Sergio Benedetto, Roberto Garello, G. Montorsi · 2002
Systematic recursive convolutional encoders have been shown to play a crucial role in the design and implementation of parallel concatenated codes ("turbo codes"). We present here a canonical structure of minimal linear systematic rate k/n encoders and use it in the search for good constituent codes of parallel concatenated codes. Tables of the best encoders for various rates are also presented.
Cited by 2
Ravi Sivasankaran, Stephen McLaughlin · IEEE Transactions on Communications · 2001
We present a method for soft-in/soft-out sequential decoding of recursive systematic convolutional codes. The proposed decoder, the twin-stack decoder, is an extension of the well-known ZJ stack decoder, and it uses two stacks. The use of the two stacks lends itself to the generation of soft outputs, and the decoder is easily incorporated into the iterative "turbo" configuration. Under thresholded decoding, it is observed that the decoder is capable of achieving near-maximum a posteriori bit-error rate performance at moderate to high signal-to-noise ratios (SNRs). Also, in the iterative (turbo) configuration, at moderate SNRs (above 2.0 dB), the performance of the proposed decoder is within 1.5 dB of the BCJR algorithm for a 16-state, R=1/3, recursive code, but this difference narrows progressively at higher SNRs. The complexity of the decoder asymptotically decreases (with SNR) as 1/(number of states), providing a good tradeoff between computational burden and performance. The proposed decoder is also within 1.0 dB of other well-known suboptimal soft-out decoding techniques.
Cited by 9
A. N. Khmelkov · Telecommunications and Radio Engineering · 2010
An analysis expression for computation of a syndrome sequence of a systematic recursive convolutional code has been produced. A method for decomposition of localized syndromes for determining distorted elements in a code sequence of a turbo code, which makes it possible to develop an approach to synthesis of optimal syndrome decoders both with a "hard" and "soft" solution of turbo codes with component systematic recursive convolutional codes, has been proposed.
Cited by 0
Punya Thitimajshima · 2002
This paper deals with a new class of convolutional codes called recursive systematic convolutional (RSC) codes. These codes are very attractive when compared with the best known convolutional codes at low signal to noise ratio (SNR) and high code rate. A comparison with the best known convolutional codes is performed in terms of weight spectrum and bit error rate (BER) on a memoryless Gaussian channel. A new design of parallel concatenation is proposed, well matched to RSC codes and much more attractive than serial concatenation for it needs only one clock timing recovery for the decoding.
Cited by 7
Ravi Sivasankaran · UPT. Syiah Kuala University Library (Syiah Kuala University) · 2000
Cited by 0Open access
Fabio Fagnani, Sandro Zampieri · Linear Algebra and its Applications · 2003
Cited by 13
Reed,I S · Defense Technical Information Center (DTIC) · 1984
In this report, pruned error-trellis decoding of systematic and nonsystematic convolutional codes with a delay-free inverse has been developed in detail, including quantitative formulas for the number of states and transitions which remain in the pruned error trellis. Currently, the problem of trellis pruning of other non-systematic CCs is being investigated. Finally, the reduced hardware requirements for pruned error-trellis decoding versus standard Viterbi decoding is being studied, and a preliminary architecture has already been found for the dual-K decoding algorithm developed in this report. (Author)
Cited by 0
Patenaude François, Wang Sichun · SHILAP Revista de lepidopterología · 2006
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Kwame Ackah Bohulu, Chenggao Han · 2022
In this paper, we present a systematic method to determine not only the multiplicity, but also detailed patterns of low-weight parity-check components and systematic components with Hamming weight up to 4 for a rate r = 1=2 recursive systematic convolutional code, simply by referring to its generator function. The detailed patterns of the low-weight codewords are then established by identifying those with low-weight parity-check components or systematic components. This method is also applied to non-recursive systematic convolutional codes by tweaking the generator function of the recursive systematic convolutional code. The union bound is obtained by comparing it to those obtained from the transfer function and the bit error rate curve obtained from simulation results. The comparison is solely for validating the proposed method and no significant counting loss is detected. Possible applications of our proposed method to concatenated code design are briefly discussed.
Cited by 0
S.S. Pietrobon, A.S. Barbulescu · 1994
this paper we present a simplified APP algorithm which was successfully tested using the rate half systematic convolutional 16 state Turbo code given in [2], with a 20#20 block interleaver of 400 bits. For an E b /N 0 = 2.0 dB and eight iterations, an output bit error ratio P b # 1.5 # 10
Cited by 54
I.L. Turner · 2003
The Bahl algorithm (1974) is a maximum a posteriori (MAP) decoding method for linear codes which minimizes the bit error probability by estimating the a posteriori probabilities (APP) of the states and transitions of a Markov source observed through a discrete memoryless channel. A modified version of the Bahl algorithm was presented by Berrou, Glavieux and Thitimajshima (1993) for iteratively decoding turbo codes for the additive white Gaussian noise channel. In this paper we consider MAP decoding of turbo codes using the Bahl algorithm for a memoryless Rayleigh fading channel.
Cited by 1
Pavlo M. Kurbet · Cybersecurity Education Science Technique · 2023
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.
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Kwame Ackah Bohulu, Chenggao Han · IEEE Transactions on Information Theory · 2025
In this research paper, we present a novel method for obtaining the patterns of inputs that generate low-weight codewords in Recursive Systematic Convolutional (RSC) codes, hereafter referred to as low-weight inputs. RSC codes are commonly used as component codes for various concatenated schemes, including the popular Turbo codes. Efficient interleaver design is crucial in improving the error-correcting performance of Turbo codes; therefore, understanding the low-weight input patterns specific to the selected RSC code is essential. Existing graph-based search algorithms face increasing complexity as the constraint length of the RSC code increases. To address this issue, we introduce a method that directly derives the critical low-weight input patterns (up to Hamming weight 4) from the generator function of the RSC code. The proposed method addresses the complexity issue and can be extended to non-recursive systematic convolutional (NRSC) codes by modifying the generator function. To validate our novel method, we compare the union bound obtained using our approach to that obtained via the transfer function method and the simulation results for selected RSC codes. This comparison demonstrates the effectiveness of our method, which shows no significant counting losses.
Cited by 0
Hideki Yoshikawa, Yoshitake Kawadai · 2010
In this paper, a theoretical analysis of bit error probability for recursive systematic 4-state convolutional code with Max-Log-maximum a posteriori probability (MAP) decoding is presented. The results show that recursive systematic convolutional codes give better performance than non-systematic convolutional codes for very noisy channel.
Cited by 2
Melinda Melinda · 2011
Convolutional codes are used extensively in numerous applications in order to achieve reliable data transfer. In this paper, the parameters of Convolutional codes are introduced and used to investigate its applications, characteristics and performance when employed as inner and outer code in decoding method. To evaluate the parameters, four schemes of Convolutional codes: non-systematic-recursive, systematic-recursive, non-systematic-non-recursive and systematic-non-recursive; are applied. In addition, the implementation of BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm is discussed by applying APP-SISO (a posteriori probabilities - Soft Input Soft Output) decoding for Convolutional codes. The proposed scheme employing inner and outer decoding of Convolutional codes are analysed and compared by using EXIT characteristic of Convolutional decoders. The channel capacity measurements for different rates inner Convolutional codes are described by using BPSK modulation over AWGN channel. BER performances of outer decoding of Convolutional codes are observed for different schemes which are described the process of area beneath in the inverted EXIT function. This is essential to obtain better performance of BER plot indeed. The result shows that inner decoding of Convolutional codes is the best performance for the EXIT function, particularly for non-systematic-recursive. However, outer decoding of this code has not good performance due to having quite larger area beneath than inner code.
Cited by 1
Е. Г. Макейчик, A. I. Korolev, V. K. Kanapelka · SHILAP Revista de lepidopterología · 2019
The organization methods of dependent (packet) error correction by the turbocodecs based both on a sub systematic convolutional codes with uniform threshold decoding algorithm and recursive systematic convolutional codes are considered. The effectiveness of the proposed methods for data coding by two- and three-components turbocodes is evaluated. It is found that turbocodecs, based on nested uniform and recursive convolutional codes, provide fold a decrease in 1,34 times of the transmitted information redundancy in comparison with the known principle turbocodes construction through recursive convolutional codes.
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Pavlo M. Kurbet · Cybersecurity Education Science Technique · 2024
The article is devoted to increasing the efficiency of wireless information transmission systems with adaptation due to the preparation of initial polynomials of recursive systematic convolutional codes of turbo codes using a genetic algorithm. As an objective function, an indicative number of sign changes of the a priori-posterior information of the turbo code decoder for a certain sample of data bits is proposed. As prior information, the value of channel symbols is used, taking into account the channel “reliability” function, which indicates the level of dispersion of additive white gaussian noise. The logarithm of the ratio of the likelihood functions about the transmitted bit of data is used as posterior information. The analysis of known works shows that when using adaptive systems with coding as an adaptable parameter, the coding speed is used, which is regulated by the number of check symbols from the output of the turbo code encoder, while there are no developments on the adaptation of turbo code polynomials, as well as on the rapid formation of initial polynomials recursive systematic convolutional codes turbo codes. The use of rational polynomials as initial ones during adaptation will allow more effective use of the energy efficiency of wireless data transmission systems. 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 primary polynomials of turbo codes, which were found using a genetic algorithm for a channel with additive white Gaussian noise, are given. We consider the search for initial interleavers between component recursive systematic convolutional codes of turbo codes to be the directi
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Němec, Karel · Brno University of Technology Digital Library (Brno University of Technology) · 2009
Self-orthogonal convolutional codes, which were described in the paper "Convolutional codes for the correction of random errors - 1", represent an easy-to-realize type of convolutional code for the correction of random errors, which makes use of majority decoding. There are also convolutional codes for which a majority decoder can be found without the condition of creating a self-orthogonal code being satisfied. These codes are referred to as "Orthogonizable systematic convolutional codes". The text of the paper includes the description of tree codes of this type.
Cited by 0
Laddomada, Massimiliano, Daneshgaran, F., Mondin, Marina · University of Washington Tacoma Digital Commons (University of Washington Tacoma) · 2004
This paper presents the results of the search for optimum punctured recursive convolutional codes, suitable as outer codes in a serial concatenation of convolutional codes. The mother codes that are punctured are rate 1/2 recursive convolutional codes (RCC) proposed for use in parallel and/or serial concatenation schemes. Extensive tables of optimized systematic and nonsystematic puncturing patterns for various mother codes are presented along with sample simulation results
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Laddomada, Massimiliano, Daneshgaran, F., Mondin, M. · University of Washington Tacoma Digital Commons (University of Washington Tacoma) · 2004
This letter presents the results of the search for optimum punctured recursive convolutional codes (RCCs) of rate k/k+1, for k=2,...,8, suitable for concatenated channel codes whose constituent encoders are recursive, systematic convolutional codes. The mother codes that are punctured are rate-1/2 RCCs proposed for use in parallel and/or serial concatenation schemes. Extensive tables of systematic and nonsystematic puncturing patterns, optimized relative to various objective functions suitable for concatenated channel codes, are presented for several mother codes.
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