Fucheng Guo, Frank Mueller, Yuan Liu · ArXiv.org · 2025
The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors, but when the displacement magnitude becomes large, lattice-crossing events arise beyond the correctable range of the GKP state. To address this issue, we concatenate a Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Unlike conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against both large and small displacement errors, enabling CV error correction within the continuous encoding space and contrasting with earlier approaches that concatenate GKP states with repetition codes for discrete qubit or qudit encodings. Analytical results show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors across all qumodes by up to 50 percent while enabling unbiased correction of lattice-crossing events, with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture continues to provide Gaussian-error suppression together with lattice-crossing correction, and the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides new insight into the design of concatenated CV error-correcting architectures.
Cited by 0Open access
Shin Jihwan, Ho-Kyeong Lee · 2020
We consider a concatenated coding scheme which consists of the tail-biting convolutional code as an inner code and the hamming code as an outer code. They are separated by a block interleaver. The size of the row of the block interleaver is fixed to the length of the codeword of the hamming code. We select the interleaving depth, the size of the column of a block interleaver based on the burst error statistics of the outer convolutional code. We assume that the channel is correlated discrete Rayleigh fading channel which is modeled by using FSMC (Finite-State Markov Chain). Our simulation results show that the BER (Bit Error Rate) performance improvement of the convolutional code with the Hamming code.
Cited by 13
Yufan Wang, Linning Peng, Hua Fu et al. · 2019
Secret key generation from wireless channel is an emerging technique of physical layer security. At present, most of the secret key generation schemes use information reconciliation to obtain symmetric keys. This paper introduces a non-interactive information reconciliation scheme based on channel coding and stream encryption, and considering the error correction capability, we design a concatenated code of BCH and RS codes as channel coding. The performance of concatenated error correction code has been analyzed in this scheme. Then, we compare the concatenated code with first-level error correction code in different test environments. Extensive numerical simulations and experiments demonstrate that the decoding performance of this second-level concatenated code is better than the first-level error correction code, and it can also effectively eliminate third-party eavesdropping.
Cited by 4
University of Bristol 2021, Menicucci, Nicolas, Stafford, Matthew · Underline Science Inc. · 2021
Noise is ubiquitous in any realisation of a quantum computer and must be supressed using Quantum Error Correction (QEC). Recent works have shown that in the presence of biased noise significant improvements can be seen in the capabilities of error correcting codes. For continuous variable systems this bias can be artificially introduced through an appropriate choice of bosonic code. Here we study the code capacity behaviour of a biased GKP qubit concatenated with a simple n-qubit repetition code with the aim of drastically reducing the complexity of the error correction process. Preliminary findings indicate under a Gaussian displacement noise channel this code offers a performance improvement over a bare, square lattice GKP qubit.
Cited by 0Open access
Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze et al. · Signals and communication technology · 2017
Concatenation of good codes is a classic method of constructing longer codes which are good codes. As codes are increased in length it becomes progressively harder to realise a near maximum likelihood decoder. This chapter presents a novel concatenated code arrangement featuring multiple, near maximum likelihood, decoders designed for an optimised matching of codes and decoders. By using some outstanding codes as constituent codes, the concatenated coding and decoding system is able to outperform the best LDPC and Turbo coding systems with the same code parameters. The performance of a net (256,128) code achieved with the concatenated arrangement is compared to a best (256,128) LDPC code and a best (256,128) Turbo code. Similarly, the performance of a (512,256) net concatenated code is compared to a best (512,256) LDPC code and a best (512,256) Turbo code. In both cases, the new system outperformed the LDPC and Turbo systems. To date, for the AWGN channel and net, half rate codes no other codes or coding arrangement is known that will outperform the system presented in this chapter for codes of lengths 256 and 512 bits.
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Junmei Chen, Hao Chen, Zongpeng Li · Computer Networks · 2022
Cited by 1
Yi Cai, Weiming Wang, Weifeng Qian et al. · 2018
With a record 200Gbps 50-piece-FPGA implementation, we investigate performance of a concatenated-staircase-Hamming code proposed for OIF-400GZR. FPGA emulations reveal an error flare at 10−10 BER lowering the predicted BER threshold from 1.25e-2 to 1.21e-2.
Cited by 10
J. Panicker, Surinder Kumar, J.E. Salt · Canadian Journal of Electrical and Computer Engineering · 1994
Error correction coding for a slow frequency-hopped spread spectrum system using concatenated Reed-Solomon and Bose-Chowdary-Hocquenhem codes is analyzed. The system capacity in terms of the maximum number of simultaneous users is found to be similar to that of a system which uses Reed-Solomon error correction code with symbol erasures. However, the normalized throughput is found to be poorer in the concatenated coding case because of the nonavailability of the high-rate Bose-Chowdary-Hocquenhem codes with sufficient error correction capability. A complexity performance trade off is possible using concatenated codes.
Cited by 0
Zengyou Sun, Huanhuan Li · Advances in intelligent systems research/Advances in Intelligent Systems Research · 2014
According to the problem of the data transmission system of IEEE802.11b in the presence of random noise and burst interference which make the receiver error, we use the channel coding scheme of concatenated codes, RS codes and convolution codes concatenated, as a block code and non-block code concatenated coding, the outer code with RS codes, the inner code with convolution codes. And we use MATLAB to simulate the channel error correction performance of the concatenated code in the additive Gauss white noise channel. The results show that in the case of low SNR, RS+convolution concatenated codes can make the system BER down to 10 -5 below(including 10 -5 ), it is a kind of efficient error correcting code, and has high practical value in engineering.
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Tansuwannont, Theerapat, Leung, Debbie · arXiv (Cornell University) · 2020
In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the quantum error correcting code. Fortunately, some errors of different weights are logically equivalent and the same correction procedure is applicable to all equivalent errors, thus correcting high-weight errors is sometimes possible. In this work, we introduce a technique called weight parity error correction (WPEC) which can correct Pauli error of any weight in some stabilizer codes provided that the parity of the weight of the error is known. We show that the technique is applicable to concatenated codes constructed from the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a fault-tolerant error correction protocol using WPEC for the [[49,1,9]] concatenated Steane code which can correct up to 3 faults and requires only 2 ancillas.
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Long Huang, Xiaohua Wu, Tao Zhou · Physical review. A/Physical review, A · 2019
In quantum error correction, the description of the noise channel cannot be completely accurate and fluctuation always appears in the noise channel. It is found that when fluctuation of the physical noise channel is considered, the average effective channel is dependent only on the average of the physical noise channel, and the average of the physical noise channel here plays the role of the independent error model in previous works. Now one may conclude that in the independent error model, the results in previous works are also valid for the average channel where fluctuation exists. In some typical cases, our numerical simulations in the concatenated quantum error-correction protocol with a five-qubit code, seven-qubit Steane code, and nine-qubit Shor confirm this conjecture. For a five-qubit code, the effective channels approximate to the depolarizing channel as the concatenated level increases. For the Steane code, the effective channels approximate to one Pauli channel as the concatenated level increases. For the Shor code, the effective channels approximate to either a Pauli-$X$ or Pauli-$Z$ channel in each level, and in the next concatenated level, the effective channels approximate to the other. The numerical results for these codes indicate that the degree of approximation increases as the concatenated level increases, and the fluctuation of the noise channel decays exponentially as concatenated quantum error correction is performed. On the error-correction threshold, the attenuation ratio of the standard deviation of channel fidelity has a roughly stable value. In contrast, standard deviations of off-diagonal elements of the quantum process matrix (Pauli form) decay more quickly than standard deviations of diagonal elements.
Cited by 5Open access
Y.F.M. Wong, Khaled B. Letaief · IEEE Transactions on Communications · 2000
We investigate the use of forward-error correction (FEC) as well as concatenated coding for reliable data transmission in asynchronous direct-sequence code-division multiple-access communications over frequency-selective Rayleigh fading channels. The FEC scheme combines antenna diversity with low complexity concatenated codes which consist of a Reed-Solomon outer code and a convolutional inner code. Under this concatenated coding scheme, we analyze the average bit-error rate performance and capacity tradeoffs between various system parameters under a fixed total bandwidth expansion and concatenated codes constraint requirements.
Cited by 15
Johann-Philipp Thiers, Jürgen Freudenberger · Cryptography · 2021
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannheim error channel, where the error values are limited to the Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extend to the rate region, where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.
Cited by 9Open access
Ahmadreza Hedayat And, Ahmadreza Hedayat, Aria Nosratinia · 2007
We propose a general class of concatenated errorcorrecting entropy codes and channel codes. In this way we extend and generalize the existing body of work on iterative decoding of entropy and channel codes. Using the structure and properties of serial concatenated codes, we employ error-correcting entropy codes as the outer code, and a convolutional code as the inner code. The generalization from entropy codes to redundant entropy codes allows powerful error correction similar to turbo codes. We provide upper bounds for the concatenated entropy code and channel code. We also show that iterative decoding of the proposed concatenated code outperforms iterative decoding of previously reported entropy and channel codes that operate at the same overall rate.
Cited by 0
C. Pavan Kumar, R. Selvakumar · Procedia Computer Science · 2017
Error correction coding is extensively used to achieve reliability in digital communication especially in Physical Layer. In this paper, construction of concatenated kernel code defined over algebraic structure group is discussed. Minimal trellis representation is given for constructed concatenated kernel codeword. Constructed code is tested in cognitive radio network environment subjected to continuous interference due to the behavior of primary users. Proposed code is tested through simulations and its performance is analyzed in terms of Bit Error Rate (BER) in mitigating the effect of continuous interference. Maximum likelihood graph Viterbi decoding technique is used to decode the concatenated kernel code.
Cited by 3Open access
Min Liang, Li Yang · arXiv (Cornell University) · 2010
Error-correction process has to be carried out periodically to prevent accumulation of errors in fault-tolerant quantum computation. It is believed that the best choice to get maximum threshold value is carrying out an error-correction process after each quantum gate operation. Result of this note shows that the optimal error-correction period depends on the value of k which is the level number of concatenated quantum error-correction code.
Cited by 1Open access
Jos H. Weber, Khaled Abdel-Ghaffar · IEEE Transactions on Information Theory · 2000
We consider a concatenated coding scheme using a single inner code, a single outer code, and a fixed single-trial decoding strategy that maximizes the number of errors guaranteed to be corrected in a concatenated codeword. For this scheme, we investigate whether maximizing the guaranteed error correction rate, i.e., the number of correctable errors per transmitted symbol, necessitates pushing the code rate to zero. We show that this is not always the case for a given inner or outer code. Furthermore, to maximize the guaranteed error correction rate over all inner and outer codes of fixed dimensions and alphabets, the code rate of one (but not both) of these two codes should be pushed to zero.
Cited by 1
Evans, Zachary W. E., Stephens, Ashley M. · arXiv (Cornell University) · 2009
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a concatenated code independently, our method uses information about the likelihood of errors having occurred at lower levels to maximize the probability of correctly interpreting error syndromes. Results of simulations of our method applied to the [[4,1,2]] subsystem code indicate that it can correct a number of discrete errors up to half of the distance of the concatenated code, which is optimal.
Cited by 0Open access
Noah Berthusen, S. Tan, E. Huang et al. · PRX Quantum · 2025
Device error rates on current quantum computers have improved enough to where demonstrations of error correction below break even are now possible. Still, the circuits required for quantum error correction introduce significant overhead and sometimes inject more errors than they correct. In this work, we introduce adaptive syndrome extraction as a scheme to improve code performance and reduce the quantum error-correction cycle time by measuring only the stabilizer generators that are likely to provide useful syndrome information. We provide a concrete example of the scheme through the [[4,2,2]] code concatenated with a hypergraph product code and a syndrome-extraction cycle that uses quantum error detection to modify the syndrome-extraction circuits in real time. Compared to nonconcatenated codes and nonadaptive syndrome extraction, we find that the adaptive scheme achieves over an order of magnitude lower logical error rates while requiring fewer gates and physical qubits. Furthermore, we show how to achieve fault-tolerant universal logical computation with [[4,2,2]]-concatenated hypergraph product codes.
Cited by 2Open access
Kihoon Lee, Hanho Lee · 2010
This paper presents a six-iteration concatenated Bose-Chaudhuri-Hocquenghem (BCH) code and its high-speed two-parallel decoder architecture for 100 Gb/s optical communications. The proposed architecture features a very high data processing rate as well as excellent error correction capability. The proposed six-iteration concatenated BCH code structure with a block interleaving methods allows the decoder to achieve 9.19 dB net coding gain performance at 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> decoder output bit error rate to compensate for serious transmission quality degradation. Also, the proposed high-speed concatenated BCH decoder architecture was implemented to support 100 Gb/s data processing rate. Thus, it has potential applications in next generation forward error correction schemes for 100 Gb/s long-haul optical communications.
Cited by 14