Recursive Systematic Convolutional Codes Research Articles

Distributed State Estimation Using RSC Coded Smart Grid Communications

Recently, the renewable distributed energy resources (DERs) have become more and more popular due to carbon-free energy sources and environment-friendly electricity generation. Unfortunately, these power generation patterns are mostly intermittent in nature and distributed over the electrical grid, which creates challenging problems in the reliability of the smart grid. Thus, the smart grid has a strong requisite for an efficient communication infrastructure to facilitate estimating the DER states. In contrast to the traditional methods of centralized state estimation (SE), we propose a distributed approach to microgrid SE based on the concatenated coding structure. In this framework, the DER state is treated as a dynamic outer code, and the recursive systematic convolutional (RSC) code is seen as a concatenated inner code for protection and redundancy in the system states. Furthermore, in order to properly monitor the intermittent energy source from any place, this paper proposes a distributed SE method. Particularly, the outputs of the local SE are treated as measurements, which are fed into the master fusion station. At the end, the global SE can be obtained by combining local SEs with corresponding weighting factors. The weighting factors can be calculated by inspiring the covariance intersection method. The simulation results show that the proposed method is able to estimate the system state properly.

Layered Wireless Video Relying on Minimum-Distortion Inter-Layer FEC Coding

Layered video coding is capable of progressively refining the reconstructed video quality with the aid of multiple layers of unequal importance. When the base layer (BL) is corrupted or lost due to channel impairments, the enhancement layers (ELs) must be discarded by the video decoder, regardless whether they are perfectly decoded or not, which implies that the transmission power assigned to the ELs is wasted. To circumvent this problem, we proposed a bit-level inter-layer forward error correction (IL-FEC) scheme for layered video transmission in our previous work, which implanted the systematic bits of the BL into the systematic bits of the ELs using exclusive-OR operations (XOR). This allowed the receiver to exploit the implanted bits of the ELs for assisting the BL's decoding and hence improved the overall system performance of our IL-FEC aided layered video scheme. In this treatise, we find the specific FEC coding rates in a real-time on-line fashion for the sake optimizing the overall system performance. The proposed procedure is widely applicable to diverse wireless transceivers and FEC codecs. Our simulation results show that the proposed optimized IL-FEC system outperforms the traditional optimal UEP by about 1.9 dB of Eb/N0 at a peak signal-to-noise ratio (PSNR) of 38 dB. Viewing the improvements in terms of the video quality, 3.3 dB of PSNR improvement is attained at an Eb/N0 of 10 dB, when employing a recursive systematic convolutional (RSC) code.

Inter-Layer FEC Aided Unequal Error Protection for Multilayer Video Transmission in Mobile TV

Layered video coding creates multiple layers of unequal importance that enables us to progressively refine the reconstructed video quality. When the base layer (BL) is corrupted or lost during transmission, the enhancement layers (ELs) must be dropped, regardless of whether they are perfectly decoded or not, which implies that the transmission power assigned to the ELs is wasted. In this treatise, we propose an inter-layer forward error correction (FEC) coded video transmission scheme for mobile TV. At the transmitter, the proposed interlayer (IL) coding technique implants the systematic information of the BL into the ELs by using exclusive-OR operations. At the receiver, the implanted bits of the ELs may be utilized for assisting in decoding the BL. Furthermore, the data partition mode of H.264 video coding is utilized as the source encoder, where the type B and type C partitions will assist in protecting the type A partition. The IL coded bitstream will then be modulated and transmitted over a multifunctional multiple input multiple output (MF-MIMO) scheme for the sake of improving the system's performance in mobile environments. The proposed system may be readily combined with the traditional unequal error protection (UEP) technique, where extrinsic mutual information (MI) measurements are used for characterizing the performance of our proposed technique. Finally, our simulation results show that the proposed system model outperforms the traditional UEP aided system by about 2.5 dB of E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> or 3.4 dB of peak signal-to-noise ratio (PSNR) at the cost of a 21% complexity increase, when employing a recursive systematic convolutional code. Furthermore, unlike the traditional UEP strategies, where typically stronger FEC-protection is assigned to the more important layer, employing our proposed IL coding technique requires weaker FEC to the more important layer. For example, the system relying on channel coding rates of 0.85, 0.44, and 0.44 for the type A, type B, and type C H.264 video partitions, respectively, achieves the best system performance when employing a recursive systematic convolutional (RSC) code.

Exploitation of 2D binary source correlation using turbo block codes with fine-tuning

This article proposes a joint source-channel coding technique for two-dimensional (2D) binary Markov sources by using concatenated turbo block codes composed of two Bose, Chaudhuri, Hocquenghem (BCH) codes, of which output is followed by a rate-1 recursive systematic convolutional code. The source correlation of all rows and columns of the 2D source is well exploited by using a modified Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm for the decoding of the BCH codes. Simulation results show that the proposed technique outperforms in terms of bit error rate the codes that exploits one-dimensional (1D) source correlation using the modified BCJR algorithm, and obviously the conventional system without source correlation exploitation. In order to further improve the performance, this article aims to make fine-tuning of the code parameters, given the source correlation property, that can achieve performance even closer to the theoretical limit than without the fine-tuning. Finally, results of image transmission simulations using two images, one having strong and the other weak 2D correlation, are presented to demonstrate the effectiveness of our proposed technique.

Comparison of Turbo Codes and Low Density Parity Check Codes

The most powerful channel coding schemes, namely, those based on turbo codes and LPDC (Low density parity check) codes have in common principle of iterative decoding. Shannon's predictions for optimal codes would imply random like codes, intuitively implying that the decoding operation on these codes would be prohibitively complex. A brief comparison of Turbo codes and LDPC codes will be given in this section, both in term of performance and complexity. In order to give a fair comparison of the codes, we use codes of the same input word length when comparing. The rate of both codes is R = 1/2. However, the Berrou's coding scheme could be constructed by combining two or more simple codes. These codes could then be decoded separately, whilst exchanging probabilistic, or uncertainty, information about the quality of the decoding of each bit to each other. This implied that complex codes had now become practical. This discovery triggered a series of new, focused research programmes, and prominent researchers devoted their time to this new area.. Leading on from the work from Turbo codes, MacKay at the University of Cambridge revisited some 35 year old work originally undertaken by Gallagher (5), who had constructed a class of codes dubbed Low Density Parity Check (LDPC) codes. Building on the increased understanding on iterative decoding and probability propagation on graphs that led on from the work on Turbo codes, MacKay could now show that Low Density Parity Check (LDPC) codes could be decoded in a similar manner to Turbo codes, and may actually be able to beat the Turbo codes (6). As a review, this paper will consider both these classes of codes, and compare the performance and the complexity of these codes. A description of both classes of codes will be given. I. Turbo Codes There are different ways of constructing Turbo codes, but the commonality is that they use two or more codes in the encoding process. The constituent encoders are typically recursive, systematic convolutional (RSC) codes (3). Figure 1 shows a general set-up of the encoder. The number of bits in the code word varies with the rate of the code. For an overall code rate of R = 1/2, it is normal to use two R = 1/2 RSC codes, where every systematic bit is transmitted, but for the coded bits a puncturing matrix is used where only every second code bit from each of the constituent codes is included in the transmitted symbol. The permutation matrix Π permutes the systematic bits, so that the two constituent codes are excited by the same set of information bits, albeit in a different order. The permutation matrix is a critical design factor for designing good codes. The code word consists o f Ci as the systematic bit (di) and Ci and Ci which are vectors of encoded bits from the two convolution codes. These vectors can contain one or more bits and di is the information bit, Π is the permutation matrix.

Low-Complexity Soft Decoding of Huffman Codes and Iterative Joint Source Channel Decoding

Most source coding standards (voice, audio, image and video) use Variable-Length Codes (VLCs) for compression. However, the VLC decoder is very sensitive to transmission errors in the compressed bit-stream. Previous contributions, using a trellis description of the VLC codewords to perform soft decoding, have been proposed. Significant improvements are achieved by this approach when compared with prefix decoding. Nevertheless, for realistic VLCs, the complexity of the trellis technique becomes intractable. In this paper, we propose a soft-input VLC decoding method using an a priori knowledge of the lengths of the source-symbol sequence and the compressed bit-stream with Maximum A Posteriori (MAP) sequence estimation. Performance in the case of transmission over an Additive White Gaussian Noise (AWGN) channel is evaluated. Simulation results show that the proposed decoding algorithm leads to significant performance gain in comparison with the prefix VLC decoding besides exhibiting very low complexity. A new VLC decoding method generating additional information regarding the reliability of the bits of the compressed bit-stream is also proposed. We consider the serial concatenation of a VLC with two types of channel code and perform iterative decoding. Results show that, when concatenated with a recursive systematic convolutional code (RSCC), iterative decoding provides remarkable error correction performance. In fact, a gain of about 2.3 dB is achieved, in the case of transmission over an AWGN channel, with respect to tandem decoding. Second, we consider a concatenation with a low-density parity-check (LDPC) code and it is shown that iterative joint source/channel decoding outperforms tandem decoding and an additional coding gain of 0.25 dB is achieved.

Joint source/channel iterative arithmetic decoding with JPEG 2000 image transmission application

Abstract Motivated by recent results in Joint Source/Channel coding and decoding, we consider the decoding problem of Arithmetic Codes (AC). In fact, in this article we provide different approaches which allow one to unify the arithmetic decoding and error correction tasks. A novel length-constrained arithmetic decoding algorithm based on Maximum A Posteriori sequence estimation is proposed. The latter is based on soft-input decoding using a priori knowledge of the source-symbol sequence and the compressed bit-stream lengths. Performance in the case of transmission over an Additive White Gaussian Noise channel is evaluated in terms of Packet Error Rate. Simulation results show that the proposed decoding algorithm leads to significant performance gain while exhibiting very low complexity. The proposed soft input arithmetic decoder can also generate additional information regarding the reliability of the compressed bit-stream components. We consider the serial concatenation of the AC with a Recursive Systematic Convolutional Code, and perform iterative decoding. We show that, compared to tandem and to trellis-based Soft-Input Soft-Output decoding schemes, the proposed decoder exhibits the best performance/complexity tradeoff. Finally, the practical relevance of the presented iterative decoding system is validated under an image transmission scheme based on the JPEG 2000 standard and excellent results in terms of decoded image quality are obtained.

Characterization of Demapper EXIT Functions with BEC a priori Information with Applications to BICM-ID

This paper introduces a less is more approach to the modelling of iterative decoding for bit-interleaved coded modulation (BICM). It considers modelling the iterative exchange of soft a priori information between the demapper and decoder with a binary erasure channel model. This simplification, unlike the usual additive white Gaussian noise (AWGN) channel model, allows us to express the extrinsic information transfer (EXIT) chart curves for the demapper with polynomials whose order makes explicit the degrees of freedom available for design. The accuracy of our expressions simplifies the design process enabling us to compare in a more manageable manner the key performance parameters: the BER performance and the convergence threshold. This enabled us to find the pairing of memory-two recursive systematic convolutional (RSC) codes and mappers that achieve the earliest convergence threshold for a target BER floor at convergence: for 8-PSK semi-set partitioning (SSP) was optimal and converged at a signal-to-noise ratio (SNR)= 3.0 dB for a BER target of at least 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> ; two new mappings were the optimal pairings for 16-QAM, where the L4b2 mapping converged at 2.9 dB for a BER floor ≤ 3.46 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> and the H2b2 mapping converged at 3.1 dB for a BER floor ≤ 2.44 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

Low complexity Chase-2 decoding of concatenated codes

The concatenated codes are widely used in current communication systems, such as satellite communication systems and WiMAX system. The objective of this study was to present a low complexity iterative soft decoding algorithm for concatenated codes. The concatenation was between a Reed-Solomon (RS) code and recursive systematic convolutional (RSC) code. The reduction in computational complexity was achieved by simplifying the Chase-2 decoder for RS codes with limited usage of test patterns. The processing of soft information between inner and outer decoders was also discussed. Simulation results showed that the proposed algorithm could achieve a good trade-off between complexity and performance.

Capacity-Approaching Irregular Turbo Codes for the Binary Erasure Channel

In this paper, we propose a class of irregular turbo codes that approach the capacity of the binary erasure channel. First, an analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This expression will then be used to study the density evolution of turbo codes over the binary erasure channel, that will allow for the design of capacity-approaching infinite-length irregular turbo codes. Next, a graph-optimal interleaver for finite-length irregular turbo codes is proposed. Finally, simulation results for different coding rates are shown.

Distributed Self-Concatenated Coding for Cooperative Communication

In this paper, we propose a power-efficient distributed binary self-concatenated coding scheme using iterative decoding (DSECCC-ID) for cooperative communications. The DSECCC-ID scheme is designed with the aid of binary extrinsic information transfer (EXIT) charts. The source node transmits self-concatenated convolutional coded (SECCC) symbols to both the relay and destination nodes during the first transmission period. The relay performs SECCC-ID decoding, where it may or may not encounter decoding errors. It then reencodes the information bits using a recursive systematic convolutional (RSC) code during the second transmission period. The resultant symbols transmitted from the source and relay nodes can be viewed as the coded symbols of a three-component parallel concatenated encoder. At the destination node, three-component DSECCC-ID decoding is performed. The EXIT chart gives us an insight into operation of the distributed coding scheme, which enables us to significantly reduce the transmit power by about 3.3 dB in signal-to-noise ratio (SNR) terms, as compared with a noncooperative SECCC-ID scheme at a bit error rate (BER) of 10-5. Finally, the proposed system is capable of performing within about 1.5 dB from the two-hop relay-aided network's capacity at a BER of 10-5, even if there may be decoding errors at the relay.

Near-capacity iterative decoding of binary self-concatenated codes using soft decision demapping and 3-D EXIT charts

In this paper 3-D Extrinsic Information Transfer (EXIT) charts are used to design binary Self-Concatenated Convolutional Codes employing Iterative Decoding (SECCC-ID), exchanging extrinsic information with the soft-decision demapper to approach the channel capacity. Recursive Systematic Convolutional (RSC) codes are selected as constituent codes, an interleaver is used for randomising the extrinsic information exchange of the constituent codes, while a puncturer helps to increase the achievable bandwidth efficiency. The convergence behaviour of the decoder is analysed with the aid of bit-based 3-D EXIT charts, for accurately calculating the operating EbN0 threshold, especially when SP based soft demapper is employed. Finally, we propose an attractive system configuration, which is capable of operating within about 1 dB from the channel capacity.

Iterative joint source–channel decoding of H.264 compressed video

This paper proposes an Iterative Joint Source–Channel Decoding (IJSCD) scheme for error resilient transmission of H.264 compressed video over noisy channels by using the available H.264 compression, e.g., Context-based Adaptive Binary Arithmetic Coding (CABAC), and channel coding, i.e., rate-1/2 Recursive Systematic Convolutional (RSC) code, in transmission. At the receiver, the turbo decoding concept is explored to develop a joint source–channel decoding structure using a soft-in soft-out channel decoder in conjunction with the source decoding functions, e.g., CABAC-based H.264 semantic verification, in an iterative manner. Illustrative designs of the proposed IJSCD scheme for an Additive White Gaussian Noise (AWGN) channel, including the derivations of key parameters for soft information are discussed. The performance of the proposed IJSCD scheme is shown for several video sequences. In the examples, for the same desired Peak Signal-to-Noise Ratio (PSNR), the proposed IJSCD scheme offers a savings of up to 2.1 dB in required channel Signal-to-Noise Ratio (SNR) as compared to a system using the same RSC code alone. The complexity of the proposed scheme is also evaluated. As the number of iterations is controllable, a tradeoff can be made between performance improvement and the overall complexity.

Investigation of Turbo Code Polynimials under Constraints Length Four and Deterministic Interleaver

Turbo coding Technique is one from very powerful error correction techniques that have made a tremendous impact on channel coding in the last few years. It had been recommended for increased capacity at higher transmission rates due to their superior performance over conventional codes. Recursive systematic convolutional (RSC) turbo code uses two polynomials in its encoding circuit which are feed-forward and feed-back polynomials. Those polynomials make great effects on performance of turbo codes in all regions. In this paper, the primitive and non-primitive polynomials will be investigated which are not clarified until now. Their effects on the performance in water-fall region and error floor regions will be elaborated. The minimum Hamming distance and their multiplicities are the criteria for comparison. Simulation results over the AWGN channel show that primitive polynomials in the Feed-back and feed-forward can achieve better performance at high SNR by improving the minimum distance (large minimum distance) which leads to decrease BER in the region of high signal to noise ratio to be used in the satellites new missions. Moreover, the results give a larger minimum distance by factor of 1.12dB compared with the CCSDS interleaver. The simulation is applied for frame length 1784, and code rate 1/2.

Reliable Wireless Communication for Medical Devices Using Turbo Convolution Code

Wireless technology is now being used to bring significantly innovative products and services in the healthcare sector, enabling new medical sensors, and treatment methods. In this paper, a new and improved communication system for communicating signals among different medical devices and a console is presented. Considering the need for very high degree of functional reliability of communication link in RF challenged environment (indoor), a novel algorithm called bi-directional “Soft Output Viterbi Algorithm (SOVA)” decoding for double-binary Circular Recursive Systematic Convolutional (CRSC) turbo codes is presented. The bi-directional SOVA is considered in view of its better performance and implementation complexity trade-off. The basic SOVA has been described for binary turbo code. We have extended it for double binary case, which is useful for high data rate healthcare applications using real time streaming data. Necessary changes in basic message passing equations for double-binary case have been introduced. Coding gain can be used to increase the robustness and immunity to interference. Decoding of CRSC codes requires a prologue decoder, prior to the actual trellis decoding, to estimate the initial state. Efficient determination of circulation state through prologue decoding has helped in achieving impressive error performance for CRSC codes. The issues related to digital implementation of turbo encoder/decoder and their effects on error performance have also been discussed. Adequate simulation results have been included.

Cooperative Network Coding with Soft Information Relaying in Two-way Relay Cchannels

Network coding in wireless network can improve network throughput by exploiting the broadcast nature of the wireless network. Taking into consideration the error prone nature of wireless networks, we investigate the design of network coding implemented in physical layer, and propose a cooperative network coding scheme with soft information forwarding (SIR), which combines soft network coding and distributed turbo coding scheme in two-way relay channels (TWRC) in this paper. In order to mitigate the error propagation effect due to the imperfect decoding at the relay, soft network coding is deployed in the proposed scheme, where soft-input soft-output (SISO) encoder and decoder for recursive systematic convolutional (RSC) codes are implemented. Moreover, the soft information of both systematic bits and redundancy parity bits are forwarded at the relay by using higher-order constellations to achieve diversity gain. Aided by distance spectrum of turbo codes, concept of uniform interleaver, and Gaussian approximation of soft decoding information, union bound on the error performance of our scheme is analyzed. Both the analysis and simulation confirm that the proposed scheme achieves significant gain over conventional network coding in quasi-static fading channels.

Iterative AMR-WB Source and Channel Decoding Using Differential Space–Time Spreading-Assisted Sphere-Packing Modulation

In this paper, we present a novel system that invokes jointly optimized iterative source and channel decoding for enhancing the error resilience of the adaptive multirate wideband (AMR-WB) speech codec. The resultant AMR-WB-coded speech signal is protected by a recursive systematic convolutional (RSC) code and transmitted using a noncoherently detected multiple-input-multiple-output (MIMO) differential space-time spreading (DSTS) scheme. To further enhance the attainable system performance and to maximize the coding advantage of the proposed transmission scheme, the system is also combined with multidimensional sphere-packing (SP) modulation. Furthermore, the convergence behavior of the proposed scheme is evaluated with the aid of extrinsic information transfer (EXIT) charts. The proposed system exhibits an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Eb</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> gain of about 1 dB, as compared with the benchmark scheme carrying out joint channel decoding and DSTS-aided SP demodulation in conjunction with separate AMR-WB decoding, when using only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">system</sub> = 2 system iterations and when communicating over narrow-band correlated Rayleigh fading channels.

Message-passing iterative decoding between detector and RSC code decoder for PMR channel

For higher density perpendicular magnetic recording (PMR) systems, it is difficult to expect an improvement in performance when only partial response maximum likelihood (PRML) or noise predictive maximum likelihood (NPML) detection is used. Hence, we consider a system that performs better than either PRML or NPML. We concatenate a channel detector using a recursive systematic convolutional (RSC) code decoder and a message-passing algorithm. The RSC code itself is simple but its performance is inferior to other iterative decoding methods. Therefore, we used channel iteration between the channel detector and the RSC decoder in order to improve performance. We also used a precoding and random interleaver. We evaluated the performance on the PMR channel with jitter noise.

Turbo Detection of Precoded Sphere Packing Modulation Using Four Transmit Antennas for Differential Space-Time Spreading

This paper presents a novel turbo-detected multidimensional sphere packing (SP) modulation scheme using four transmit antennas combined with differentially encoded space-time spreading (DSTS). The DSTS scheme can be readily combined with PSK, QAM as well as SP modulation schemes. The SP-aided DSTS system advocated has low-complexity encoding and decoding algorithms that require no channel knowledge and it is capable of outperforming the DSTS system dispensing with sphere packing. Further system performance improvements can be attained by serially concatenated convolutional encoding combined with a unity-rate code (URC) referred to as a precoder. Then, at the receiver side, iterative decoding is invoked by exchanging extrinsic information between the precoder's decoder as well as the outer recursive systematic convolutional (RSC) code's decoder. Moreover, the convergence behaviour of the proposed system is evaluated with the aid of extrinsic information transfer (EXIT) charts. Explicitly, the turbo-detected precoded DSTS-SP system performs within 1.6 dB of the achievable multiple-input multiple output (MIMO) capacity. Finally, in contrast to an equivalent 0.5 bit/symbol throughput turbo- detected DSTS-SP scheme using no preceding, the turbo-detected precoded DSTS-SP scheme exhibits no error floor.

Performance analysis of turbo codes in quasi-static fading channels

The performance of turbo codes in quasi- static fading channels both with and without antenna diversity is investigated. In particular, simple analytic techniques that relate the frame error rate of a turbo code to both its average distance spectrum as well as the iterative decoder convergence characteristics are developed. Both by analysis and simulation, the impact of the constituent recursive systematic convolutional ( RSC) codes, the interleaver size and the number of decoding iterations on the performance of turbo codes are also investigated. In particular, it is shown that in systems with limited antenna diversity different constituent RSC codes or interleaver sizes do not affect the performance of turbo codes. In contrast, in systems with significant antenna diversity, particular constituent RSC codes and interleaver sizes have the potential to significantly enhance the performance of turbo codes. These results are attributed to the fact that in single transmit - single receive antenna systems, the performance primarily depends on the decoder convergence characteristics for E-b/N-o values of practical interest. However, in multiple transmit - multiple receive antenna systems, the performance depends on the code characteristics.