Systematic Convolutional Codes Research Articles

Study of the block and convolutional code decoding efficiency using a turbo code decoder

An urgent task is to correct errors that occur during the transmission and storage of information. To solve this problem, various noise-resistant codes have recently been increasingly used. Turbo codes have the best correcting ability in data transmission channels with a high probability of an erroneous bit. To obtain the necessary characteristics, various combinations of codes and encoding and decoding methods are used. If another block of information bits is added to the codeword of a systematic block or systematic convolutional code, then it will be possible to implement decoding of such a codeword by a turbo code decoder. The disadvantage of the resulting combined code is its extremely low correcting ability in the presence of errors in the check bits of the codeword. The article shows that the correcting ability of the presented code can be significantly increased by multiplying the decoded values of the check bits by reduction factors.

Concatenated turbo polar-convolutional codes based on soft cancellation algorithm

This paper presents the Parallel and Serial Concatenated Turbo Polar-Convolutional Codes (CTPCCs) to improve the performance of polar codes in the finite code length regime. Both proposed concatenated codes use the Systematic Polar Code (SPC) and Recursive Systematic Convolutional (RSC) code as constituent codes. The iterative decoding algorithms of the proposed systems consist of a Soft Cancellation (SCAN) decoder with a single internal iteration for the SPC and SOVA or LogMap decoder for the RSC code. The simulation results show that the performance of the Parallel Concatenated Turbo Polar-Convolutional Code (PCTPCC) at low signal-to-noise ratios (SNRs) is better than that of the Serial Concatenated Turbo Polar-Convolutional Code (SCTPCC) and also better than the performance of other Turbo Polar Codes (TPCs). At BER=10−2, the proposed PCTPCC with SOVA and LogMap algorithms has about 0.3 dB and 0.25 dB performance gains over the SCTPCC models, respectively. In the high SNR regions, the performance of the SCTPCC with the LogMap algorithm significantly outperforms that of other models. At BER=10−6, the proposed SCTPCC models with SOVA and LogMap algorithms outperform the PCTPCC model by gains of 0.3 dB and 0.25 dB, respectively. The PCTPCC model with the SOVA decoder is superior to other models in terms of complexity.

METHOD FOR ADAPTING RECURSIVE SYSTEMATIC CONVOLUTIONAL CODES OF TURBO CODES BY BYPASSING THE NODES OF THE SPATIAL GRID

The article is devoted to increasing the efficiency of the functioning of wireless information transmission systems due to the adaptation of the parameters of recursive systematic convolutional codes of turbo codes by bypassing the nodes of the spatial grid and calculating the objective function. The probability of a white error of information decoding is chosen as the objective function. To calculate the chosen probability of a white error of information decoding, it is proposed to use Bowes-Choudhury-Hockingham codes, since for turbo codes there are only approximate asymptotic characteristics that give a large error at small values ​​of the signal-to-noise ratio. Analysis of known works shows that adaptation schemes of these codes are used to improve the reliability of information. At the same time, during adaptation, in the vast majority of works, only one parameter changes - the coding speed, which does not fully increase the effectiveness of corrective coding schemes. That is why it is proposed to use several parameters during adaptation, namely the polynomials of forward and backward connections of recursive systematic convolutional codes and the coding speed of turbo codes. The article consists of an introduction, which highlights the problem, analyzes the latest research and publications on this topic, and formulates the purpose of the article. The results of the research are shown, conclusions and prospects for further research are drawn. The article ends with a list of used sources. As a result of the work of the proposed method, the parameters of the turbo codes, which were found using the method for the channel with additive white Gaussian noise for different sizes of the input data block, are given. We consider the direction of further research to expand the space of the spatial lattice to take into account more parameters of turbo codes during adaptation, while the following can be foreseen: the number of bits in the block, types of interleavers, decoding algorithms, decoding iterations, etc.

Soft values based detector for bit interleaved coded modulation multi input multi output systems

With the advantages of spatial multiplexing multi input multi output (MIMO) systems in terms of high transmission capacity, the high complexity of the detector at the receiver side of such systems is a major issue. Performance, in terms of bit error rate (BER) is studied for bit interleaved coded modulation (BICM) MIMO systems. List based generation of (bits) soft values is considered for 2 by 2, 4 by 4 systems with 16,64 quadrature amplitude modulation (QAM) and different list sizes utilizing a non systematic convolutional code. Using a sphere detector partial tree search, a scheme is suggested and shown to be more computationally efficient (in terms of the average number of scanned nodes) than a reported alternative for block, flat fading channels. Simulation results reveal that performance in terms of BER can still be maintained.

A novel method for identifying recursive systematic convolutional encoders based on the cuckoo search algorithm

The existing methods for identifying recursive systematic convolutional encoders with high robustness require to test all the candidate generator matrixes in the search space exhaustively. With the increase of the codeword length and constraint length, the search space expands exponentially, and thus it limits the application of these methods in practice. To overcome the limitation, a novel identification method, which gets rid of exhaustive test, is proposed based on the cuckoo search algorithm by using soft-decision data. Firstly, by using soft-decision data, the probability that a parity check equation holds is derived. Thus, solving the parity check equations is converted to maximize the joint probability that parity check equations hold. Secondly, based on the standard cuckoo search algorithm, the established cost function is optimized. According to the final solution of the optimization problem, the generator matrix of recursive systematic convolutional code is estimated. Compared with the existing methods, our proposed method does not need to search for the generator matrix exhaustively and has high robustness. Additionally, it does not require the prior knowledge of the constraint length and is applicable in any modulation type.

LOW POWER CODER FOR WIRELESS SENSOR NETWORKS

An Energy efficiency technique is a important subject for Wireless Sensor Networks (WSNs), that have received extensive attention to reduce energy consumption and improve network lifetime. Most of the power in sensor networks is consumed by data transmission and reception. This power can be reduced by using suitable data compression technique which reduces transmitted data over wireless channels. In this article, the design of an energy efficient coder is proposed. When this algorithm is applied to recursive systematic convolutional (RSC) code, it reduces both computation complexity and decode error probability. Applying this RSC code to wireless sensor network ensures correct data reception and reduced energy consumption. To validate and evaluate our work, simulation is done in Xilinx software and Power is calculated using Xilinx xpower tool. The simulation result shows that the proposed algorithm performs better than existing one

On the Performance of Self‐Concatenated Coding for Wireless Mobile Video Transmission Using DSTS‐SP‐Assisted Smart Antenna System

In the current age of advanced technologies, there is an escalating demand for reliable wireless systems, catering to the high data rates of mobile multimedia applications. This article presents a novel approach to the concept of Self‐Concatenated Convolutional Coding (SECCC) with Sphere Packing (SP) modulation via Differential Space‐Time Spreading‐ (DSTS‐) based smart antennas. The two transmitters provide transmit diversity which is capable of recuperating the signal from the effects of fading, even with a single receiving antenna. The proposed DSTS‐SP SECCC scheme is probed for the Rayleigh fading channel. The SECCC structure is developed using the Recursive Systematic Convolutional (RSC) code with the aid of an interleaver. Interleaving generates randomness in exchange for extrinsic information between the constituent decoders. Iterative decoding is invoked at the receiving side to enhance the output performance by attaining fruitful convergence. The convergence behaviour of the proposed system is investigated using EXtrinsic Information Transfer (EXIT) curves. The performance of the proposed system is ascertained with the H.264 standard video codec. The perceived video quality of DSTS‐SP SECCC is found to be significantly better than that of the DSTS‐SP RSC. To be more precise, the proposed DSTS‐SP SECCC system exhibits an Eb/N0 gain of 8 dB at the PSNR degradation point of 1 dB, relative to the equivalent rate DSTS‐SP RSC. Similarly, an Eb/N0 gain of 10 dB exists for the DSTS‐SP SECCC system at 1 dB degradation point when compared with the SECCC scheme dispensing with the DSTS‐SP approach.

On the Performance of Wireless Video Communication Using Iterative Joint Source Channel Decoding and Transmitter Diversity Gain Technique

In this research work, we have presented an iterative joint source channel decoding- (IJSCD-) based wireless video communication system. The anticipated transmission system is using the sphere packing (SP) modulation assisted differential space-time spreading (DSTS) multiple input-multiple output (MIMO) scheme. SP modulation-aided DSTS transmission mechanism results in achieving high diversity gain by keeping the maximum possible Euclidean distance between the modulated symbols. Furthermore, the proposed DSTS scheme results in a low-complexity MIMO scheme, due to nonemployment of any channel estimation mechanism. Various combinations of source bit coding- (SBC-) aided IJSCD error protection scheme has been used, while considering their identical overall bit rate budget. Artificial redundancy is incorporated in the source-coded stream for the proposed SBC scheme. The motive of adding artificial redundancy is to increase the iterative decoding performance. The performance of diverse SBC schemes is investigated for identical overall code rate. SBC schemes are employed with different combinations of inner recursive systematic convolutional (RSC) codes and outer SBC codes. Furthermore, the convergence behaviour of the employed error protection schemes is investigated using extrinsic information transfer (EXIT) charts. The results of experiments show that our proposed R a t e − 2 / 3 SBC-assisted error protection scheme with high redundancy incorporation and convergence capability gives better performance. The proposed R a t e − 2 / 3 SBC gives about 1.5 dB E b / N 0 gain at the PSNR degradation point of 1 dB as compared to R a t e − 6 / 7 SBC-assisted error protection scheme, while sustaining the overall bit rate budget. Furthermore, it is also concluded that the proposed R a t e − 2 / 3 SBC-assisted scheme results in E b / N 0 gain of 24 dB at the PSNR degradation point of 1 dB with reference to R a t e − 1 SBC benchmarker scheme.

Error correction for low power sensors in asynchronous communication

We propose a forward error correction scheme for asynchronous sampling via level crossing (LC) sampling and time encoding, where the dominant errors consist of pulse deletions and insertions, and where encoding is required to take place in an instantaneous fashion. For LC sampling the presented scheme consists of a combination of an outer systematic convolutional code, an embedded inner marker code, and power-efficient frequency-shift keying modulation at the sensor node. Decoding is first obtained via a maximum a-posteriori (MAP) decoder for the inner marker code, which achieves synchronization for the insertion and deletion channel, followed by MAP decoding for the outer convolutional code. Besides investigating the rate trade-off between marker and convolutional codes, we also show that residual redundancy in the asynchronously sampled source signal can be successfully exploited in combination with redundancy only from a marker code. This provides a low complexity alternative for deletion and insertion error correction compared to using explicit redundancy. For time encoding, only the pulse timing is of relevance at the receiver, and the outer channel code is replaced by a quantizer to represent the relative position of the pulse timing. Numerical simulations show that LC sampling outperforms time encoding in the low to moderate signal-to-noise ratio regime by a large margin.

Performances of BICM-ID system using CRSC code in optical transmissions

Abstract Recently, using iterative decoding algorithms to achieve an interesting bit error rate for spectrally efficient modulation become a necessity for optical transmission, in this paper, we propose a coded modulation scheme based on bit interleaving circular recursive systematic convolutional (CRSC) code and 16-QAM modulation. The proposal system considered as a serial concatenation of a channel encoder, a bit interleaver and M-ary modulator can be flexible easy to implement using a short code length. For a spectral efficiency η = 3 bit / s / H z $\eta =3\text{bit}/s/Hz$ , the coding gain at a bit error rate of 10−6 is about 8 dB.

1/n Turbo codes from linear system point of view

The performance of turbo codes at the error floor region is largely determined by the effective free distance, which corresponds to the minimum Hamming weight among all codeword sequences generated by input sequences of weight two. In this paper, we study turbo codes of dimension one obtained from the concatenation of two equal codes and present an upper bound on the effective free distance of a turbo code with these parameters defined over any finite field. We do that making use of the so-called (A, B, C, D) state-space representations of convolutional codes and restrict to the case where A is invertible. A particular construction, from a linear systems point of view, of a recursive systematic convolutional code of rate 1/n so that the effective free distance of the corresponding turbo code attains this upper bound is also presented.

Blind parameter estimation of turbo convolutional codes: Noisy and non-synchronized scenario

Blind estimation of forward error correction code parameters at the receiver plays a significant role in non-cooperative communication, adaptive modulation and coding systems, and reconfigurable receiver systems. Turbo convolutional codes, a parallel concatenation of multiple convolutional codes, are used in digital communication and storage systems to achieve low bit error rate. The present paper proposes innovative algorithms for the blind estimation of code parameters and reconstruction of turbo convolutional encoder over noisy scenario. The turbo convolutional code is designed using two component codes along with an interleaver. Recursive systematic convolutional codes are used as component codes. Any imperfection in synchronization of received data for the proposed code parameter estimation algorithm is compensated through a bit position adjustment parameter. The performance of the proposed algorithms in terms of parameter estimation accuracy is investigated for different modulation order, code rate, and constraint length values. It is observed that the performance improves with decrease in modulation order and constraint length values.

IoT Communications Network for Wireless Power Transfer System State Estimation and Stabilization

Wireless energy harvesting has emerged as an appealing solution to prolong the lifespan of energy-constrained wireless networks and been regarded as a main functional unit for almost all perpetual communications. This paper proposes a channel coding-based Internet of Things communication network, and state estimation as well as stabilization algorithms for wireless power transfer systems. After modeling the energy harvesting module like wireless energy transfer systems as a state-space framework, Web-enabled smart sensors are deployed to obtain measurements. The sensing information is transmitted to the nearby base station for collection and digital communication under the condition of packet losses. A recursive systematic convolutional code is used to add redundancy into the quantize system states. After digital modulation, the signal is transmitted to a control center for system state estimation and stabilization. The optimal gain of the state estimation scheme is determined after minimizing the mean squared errors. Afterward, a stabilization algorithm is designed considering packet losses in the communication networks using the semidefinite programming approach. Furthermore, the convergence of the developed estimation algorithm is proved. Numerical simulation results demonstrate, considering packet loss, sensor faults, disturbances, and delay into account, that the proposed algorithms can estimate and stabilize the system states within a short period of time.

Wireless Holographic Image Communications Relying on Unequal Error Protected Bitplanes

Holography is considered to be one of the most promising techniques of goggle-free visualization for the near-future. We consider wireless transmission of digital holograms, which are partitioned into multiple bitplanes that are then independently encoded by a forward error correction (FEC) code for transmission over wireless channels. The coding rates of these bitplanes will be optimized at the transmitter for the sake of achieving an improved holographic peak signal-to-noise ratio (PSNR) at the receiver. Our simulation results show that up to 2.6 dB of $E_{b}/N_{0}$ or 12.5 dB of PSNR improvements may be achieved when employing a recursive systematic convolutional code.

Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding.

Structural adaptation of the turbo code coder and decoder for generating the transmission repeat request under conditions of uncertainty

The paper deals with the issue of enhancing the performance efficiency of wireless networks built by using the with automatic repeat request scheme for retransmission. The proposed method is based on adaptive change of polynomials of recursive systematic convolutional codes forming a part of turbo codes and aimed at enhancing their correcting properties at the expense of increasing the code limitation at each data block retransmission for the set coding rate. In this case, the decoding algorithm of turbo codes is modified in respect of using the introduced additional a priori information during the calculation of logarithmic ratios of likelihood functions or log-likelihood ratios (LLR) for each component decoder obtained during the earlier repeat requests for retransmission. The results of simulation modeling showed that the application of this technique made it possible to obtain the energy gain in coding and enhance the data transmission accuracy as compared to the fourth generation mobile communication system, such as 4G LTE-Advanced.

On the MacWilliams Identity for Classical and Quantum Convolutional Codes

The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing- Luerssen and Schneider in the case of minimal encoders, and generalized by Forney. We consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this MacWilliams identity in the case of minimal encoders. For our purpose, we choose a different representation for the exact weight generating function (EWGF) of a block code, by defining it as a linear combination of orthonormal vectors in Dirac bra-ket notation. This representation provides great flexibility so that general split weight generating functions and their MacWilliams identities can be easily obtained from the MacWilliams identity for EWGFs. As a result, we also obtain the MacWilliams identity for the input-parity weight adjacency matrices of a systematic convolutional code and its dual. Finally, paralleling the development of the classical case, we establish the MacWilliams identity for quantum convolutional codes.

Turbo coding for the noisy 2-user binary adder channel with punctured convolutional codes

This paper investigates the use of punctured recursive systematic convolutional codes for turbo coding in a 2-user binary adder channel (2-BAC) in the presence of additive white Gaussian noise, aiming to achieve a higher transmission sum rate with reduced decoding complexity. The encoders for the 2-BAC are assumed to be block synchronized and to employ identical puncturing patterns. Iterative decoding combining the Bahl Cocke Jelinek Raviv algorithm and a two-user punctured trellis is employed. For each user and for a fixed puncturing pattern, random interleavers of length 256 bits or 1024 bits, respectively, are simulated and corresponding curves relating bit error rate versus signal to noise ratio are presented for performance comparison purposes. Computer simulation indicates that the loss in performance of a punctured turbo code can be negligible when longer interleavers are used for both users, similarly to the single user case.

Adaptive-Truncated-HARQ-Aided Layered Video Streaming Relying on Interlayer FEC Coding

Interlayer forward error correction (IL-FEC) coding constitutes an effective unequal error protection (UEP) scheme conceived for transmitting layered video over wireless channels. In contrast to traditional UEP schemes, it operates by embedding extra information concerning the base layer (BL) into the enhancement layers (ELs) without requiring extra transmission resources. The received EL packets assist in the decoding of the BL to reduce the distortion of the reconstructed video. The optimum scheduling of the IL-FEC coded layered video streaming in a truncated hybrid automatic repeat request (THARQ)-aided system is an open problem. Hence, in this paper, we conceive an adaptive THARQ (ATHARQ) algorithm for finding the most appropriate scheduling of the IL-FEC coded layered video packets for the sake of minimizing the video distortion under the constraint of a given total number of transmission time slots (TSs). Furthermore, we develop a method of online coding-rate optimization algorithm for our IL-ATHARQ transmission scheme to find the best FEC code rate distribution among the video layers that results in the lowest possible video distortion. When using a recursive systematic convolutional (RSC) code, our simulation results show that the proposed rate-optimized (RO) IL-ATHARQ system outperforms the traditional THARQ transmission scheme by about 5.3 dB of $E_{b}/N_{0}$ at a peak signal-to-noise ratio (PSNR) of 38.5 dB. Viewing the improvements in terms of the video quality, 2.5 dB of PSNR improvement is attained at an $E_{b}/N_{0}$ of 15 dB.

Practical Design and Decoding of Parallel Concatenated Structure for Systematic Polar Codes

In this paper, a parallel concatenated structure is proposed to improve the performance of polar codes in finite length in which multiblocks systematic polar codes (SPC) and recursive systematic convolutional codes (RSC) are combined. We first design a weighted iterative decoding algorithm for the proposed structure such that better bit error rate performance can be obtained. Then, a deliberated interleaver is optimized for the new scheme. Thereafter, we introduce a strategy to estimate the minimum distance of the concatenation codeword, where an asymptotic performance and convergence behavior analysis are elaborated. Finally, the error performance of the proposed scheme is evaluated via simulations. The results show that our scheme almost outperforms all the existed concatenation ones using polar codes, making the codes more practical.