Decoding Delay Research Articles

Cubic-Permutation-Polynomial-Based Sliding Window Network Coding Algorithm in IoT

Network coding (NC) is an information transmission technology that encodes and transmits data packets on a network. NC can be applied to the Internet of Things (IoT) and can effectively improve the data transmission quality and throughput of the IoT. The complexity of data packets encoding and decoding is an important problem in NC applications. The cubic permutation polynomial (CPP) can better optimize the data packets participating in NC, reduce the computational complexity of data packet encoding/decoding, and improve the data packet transmission bandwidth and data throughput of the IoT. This paper proposes a Cubic Permutation Polynomial-based Sliding Window NC algorithm in IoT (CPP-SWNC). In the paper, firstly, the fusion theory of CPP and sliding window (SW) was discussed. Secondly, the theory that optimize the size of sliding windows was demonstrated. Thirdly, an analysis was conducted from the perspective of mathematical theory. Finally, simulation experiments were conducted to evaluate the performance of the CPP-SWNC algorithm using Network Simulation (NS) software, mainly by comparing and analyzing the network throughput, average packet encoding overhead, and packet decoding delay. The simulation results show that CPP-SWNC algorithm can improve the performance and data packet transmission quality of the IoT, and can further improve the application field of the IoT.

New low power and fast SEC-DAEC and SEC-DAEC-TAEC codes for memories in space application

Multiple cell upset (MCU) caused by cosmic radiation is a serious issue related to the reliability of static random access memories (SRAMs) in space application. Due to radiation, single cell or multiple cells of a memory are corrupted. The chances of errors in more than one memory cells are also increasing due to continuous down scaling of technology. Single error, double or triple adjacent errors are most common in this case. Several error correction codes are already introduced for protecting the memories. But many existing error correcting codes have either higher delay and/or power consumption and/or decoder error rate. In this paper, we have introduced 16-bit, 32-bit and 64-bit information length, uniquely decodable single error correction-double adjacent error correction (SEC-DAEC) and single error correction-double adjacent error correction-triple adjacent error correction (SEC-DAEC-TAEC) codes with lower power consumption and delay. In our design, same H-matrix is used for implementing both SEC-DAEC and SEC-DAEC-TAEC codes. Both FPGA and ASIC based synthesis results show that proposed SEC-DAEC and SEC-DAEC-TAEC codes with dimensions (24, 16), (41, 32) and (75, 64) are better compared to existing same dimension codes with respect to area, power and delay. Since, the proposed SEC-DAEC and SEC-DAEC-TAEC codes have low encoder and decoder delay which corresponds to low writing and reading time, consume significantly low power and have zero decoder error rate, so proposed codec can be used for memories in space application.

A Parallel Turbo Decoder Based on Recurrent Neural Network

A neural network-based decoder, based on a long short-term memory (LSTM) network, is proposed to solve the problem that large decoding delay and performance degradation under non-Gaussian noise due to poor parallelism of existing turbo decoding algorithms. The proposed decoder refers to a unique component coding concept of turbo codes. First, each component decoder is designed based on an LSTM network. Next, each layer of the component decoder is trained, and the trained weights are loaded into the turbo code decoding neural network as initialization parameters. Then, the turbo code decoding network is trained end-to-end. Finally, a complete turbo decoder is realized. The structural advantage of turbo code component coding is fully considered in the design process, and the problem of decoding delay caused by the existence of interleaver is cleverly avoided. The introduction of deep learning technology provides a new idea to solve the traditional communication problems. Simulation results show that the performance of the proposed decoder is improved by 0.5–1.5 dB compared with the traditional serial decoding algorithm in Gaussian white noise and t-distribution noise. When BER performance is close, the LSTM decoder requires half or even less than that of BCJR. Moreover, the results demonstrate that the proposed decoder is adaptive and can be applied to communication systems with various turbo codes. The LSTM decoder shows lower bit error rate, computational complexity and higher decoding efficiency under the same conditions. Therefore, it is necessary to study the turbo code decoding technology based on deep learning combined with the actual channel environment.

Sliding Network Coding for URLLC

In this paper, we propose a network coding (NC) based approach to ultra-reliable low-latency communication (URLLC) over erasure channels. In transmitting multiple data packets, we demonstrate that the use of random NC can improve the reliability in terms of decoding error probability, while it incurs a longer decoding delay than a well-known <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-repetition. To avoid a long decoding delay, we consider a sliding NC (SNC) design that allows a highly reliable transmission of each data packet with a guaranteed decoding delay. A few design examples are derived and their decoding error rates are analyzed. Through the analysis, we can show that the decoding error rate of SNC is much lower than that of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-repetition at the same spectral efficiency, which means a more reliable transmission can be achieved using SNC than <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-repetition.

Construction and Characterization of Optical Orthogonal Codes (n,w,1) for Fast Frequency Hopping-Optical Code Division Multiple Access

This paper investigates a new combinatorial construction approach based on cyclic difference packings for the construction of an optical orthogonal code that is suitable as a time spreading sequence for fast frequency hopping optical code division multiple access (OCDM) systems. The proposed construction provides a solution to the electrical decoding delay problem when compared to its optical counterpart, as well as other optimization issues. The criteria for optimizing the performance of such an OCDMA system are provided, namely: the flexibility and simplicity in constructing the optimal code for any length and weight, a reduction in the encoding/decoding complexity that complies with changes in the fast frequency hopping system, and the provision of system transfer transparency, a decoding rule that exploits the embedded asymmetric error correcting capability of the code. Our neighbor difference approach refers to the partition of different solutions into sub-classes, given in the correlation matrix form. It takes into account both direct and recursive combinatorial code construction methods, and the resulting characteristics are evaluated accordingly. A performance analysis based on the OCDMA channel is given, and a comparison with other difference family solutions is performed.

Channel Noise Optimization of Polar Codes Decoding Based on a Convolutional Neural Network

Polar code has the characteristics of simple coding and high reliability, and it has been used as the control channel coding scheme of 5G wireless communication. However, its decoding algorithm always encounters problems of large decoding delay and high iteration complexity when dealing with channel noise. To address the above challenges, this paper proposes a channel noise optimized decoding scheme based on a convolutional neural network (CNN). Firstly, a CNN is adopted to extract and train the colored channel noise to get more accurate estimation noise, and then, the belief propagation (BP) decoding algorithm is used to decode the polar codes based on the output of the CNN. To analyze and verify the performance of the proposed channel noise optimized decoding scheme, we simulate the decoding of polar codes with different correlation coefficients, different loss function parameters, and different code lengths. The experimental results show that the CNN‐BP concatenated decoding can better suppress the colored channel noise and significantly improve the decoding gain compared with the traditional BP decoding algorithm.

Lightweight hamming product code based multiple bit error correction coding scheme using shared resources for on chip interconnects

In this paper, we present multiple bit error correction coding scheme based on extended Hamming product code combined with type II HARQ using shared resources for on chip interconnect. The shared resources reduce the hardware complexity of the encoder and decoder compared to the existing three stages iterative decoding method for on chip interconnects. The proposed method of decoding achieves 20% and 28% reduction in area and power consumption respectively, with only small increase in decoder delay compared to the existing three stage iterative decoding scheme for multiple bit error correction. The proposed code also achieves excellent improvement in residual flit error rate and up to 58% of total power consumption compared to the other error control schemes. The low complexity and excellent residual flit error rate make the proposed code suitable for on chip interconnection links.

Optimized Design for NB-LDPC-Coded High-Order CPM: Power and Iterative Efficiencies

In this paper, a non-binary low-density parity-check (NB-LDPC) coded high-order continuous phase modulation (CPM) system is designed and optimized to improve power and iterative efficiencies. Firstly, the minimum squared normalized Euclidean distance and the 99% double-sided power bandwidth are introduced to design a competitive CPM, improving its power efficiency under a given code rate and spectral efficiency. Secondly, a three-step method based on extrinsic information transfer (EXIT) and entropy theory is used to design NB-LDPC codes, which reduces the convergence threshold approximately 0.42 and 0.58 dB compared with the candidate schemes. Thirdly, an extrinsic information operation is proposed to address the positive feedback issue in iterative detection and decoding and the value of bit error rate (BER) can approximately be reduced by 5×10−3. Finally, iteration optimization employing the EXIT chart and mutual information between demodulation and decoding is performed to achieve a suitable tradeoff for the communication reliability and iterative decoding delay. Simulation results show that the resulting scheme provides an approximately 3.95 dB coding gain compared to the uncoded CPM and achieves approximately 0.5 and 0.7 dB advantages compared with the candidate schemes. The resulting NB-LDPC-coded high-order CPM for a given code rate and spectral efficiency converges earlier into a turbo cliff region compared with other competitors and significantly improves power and iterative efficiencies.

Rate-Optimal Streaming Codes for Channels With Burst and Random Erasures

In this paper, we design erasure-correcting codes for channels with burst and random erasures, when a strict decoding delay constraint is in place. We consider the sliding-window-based packet erasure model proposed by Badr et al., where any time-window of width $w$ contains either up to $a$ random erasures or an erasure burst of length at most $b$ . One needs to recover any erased packet with a strict decoding delay deadline of $\tau $ , where erasures are as per the channel model. Presently existing rate-optimal constructions in the literature require, in general, a field-size which grows exponential in $\tau $ , as long as $\frac {a}{\tau }$ remains a constant. In this work, we present a new rate-optimal code construction covering all channel and delay parameters, which requires an $O(\tau ^{2})$ field-size. As a special case, when $(b-a)=1$ , we have a field-size linear in $\tau $ . We also present two other constructions having linear field-size, under certain constraints on channel and decoding delay parameters. As a corollary, we obtain low field-size, rate-optimal convolutional codes for any given column distance and column span. Simulations indicate that the newly proposed streaming code constructions offer lower packet-loss probabilities compared to existing schemes, for selected instances of Gilbert-Elliott and Fritchman channels.

End-to-End Performance Analysis of Delay-Sensitive Multi-Relay Networks

We study the end-to-end (E2E) performance of multi-relay networks in delay-constrained applications. The results are presented for both decode-and-forward (DF) and AF (A: amplify) relaying schemes. We use some fundamental results on the achievable rates of finite-length codes to analyze the system performance in the cases with short packets. Taking the message decoding delays and different numbers of hops into account, we derive closed-form expressions for the E2E packet transmission delay, the E2E error probability as well as the E2E throughput. Moreover, for different message decoding delays, we determine the appropriate codeword length and the relay power such that the same E2E error probability and packet transmission delay are achieved in the AF- and DF-relay networks. As we show, for different codeword lengths and numbers of hops, the E2E performance of multi-relay networks are affected by the message decoding delay of the nodes considerably.

Investigation of the Effect of Intra-Cavity Propagation Delay in Secure Optical Communication Using Chaotic Semiconductor Lasers

The influence of intra-cavity propagation delay in message encoding and decoding using chaotic semiconductor lasers is numerically investigated. A message is encoded at the transmitter laser by a chaos shift keying scheme and is decoded at the receiver by comparing its output with the transmitter laser. The requisite intra-cavity propagation delay in achieving synchronization of optical chaos is estimated by cross-correlation analysis between the transmitter and receiver lasers’ output. The effect of intra-cavity propagation delay on the message recovery has been analyzed from the bit error rate performance. It is found that despite the intra-cavity propagation delay magnitude being less, it has an impact on the quality of message recovery. We also examine the dependency of injection rate, frequency detuning, modulation depth and bit rate on intra-cavity propagation delay and associated message recovery quality. We found that the communication performance has been adequately improved after incorporating intra-cavity propagation delay correction in the synchronization system.

Low Delay 3-Bit Burst Error Correction Codes

The increasing importance of Multiple Cell Upsets (MCUs) in modern memories has spurred research on error correction codes that can correct adjacent bit errors. For example, Double Adjacent Error Correction (DAEC), 3-bit burst and 4-bit burst codes have been proposed in the last years. However, as the error correction capabilities are increased so is the complexity of the encoder and decoder circuits. This directly impacts the encoding and decoding delay and thus limits the use of the codes in high speed memories. To reduce the complexity, some techniques have been proposed recently. Those include more advanced optimization programs to find codes with a lower number of ones in the parity check matrix or the interleaving of data and parity check bits to simplify the decoding. In this paper, those techniques are combined to design more efficient 3-bit burst error correction codes. The encoders and decoders for the proposed codes have been implemented and compared with the state of the art 3-bit burst error correction codes. The results show that the new codes reduce the encoder and decoder delay significantly. Therefore, the proposed codes provide memory designers with a more efficient option to implement protection against 3-bit burst errors for high speed memories.

A Low-Complexity Belief Propagation Based Decoding Scheme for Polar Codes - Decodability Detection and Early Stopping Prediction

In the 5G communication systems, polar code has been adapted as the control channel coding solution in the enhanced mobile broadband (eMBB) scenario. Although different decoding schemes, including belief propagation (BP) and successive cancellation (SC) based algorithms, have been proposed, the decoding complexity as well as the latency are still significant. To address this critical issue, several low-complexity schemes, e.g., the use of simplified decoding operation and stop the decoding operation in earlier stage, have been proposed recently. However, conventional early stopping strategies have to check a pre-defined metric in each iteration, and the associated decoding delay is significant. In this paper, to address this challenge, we proposed a low-complexity BP based decoding scheme, which contains the decodability detection stage and the early stopping prediction stage. The decodability detection stage can identify the codewords in the deep channel fading environment and eliminate the unnecessary decoding operations to reduce the decoding complexity, while the early stopping prediction stage can directly predict the required number of iterations rather than checking the metric in each iteration to avoid the associated decoding delay. Through the above two approaches, our proposed scheme is shown to achieve 71% decoding delay reduction and maintain the same decoding performance as traditional BP, G-matrix, MinLLR schemes.

Multi-CRC Polar Codes and M-SCFlip-Based Decoding

A multi-cyclic redundancy check (Multi-CRC) polar code construction algorithm is proposed in this paper to solve the error propagation problem of successive cancellation decoding for polar codes. In this algorithm, the information sequence is optimized into several segments to allow decoding errors to be corrected in time, minimizing the impact of error propagation. An improved multi-successive cancellation bit flipping (M-SCFlip) decoding algorithm is proposed to execute the bit flipping operation after CRC check-in each segment. In the low-SNR region, the proposed new multi-CRC polar code with successive cancellation list (SCL) decoding has a slight frame-error rate (FER) degradation compared with the original CRC polar code. With the M-SCFlip decoding algorithm developed in this paper, it achieves a better FER performance compared with the CRC polar code with successive cancellation (SC) and SCL ( $L\!=\!2$ ) decoding algorithms. In addition, it has a lower decoding delay and requires a lower memory space. For example, at a FER of 10−4 with the same code length and effective code rate, the proposed multi-CRC polar code with M-CFlip decoding achieves a 1.19 dB and 0.79 dB gains over existing CRC polar codes with the SC and SCL ( $L\!=\!2$ ) decoding algorithms, respectively.

A Degrees-of-Freedom-Achieving Scheme for the Temporally Correlated MIMO Interference Channel With Delayed CSIT

A simple scheme is proposed to achieve the optimal degrees of freedom (DoF) of the temporally correlated two-user multiple-input-multiple-output interference channel with delayed channel state information at the transmitter (CSIT). The delayed CSIT is exploited for temporal alignment at the transmitters and spatial zero-forcing of interference at the receivers. The transmitters estimate the current CSIT using perfect delayed CSIT. For most antenna configurations, the proposed scheme achieves the optimal DoF-region of this channel by precoding (resp. decoding) over a finite number of time slots at each transmitter (resp. receiver). This is an improvement over existing achievable methods, which require infinite channel extensions (hence, infinite decoding delay) and involve complicated encoding and decoding procedures.

Fast Channel Navigation of Internet Protocol Television Using Adaptive Hybrid Delivery Method

The Internet protocol television brought seamless potential that has revolutionized the media and telecommunication industries by providing a platform for transmitting digitized television services. However, zapping delay is a critical factor that affects the quality of experience in the Internet protocol television. This problem is intrinsically caused by command processing time, network delay, jitter, buffer delay, and video decoding delay. The overarching objective of this paper is to use a hybrid delivery method that agglutinates multicast- and unicast-enabled services over a converged network to minimize zapping delay to the bare minimum. The hybrid method will deliver Internet protocol television channels to subscribers using the unicast stream coupled with differentiated service quality of experience when zapping delay is greater than 0.43 s. This aids a faster transmission by sending a join message to the multicast stream at the service provider zone to acquire the requested channel. The hybrid method reported in this paper is benchmarked with the state-of-the-art multicast stream and unicast stream methods. Results show that the hybrid method has an excellent performance by lowering point-to-point queuing delay, end-to-end packet delay, and packet variation and increasing throughput rate.

Reduced decoding time of LDPC code using convolutional code with Vitrebi decoding in Underwater Communication

Low Density Parity Check code is the more efficient technique to attain the minimal error rate in the underwater channel. To reduce the processing delay in the LDPC decoding, convolutional code with high code rate is used. The result showed that the BER of 10-4 can be obtained with Eb/No value of 20 for code rate of ½ and 12 for code rate of 1/8. It is also showed in result that the decoding time is reduced one-third for data size of 500 and one-tenth for the data size of 1500 bits.

Data Dissemination Using Instantly Decodable Binary Codes in Fog-Radio Access Networks

This paper considers a device-to-device (D2D) fog-radio access network wherein a set of users are required to store/receive a set of files. The D2D devices are connected to a subset of the cloud data centers and thus possess a subset of the data. This paper is interested in reducing the total time of communication, i.e., the completion time, required to disseminate all files among all devices using instantly decodable network coding (IDNC). Unlike previous studies that assume a fully connected communication network, this paper tackles the more realistic scenario of a partially connected network in which devices are not all in the transmission range of one another. The joint optimization of selecting the transmitting device(s) and the file combination(s) is first formulated, and its intractability is exhibited. The completion time is approximated using the celebrated decoding delay approach by deriving the relationship between the quantities in a partially connected network. The paper introduces the cooperation graph and demonstrates that the problem is equivalent to a maximum weight clique problem over the newly designed graph. Extensive simulations reveal that the proposed solution provides noticeable performance enhancement and outperforms previously proposed IDNC-based schemes.

Iterative hard­-decision decoding of combined cyclic codes

We propose error correction iteratively decodable cyclic codes (IDCC) that consist of two cyclic Hamming codes with different generator polynomials. As a mathematical apparatus, we apply the theory of linear finite-state machines (LFSM) in binary Galois fields. A generalized decoding algorithm was constructed based on power permutation of bits in the code word and the new technique for combining the codes. By using hard decisions only, it is possible to achieve high speed and simple hardware-software implementation of encoder and decoder on linear feedback shift registers. The IDCC (n, k)-code makes it possible to correct the errors of multiplicity to (n−k). A code word may have arbitrary length: both small and large. Code rate (k/n) is close to one. It was established in the course of research that approaching the theoretical limit (border) by Shannon maximally close significantly increases length of codes, complicates encoders and decoders, increases a delay in decoding, and other problems appear. That is why the main criterion for the optimality of error correction coding is proposed to be those code characteristics that are important for practical application (time and hardware costs, focus on contemporary circuitry and parallel processing). From this point of view, the developed IDCC codes can be considered as an alternative to well-known iterative codes (LDPC codes and turbo codes) whose main advantage is the maximum proximity to the Shannon limit. This is important because at the present stage of development of science and technology one of the relevant scientific and technological problems is the task on ensuring high reliability of data transmission in different systems of digital communication. The proposed codes make it possible to solve the specified task at minimal resource costs and high efficiency.

A Hardware Structure for FAST Protocol Decoding Adapting to 40Gbps Bandwidth

FAST protocol is a kind of Data Compression Protocols which is widely used in Highfrequency trading. So far, implements of fast protocol decoding mainly depend on software. On the other hand, transmission delay of decoding can be effectively decreased by customized hardware instead of software. However, most of FPGA hardware architectures are serial. A parallel FPGA hardware structure for fast protocol decoding adapting to 40Gbps bandwidth is proposed in this paper. The structure includes 3 modules: field dividing module, field matching module and parallel decoding units. The practicability and efficiency of the proposed architecture is verified in System C platform and it takes 173ns to decode a message whose field number is 64. At last, influence of three factors to transmission delay is discussed in this paper, including decoding unit number, field type and sequence length of message.