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Raditya Weda Bomantara - One of the best experts on this subject based on the ideXlab platform.
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quantum Repetition Codes as building blocks of large period discrete time crystals
Physical Review B, 2021Co-Authors: Raditya Weda BomantaraAbstract:Discrete time crystals (DTCs) are exotic many-body phases of matter in which some observables exhibit robust subharmonic response to periodic driving. By highlighting the connection between DTCs and a quantum error correction model, we devise a general and realistic scheme for building DTCs exhibiting large period observable dynamics. This is accomplished by utilizing a series of Ising spin-1/2 chains, each of which simulates a quantum Repetition Code at the hardware level, and devising a time-periodic Hamiltonian which simulates the fault-tolerant implementation of appropriate logical quantum gates.
Joseph M Kahn - One of the best experts on this subject based on the ideXlab platform.
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rate adaptive modulation and coding for optical fiber transmission systems
Journal of Lightwave Technology, 2012Co-Authors: Joseph M KahnAbstract:We propose a rate-adaptive optical transmission scheme using variable-rate forward error correction (FEC) Codes and variable-size constellations at a fixed symbol rate, quantifying how achievable bit rates vary with distance. The scheme uses serially concatenated Reed-Solomon Codes and an inner Repetition Code to vary the Code rate, combined with single-carrier polarization-multiplexed -ary quadrature amplitude modulation with variable and digital coherent detection. Employing , the scheme achieves a maximum bit rate of 200 Gb/s in a nominal 50-GHz channel bandwidth. A rate adaptation algorithm uses the signal-to-noise ratio (SNR) or the FEC deCoder input bit-error ratio (BER) estimated by a receiver to determine the FEC Code rate and constellation size that maximizes the information bit rate while yielding a target FEC deCoder output BER and a specified SNR margin. We simulate single-channel transmission through long-haul fiber systems with or without inline chromatic dispersion compensation, incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, we achieve bit rates of 200/100/50 Gb/s over distances of 640/2080/3040 km and 1120/3760/5440 km in dispersion-compensated and dispersion-uncompensated systems, respectively. Compared to an ideal coding scheme, the proposed scheme exhibits a performance gap ranging from about 6.4 dB at 640 km to 7.6 dB at 5040 km in compensated systems, and from about 6.6 dB at 1120 km to 7.5 dB at 7600 km in uncompensated systems. We present limited simulations of three-channel transmission, showing that interchannel nonlinearities decrease achievable distances by about 10% and 7% for dispersion-compensated and dispersion-uncompensated systems, respectively.
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rate adaptive coding for optical fiber transmission systems
Journal of Lightwave Technology, 2011Co-Authors: Lauren Klak, Joseph M KahnAbstract:We propose a rate-adaptive transmission scheme using variable-rate forward error correction (FEC) Codes with a fixed signal constellation and a fixed symbol rate, quantifying how achievable bit rates vary with distance in a long-haul fiber system. The FEC scheme uses serially concatenated Reed-Solomon (RS) Codes with hard-decision decoding, using shortening and puncturing to vary the Code rate. An inner Repetition Code with soft combining provides further rate variation. While suboptimal, Repetition coding allows operation at very low signal-to-noise ratio (SNR) with minimal increase in complexity. A rate adaptation algorithm uses the SNR or the FEC deCoder input bit-error ratio (BER) estimated by a receiver to determine the combination of RS-RS and Repetition Codes that maximizes the information bit rate while satisfying a target FEC deCoder output BER and providing a specified SNR margin. This FEC scheme is combined here with single-carrier polarization-multiplexed quadrature phase-shift keying (PM-QPSK) and digital coherent detection, achieving 100-Gbit/s peak information bit rate in a nominal 50-GHz channel bandwidth. We simulate variable-rate single-channel transmission through a long-haul system incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, achievable information bit rates vary from 100 Gbit/s at 2000 km, to about 60 Gbit/s at 3000 km, to about 35 Gbit/s at 4000 km. Compared to an ideal coding scheme achieving information-theoretic limits on an AWGN channel, the proposed coding scheme exhibits a performance gap ranging from about 5.9 dB at 2000 km to about 7.5 dB at 5000 km. Much of the increase in the gap arises from the inefficiency of the Repetition coding used beyond 3280 km. Rate-adaptive transmission can extend reach when regeneration sites are not available, helping networks adapt to changing traffic demands. It is likely to become more important with the continued evolution toward optically switched mesh networks, which make signal quality more variable.
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rate adaptive modulation and coding for optical fiber transmission systems
Proceedings of SPIE the International Society for Optical Engineering, 2010Co-Authors: Joseph M KahnAbstract:Rate-adaptive optical transmission techniques adjust information bit rate based on transmission distance and other factors affecting signal quality. These techniques enable increased bit rates over shorter links, while enabling transmission over longer links when regeneration is not available. They are likely to become more important with increasing network traffic and a continuing evolution toward optically switched mesh networks, which make signal quality more variable. We propose a rate-adaptive scheme using variable-rate forward error correction (FEC) Codes and variable constellations with a fixed symbol rate, quantifying how achievable bit rates vary with distance. The scheme uses serially concatenated Reed-Solomon Codes and an inner Repetition Code to vary the Code rate, combined with single-carrier polarization-multiplexed M-ary quadrature amplitude modulation (PM-M-QAM) with variable M and digital coherent detection. A rate adaptation algorithm uses the signal-to-noise ratio (SNR) or the FEC deCoder input bit-error ratio (BER) estimated by a receiver to determine the FEC Code rate and constellation size that maximizes the information bit rate while satisfying a target FEC deCoder output BER and an SNR margin, yielding a peak rate of 200 Gbit/s in a nominal 50-GHz channel bandwidth. We simulate single-channel transmission through a long-haul fiber system incorporating numerous optical switches, evaluating the impact of fiber nonlinearity and bandwidth narrowing. With zero SNR margin, we achieve bit rates of 200/100/50 Gbit/s over distances of 650/2000/3000 km. Compared to an ideal coding scheme, the proposed scheme exhibits a performance gap ranging from about 6.4 dB at 650 km to 7.5 dB at 5000 km.
Samuel Zbarsky - One of the best experts on this subject based on the ideXlab platform.
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efficient low redundancy Codes for correcting multiple deletions
IEEE Transactions on Information Theory, 2018Co-Authors: Joshua Brakensiek, Venkatesan Guruswami, Samuel ZbarskyAbstract:We consider the problem of constructing binary Codes to recover from $k$ –bit deletions with efficient encoding/decoding, for a fixed $k$ . The single deletion case is well understood, with the Varshamov–Tenengolts–Levenshtein Code from 1965 giving an asymptotically optimal construction with $\approx ~2^{n}/n$ Codewords of length $n$ , i.e., at most $\log n$ bits of redundancy. However, even for the case of two deletions, there was no known explicit construction with redundancy less than $n^{\Omega (1)}$ . For any fixed $k$ , we construct a binary Code with $c_{k} \log n$ redundancy that can be deCoded from $k$ deletions in $O_{k}(n \log ^{4} n)$ time. The coefficient $c_{k}$ can be taken to be $O(k^{2} \log k)$ , which is only quadratically worse than the optimal, non-constructive bound of $O(k)$ . We also indicate how to modify this Code to allow for a combination of up to $k$ insertions and deletions. We also note that among linear Codes capable of correcting $k$ deletions, the $(k+1)$ -fold Repetition Code is essentially the best possible.
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efficient low redundancy Codes for correcting multiple deletions
Symposium on Discrete Algorithms, 2016Co-Authors: Joshua Brakensiek, Venkatesan Guruswami, Samuel ZbarskyAbstract:We consider the problem of constructing binary Codes to recover from k-bit deletions with efficient encoding/decoding, for a fixed k. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein Code from 1965 giving an asymptotically optimal construction with a 2n/n Codewords of length n, i.e., at most log n bits of redundancy. However, even for the case of two deletions, there was no known explicit construction with redundancy less than nΩ(1). For any fixed k, we construct a binary Code with ck log n redundancy that can be deCoded from k deletions in Ok(nlog4 n) time. The coefficient ck can be taken to be O(k2 log k), which is only quadratically worse than the optimal, non-constructive bound of O(k). We also indicate how to modify this Code to allow for a combination of up to k insertions and deletions. We also note that among linear Codes capable of correcting k deletions, the (k + 1)-fold Repetition Code is essentially the best possible.
Osvaldo Simeone - One of the best experts on this subject based on the ideXlab platform.
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improved latency communication trade off for map shuffle reduce systems with stragglers
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Jingjing Zhang, Osvaldo SimeoneAbstract:In a distributed computing system operating according to the map-shuffle-reduce framework, coding data prior to storage can be useful both to reduce the latency caused by straggling servers and to decrease the inter-server communication load in the shuffle phase. In prior work, a concatenated coding scheme was proposed for a matrix multiplication task. In this scheme, the outer Maximum Distance Separable (MDS) Code is leveraged to correct erasures caused by stragglers, while the inner Repetition Code is used to improve the communication efficiency in the shuffle phase by means of Coded multi-casting. In this work, it is demonstrated that it is possible to leverage the redundancy created by Repetition coding in order to increase the rate of the outer MDS Code and hence to increase the multicasting opportunities in the shuffle phase. As a result, the proposed approach is shown to improve over the best known latency-communication overhead trade-off.
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improved latency communication trade off for map shuffle reduce systems with stragglers
arXiv: Information Theory, 2018Co-Authors: Jingjing Zhang, Osvaldo SimeoneAbstract:In a distributed computing system operating according to the map-shuffle-reduce framework, coding data prior to storage can be useful both to reduce the latency caused by straggling servers and to decrease the inter-server communication load in the shuffling phase. In prior work, a concatenated coding scheme was proposed for a matrix multiplication task. In this scheme, the outer Maximum Distance Separable (MDS) Code is leveraged to correct erasures caused by stragglers, while the inner Repetition Code is used to improve the communication efficiency in the shuffling phase by means of Coded multicasting. In this work, it is demonstrated that it is possible to leverage the redundancy created by Repetition coding in order to increase the rate of the outer MDS Code and hence to increase the multicasting opportunities in the shuffling phase. As a result, the proposed approach is shown to improve over the best known latency-communication overhead trade-off.
Tomoaki Ohtsuki - One of the best experts on this subject based on the ideXlab platform.
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rate adaptive indoor infrared wireless communication systems using repeated and punctured convolutional Codes
IEEE Communications Letters, 2000Co-Authors: Tomoaki OhtsukiAbstract:We propose a rate-adaptive transmission scheme using repeated and punctured convolutional Codes for indoor infrared wireless communications. The proposed system uses a coding scheme consisting of an outer punctured convolutional Code and an inner Repetition Code, and varies Code rate, i.e., bit rate adaptively depending on channel conditions. We show that the proposed system can realize communications in worse channel conditions at the expense of bit rate, while maximizing the throughput available to a user on his position.
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Rate adaptive indoor infrared wireless communication systems using repeated and punctured convolutional Codes
1999 IEEE International Conference on Communications (Cat. No. 99CH36311), 1999Co-Authors: Tomoaki OhtsukiAbstract:We propose a rate adaptive transmission scheme using repeated and punctured convolutional Codes for indoor infrared wireless communications. The proposed system uses a coding scheme consisting of an outer punctured convolutional Code and an inner Repetition Code of length RR used for each punctured convolutional Code symbol, and varies the Code rate of the punctured convolutional Codes and the rate reduction factor of the Repetition Codes, that is, the bit rate varies adaptively depending on the channel conditions. We analyze the performance and show that the proposed system can realize communications in worse channel conditions at the expense of the bit rate, while maximizing the throughput available to a user on his position.