July 2024
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11 Reads
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July 2024
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11 Reads
September 2023
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7 Reads
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1 Citation
September 2023
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19 Reads
August 2023
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32 Reads
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4 Citations
IEEE Transactions on Information Theory
This paper studies specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over the Galois extension fields GF with used with QAM signaling. Performance of NB LDPC coded transmission strongly depends on the mapping of nonbinary symbols to signal constellation points. We obtain a random coding bound on the maximum-likelihood decoding error probability for an ensemble of random irregular NB LDPC codes used with QAM signaling for specific symbol-to-signal point mappings. This bound is based on the ensemble average squared Euclidean distance spectra derived for these mappings. The simulation results for the belief-propagation decoding in the coded modulation schemes with the NB quasi-cyclic (QC)-LDPC codes under different mappings are given. Comparisons with the optimized binary QC-LDPC codes in the WiFi and 5G standards, as well as with the new bound, are performed.
June 2023
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11 Reads
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3 Citations
November 2022
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20 Reads
June 2022
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58 Reads
May 2022
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26 Reads
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12 Citations
IEEE Transactions on Communications
We propose a novel approach to optimization of irregular nonbinary (NB) quasi-cyclic (QC)-LDPC codes over small alphabets. In this approach, first, the base parity-check matrices are constructed by a simulated annealing method, and then these matrices are labeled by the field elements while maximizing the so- called generalized girth of the Tanner graph. In order to analyze the performance of the constructed irregular NB LDPC codes, a new ensemble of irregular NB LDPC codes over the extensions of the binary Galois field is introduced. A finite-length random coding bound on the error probability of the maximum-likelihood (ML) decoding over the binary phase shift keying (BPSK) input AWGN channel for the new code ensemble is derived. The frame error rate (FER) performance of the sum-product belief-propagation (BP) decoding of the constructed NB QC-LDPC block codes is compared to that of both the optimized binary QC-LDPC block codes in the 5G standard and the best known NB QC-LDPC codes as well as to the derived random coding bound on the ML decoding error probability. It is shown that the obtained bound predicts the behavior of BP decoding performance of practical NB QC-LDPC codes more accurately than the BP decoding thresholds do.
October 2021
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8 Reads
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2 Citations
August 2021
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17 Reads
The goal of the paper is to study specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over extensions of the Galois field GF with used with QAM signaling. Performance of NB QC LDPC coded transmission strongly depends on mapping of nonbinary symbols to signal constellation points. We obtain a random coding bound on the maximum-likelihood decoding error probability for an ensemble of random irregular NB LDPC codes used with QAM signaling for specific symbol-to-signal point mappings. This bound is based on the ensemble average Euclidean distance spectra derived for these mappings. The simulation results for the belief-propagation decoding in the coded modulation schemes with the NB quasi-cyclic (QC)-LDPC codes under different mappings are given. Comparisons with the optimized binary QC-LDPC codes in the WiFi and 5G standards, as well as with the new bound, are performed.
... QAM symbol error corrections often employ block codes over GF(2 q ) accompanied by a bijective map between the symbols and the elements of Galois field [3,4]. However, the error correction coding and decoding must be changed each time different modulation order of QAM is selected. ...
August 2023
IEEE Transactions on Information Theory
... In this section, a general construction approach of QC-LDPC codes based on base and exponent matrices is first introduced. Compared to the QC-LDPC codes generated by the finite field construction [33], the QC-LDPC codes constructed by this approach have a more flexible code length and code rate and are easier to obtain the full-rank matrix. Then, jointly optimized construction of QC-LDPC from the view of the destination is proposed. ...
May 2022
IEEE Transactions on Communications
... The set of vertices (12) corresponds to all possible positions of ones when we fix 0 = 0. if we consider a cyclic shift or a mirror image of the true key, which satisfies 0 = 0, and represent it by the same symbol 0 , ( 0 ) is a subset of ( 0 ) by definition. Moreover, a distance between any two elements in ( 0 ) is in the distance spectrum, i.e., ( , ) ∈ ( 0 ), ∀ , ∈ ( 0 ). ...
July 2021
... Due to the growing percentage of people using these technologies, methods are needed to increase the transmission rate without reducing the quality [4] [5]. One of these methods is the Reed-Solomon (RS) and BCH codes which are used to correct errors in many systems such as Vehicular Networks, storage devices (CD, DVD, etc.) and digital video broadcasting (DVB) [6][7] [8]. An RS code word is a packet of symbols which are commonly bytes (8bit symbols), denotes as RS (n, k) where n is the number of the symbols in the encoded message and k is the number of the symbols in the original message as shown in Fig.1. ...
October 2019
Future Internet
... Sending certain messages to a legitimate receiver, and observing receiver's reactions, an adversary can statistically obtain the distance spectrum. The effectiveness of this part depends on the decoding algorithm, and it has been demonstrated that the bit-flipping (BF) decoding [7], [9]- [14], which is commonly used to decode the QC-MDPC scheme, is vulnerable to this [15]: If the legitimate receiver uses the BF decoding, the attacker can easily obtain the distance spectrum. The second part is to reconstruct the secret key from a given distance spectrum. ...
July 2019
... When the transmission fails, the header can not be decoded by the decompressor. Commonly adopted channel models include Gilbert-Elliot model [14], [16] and hidden Markov model [17]. ...
July 2019
... where x represents the original data being transmitted. Here, p denotes the packet loss rate, which reflects the probability that a data packet is completely lost during transmission due to factors such as limited bandwidth or interference among vehicles [45]. The variable η ∼ N (0, 1) represents the noise, introducing random errors that can lead to incorrect interpretations of traffic conditions [46]. ...
July 2019
IEEE Transactions on Vehicular Technology
... Two low-complexity sliding-window (SW)-decoding procedures are studied. The first one is based on ML-decoding applied to the ZT convolutional code inside the window and the second implies conventional BP decoding and BP decoding with using redundant parity-check (RPC) matrix of the same code [26,27]. As explained below, RPC matrix contains linear dependent rows which destroy stopping sets of the code and improve erasure correcting capability compared to BP decoding while preserving low decoding complexity. ...
April 2018
IEEE Transactions on Information Theory
... i , and (2) i be the probabilities that symbol i will be converted into a Case-0 (an encoded symbol that is generated only by black symbols), Case-1, or Case-2 symbol, respectively, in time period [t 0 , t 1 ]. Thus, we have ...
September 2017
IEEE Transactions on Communications
... Finite length upper bounds on error probability of ML decoding over the AWGN channel obtained by using precise average weight enumerators for both binary random regular LDPC codes and for random regular NB LDPC codes over GF(2 m ) along with the asymptotic ML decoding thresholds were derived in [17]. In this paper by using technique in [18] for computing precise average spectra for ensembles of LDPC codes, we derive a tighter bound on error probability of the ML decoding for the ensemble of 'almost regular" NB LDPC codes over GF (2 m ). ...
June 2017