDPCC) code encoding for image transmission. In this method, image data compressed by JPEG are used to construct finite fields in non-binary, then construct a base matrix in column weight two, and finally create tail biting LDPC convolution code for modulation in the next process in image transmission. The performance of the proposed method is evaluated by 30 images on USC-SIPI Image Database, and the comparison results with conventional method reveal BER is improved at most 1 dB, and PSNR is increased 2.01 dB approximately.

Efficient coding schemes for low‐rate wireless personal area networks

The emerging market of Internet of things has created great demand for low-cost, low-power wireless technologies. Existing IEEE 802.15.4 standard is designed for low-rate wireless personal area networks (LR-WPANs). However, current standard does not fully utilise the benefit of the code redundancy. In this study, the authors propose new coding schemes for LR-WPANs with improved coding gain. They first propose a block code based on extended Bose–Chaudhuri–Hocquenghem (BCH) code that increases the minimum Hamming distance compared with the existing code used in LR-WPANs. The computational complexity of the encoder and decoder remains about the same. In addition, by applying the extended BCH code directly to LR-WPANs, the data rate of the system can be increased without sacrificing coding performance. They further propose a tail-biting convolutional (TBC) code with optimum generator polynomials for LR-WPANs. The proposed TBC code enjoys significant performance improvement while preserving the effective code rate as well as a low decoding complexity. Simulation results validate the effectiveness of the proposed coding schemes.