Outer Code Research Articles

Fault-Tolerant Quantum Computation by Hybrid Qubits with Bosonic Cat Code and Single Photons

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing. Published by the American Physical Society 2024

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

Code Mixing in the Lyrics of the Song “You Never Know” by Blackpink

This research was a study of language code mixing contained in the lyrics of a song titled “You Never Know” by Blackpink. This study aimed to identify the forms of code mixing contained in the lyrics of the song you never know by black pink, identify the types of code mixing used in the song lyrics, and describe the source language of the code mixing contained in the lyrics of the song. The method used in this study was content analysis, which was a qualitatively oriented technique, usually used to determine the character of documents or to compare them. The conclusion obtained from this study was the forms of code mixing contained in the lyrics of the song You Never Know by Blackpink consisting of inserting words, phrases and clauses. Code mixing in the form of words totaling 8 data, phrases totaling 20 data and clauses totaling 10 data. The type of code mixing used in the lyrics of the song you never know by Blackpink was alternation code mixing. The outer code mixing used was 8 data. The source language contained in the lyrics of the song You Never Know by Blackpink came from English and Korean. The code-mixed from English language was 26 data and Korean was 44 data. Through this research, it can be suggested that further researchers can be developed with the theory of code switching which is closely related to code switching.

Analisis Penggunaan Campur Kode Indonesia-Inggris pada Video Iklan Produk Kecantikan Lokal

This research aims to describe and explain the types and forms of Indonesian-English code mixing used in advertising videos. This study used descriptive qualitative method. The data used in this research are advertising videos on YouTube, especially advertising videos for local beauty products such as Make Over, Avoskin, Emina, Azarine, and Wardah. By watching videos advertising local beauty products on YouTube, researchers then analyzed the types and forms of code mixing used in advertisements. The research results show that the type of code mixing used in advertising videos for local beauty products is Outer Code Mixing. Of the total of 15 advertising videos that we analyzed, there were 50 uses of Indonesian-English code mixing. The forms of code mixing used are Intra sentential code mixing, Intra-lexical code mixing, and Involving a change of pronunciation.

An LDPC-RS Concatenation and Decoding Scheme to Lower the Error Floor for FTN Signaling

Faster-than-Nyquist (FTN) signaling has attracted increasing interest in the past two decades. However, when the fifth-generation (5G) communication low-density parity check (LDPC) code is applied to FTN signaling with low Bahl–Cock–Jelinek–Raviv (BCJR) states of detection and few turbo equalization iterations, an error floor near 10−5 is found, which does not exist in the original LDPC used for orthogonal signaling. This can be eliminated through many detection and decoding iterations, but this is unacceptable considering the increase in latency and storage. To solve this problem, we propose an LDPC and Reed–Solomon (RS) concatenation code, shortening, and perturbation scheme to lower the error floor. We propose a parallel encoder architecture for RS component code and a concise algorithm to calculate its constant multiplier coefficients, leveraging a traditional serial encoder, which can also be used for other parallelisms, rates, and lengths. The simulation results show that the proposed concatenation and shortening scheme can lower the error floor to about 10−7. The proposed scheme has an error correction capability for coded FTN signaling and successfully lowers the error floor with the limitation of few turbo iterations and few BCJR states.

FLoRa+: Energy-efficient, Reliable, Beamforming-assisted, and Secure Over-the-air Firmware Update in LoRa Networks

The widespread deployment of unattended LoRa networks poses a growing need to perform Firmware Updates Over-The-Air (FUOTA). However, the FUOTA specifications dedicated by LoRa Alliance fall short of several deficiencies with respect to energy efficiency, transmission reliability, multicast fairness, and security. This article proposes FLoRa+ , energy-efficient, reliable, beamforming-assisted, and secure FUOTA for LoRa networks, which is featured with several techniques, including delta scripting, channel coding, beamforming, and securing mechanisms. Specifically, we first propose a joint differencing and compression algorithm to generate the delta script for processing gain, which unlocks the potential of incremental FUOTA in LoRa networks. Then, we design a concatenated channel coding scheme with outer rateless code and inner error detection to enable reliable transmission for coding gain. Afterward, we develop a beamforming strategy to avoid biased multicast and compromised throughput for power gain. Finally, we present a securing mechanism incorporating progressive hash chain and packet arrival time pattern verification to countermeasure firmware integrity and availability attacks for security gain. Experimental results on a 20-node testbed demonstrate that FLoRa+ improves transmission reliability and energy efficiency by up to 1.51× and 2.65× compared with LoRaWAN. Additionally, FLoRa+ can defend against 100% and 85.4% of spoofing and Denial-of-Service (DoS) attacks.

DESIGN OF SPACE TIME TRELLIS CODED OFDM

Space Time Trellis Code (STTC) is a technique that can be used to improve the performance ofthe Orthogonal Frequency Division Multiplexing (OFDM) system over wireless channels byproviding both coding gain and diversity gain. STTC is combined from two codes, Trellis CodeModulation (TCM) as an inner code and Space Time Block Code (STBC) as an outer code. TCMwhich combines the choice of a modulation scheme with that of a convolutional code provides thecoding gain, and the other code provides the diversity gain. Simulation is done over flat fading andfrequency selective Rayleigh fading channel for Eight Phase Shift Keying (8-PSK) TCM. It foundthat the best results are obtained for the case of two transmitters and three receivers which have again of about 18dB over that without STBC.

Method for changing the redundancy of sequential concatenated code

During the operation of information transmission systems errors occur in the transmitted data due to the influence of various negative factors. To correct errors the codes are currently used that can withstand both single and multiple errors. From the point of view of the ability to correct multiple errors, concatenated codes are highly efficient. When constructing a sequential concatenated code, coding is carried out first by the external, then by the internal code. A significant disadvantage of such coding is a significant increase in redundancy. It is proposed to regulate redundancy by encoding with the internal code only a certain part of the bits from the output of the external code encoder. The study showed the effectiveness of this method, which made it possible to change the parameters of the cascade code within a wide range. A method was proposed and tested to increase the corrective ability of selective coding by multiplying symbols decoded by an external code by coefficients that are different for symbols that have and have not been encoded by an internal code. Decoding of the external code was carried out according to the Viterbi algorithm. The performance of the proposed method has been confirmed experimentally.

Error-correcting codes for fermionic quantum simulation

Utilizing the framework of \mathbb{Z}_2ℤ2 lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any \lfloor \frac{d-1}{2} \rfloor⌊d−12⌋-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation

Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits for each logical qubit. A more recent protocol using quantum analogues of low-density parity-check codes needs only a constant space overhead that does not grow with the number of logical qubits. However, the overhead in the processing time required to implement this protocol grows polynomially with the number of computational steps. To address these problems, here we introduce an alternative approach to constant-space-overhead fault-tolerant quantum computing using a concatenation of multiple small-size quantum codes rather than a single large-size quantum low-density parity-check code. We develop techniques for concatenating different quantum Hamming codes with growing size. As a result, we construct a low-overhead protocol to achieve constant space overhead and only quasi-polylogarithmic time overhead simultaneously. Our protocol is fault tolerant even if a decoder has a non-constant runtime, unlike the existing constant-space-overhead protocol. This code concatenation approach will make possible a large class of quantum speedups with feasibly bounded space overhead yet negligibly short time overhead.

Representasi Pesan Moral Dalam Film Imperfect The Series

Discussions about films as a tool to convey messages are indispensable in public entertainment. With the development of the film world, Web series has recently become the talk of the community. One of the most popular is the series "Imperfect The Series" directed by Naya Anindita with a comedy-drama genre. The storyline is about boarding children with different personalities, regional origins and their purpose in boarding houses. Imperfect the Series. The semiotic theory of Roland Barthes is used by the author for research and the use of a qualitative descriptive approach is shown by dialogue, the behavior of the characters in one of the scenes. Based on the results of research and data analysis, it is obtained that there are two types of code mixing contained in the dialogue between characters. in the film Imperfect the series, namely the inner code mixing and outer code mixing. Friendship occurs because of the support of trust, acceptance and intimacy with each other. Acceptance is caused by good communication. Communication interpersonal is also an exchange namely the act of conveying and receiving messages reciprocally. The foundation of trust includes respecting each other and accepting differences. It is hoped that this research can serve as a reference for similar research in the future.

Resource-efficient fault-tolerant one-way quantum repeater with code concatenation

One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

Secure RoF system based on key nested polar code and feedback neural network.

With the development of 6 G network, the issue of information security is becoming more and more significant. In this paper, a secure RoF system based on key nested polar code and feedback neural network (FNN) is proposed. For the nested polar code, the original key is randomly selected from the constructed codebook and the index of key is encoded by inner polar code which is placed at the location with better channel quality bit of the frozen bit of outer polar code, for the other part of outer polar code, information bits are encrypted by chaotic sequence generated by 4-D cellular neural network. The polar coded sequence is mapped to the 16-QAM symbol for orthogonal frequency division multiplexing (OFDM) and then the OFDM signal is modulated to the optical pulse, which is delivered to users through 50 km standard single-mode fiber and 5 m wireless channel. In the receiver, successive cancellation list (SCL) decoder is used for decoding outer polar code and FNN is used for decoding inner polar code to reduce the latency. The experimental results show that, compared with the existing scheme, when the bit err rate is 10-3, the received optical power (ROP) gain of the proposed scheme with SCL2 decoder and SCL4 decoder is ∼1.2 dB and ∼1.6 dB, respectively. And compared with the traditional OFDM signal with polar code, when the bit err rate is 10-3, the ROP gain of the proposed scheme with SCL4 decoder is ∼1 dB. What's more, the randomness of the chaotic key sequence, the ability to resist brute-force attacks and the ability to resist chosen-plaintext attacks are elaborated. Therefore, the proposed scheme can greatly improve the security of the system while ensuring the correct transmission of information.

New Structure of Channel Coding: Serial Concatenation of Polar Codes

In this paper, we introduce a new coding and decoding structure for enhancing the reliability and performance of polar codes, specifically at low error rates. We achieve this by concatenating two polar codes in series to create robust error-correcting codes. The primary objective here is to optimize the behavior of individual elementary codes within polar codes. In this structure, we incorporate interleaving, a technique that rearranges bits to maximize the separation between originally neighboring symbols. This rearrangement is instrumental in converting error clusters into distributed errors across the entire sequence. To evaluate their performance, we proposed to model a communication system with seven components: an information source, a channel encoder, a modulator, a channel, a demodulator, a channel decoder, and a destination. This work focuses on evaluating the bit error rate (BER) of codes for different block lengths and code rates. Next, we compare the bit error rate (BER) performance between our proposed method and polar codes.

A Decoder for a Lightweight McEliece Cryptosystem Based on Concatenated Codes

Large-scale quantum computers threaten the security of today's public-key cryptography. The McEliece cryptosystem is one of the most promising candidates for post-quantum cryptography. However, the McEliece system has the drawback of large key sizes for the public key. Similar to other public-key cryptosystems, the McEliece system has a comparably high computational complexity. Embedded devices often lack the required computational resources to compute those systems with sufficiently low latency. Hence, those systems require hardware acceleration. Lately, a generalized concatenated code construction was proposed together with a restrictive channel model, which allows for much smaller public keys for comparable security levels. In this work, we propose a hardware decoder suitable for a McEliece system based on these generalized concatenated codes. The results show that those systems are suitable for resource-constrained embedded devices.

Concatenated Forward Error Correction With KP4 and Single Parity Check Codes

Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation.

Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ1 and the engineered dissipation rate κ2. Under a practical noise ratio κ1/κ2 = 10−3, the repetition-SC scheme can reach a 10−15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

CRC-Aided Sparse Regression Codes for Unsourced Random Access

This letter considers a coding scheme for unsourced random access (URA) based on sparse regression codes (SPARCs). In particular, an efficient concatenated coding scheme is proposed, which concatenates SPARCs and cyclic redundancy check-based block Markov superposition transmission (CRC-BMST) codes. A hybrid decoder consisting of a successive cancellation algorithm and a simplified approximated message passing (AMP) algorithm is presented for inner SPARCs, and an improved tree decoder is proposed for outer CRC-BMST codes by introducing a pruning technique. Simulation results show the proposed coding scheme outperforms the coded compressed sensing (CCS) scheme with lower computational complexity.

Iterative List Patterned Reed-Muller Projection Detection-Based Packetized Unsourced Massive Random Access.

In this paper, we consider a slot-controlled coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. Due to the limitations of the geometry-based decoding algorithm in single-sequence settings and due to the message interference that may result in decreased decoding performance under multi-sequence circumstances, a list PRM projection algorithm and an iterative list PRM projection algorithm are proposed to supplant the signal detector associated with the inner PRM sequences in this paper. In detail, we first propose an enhanced path-saving algorithm, called list PRM projection detection, for use in single-user scenarios that maintains multiple candidates during the first few layers so as to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for use in multi-user scenarios. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verify that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ iterative list detection in two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.

A Block-Based Concatenated LDPC-RS Code for UAV-to-Ground SC-FDE Communication Systems

To enhance the reliability of UAV-to-Ground data transmission in SC-FDE, this study proposes a combined MMSE equalization and LDPC-RS concatenated code approach, utilizing source redundancy to mitigate errors in low-elevation G2A communication. The proposed coding scheme combines a binary LDPC code as the outer code and an improved RS code as the inner code, resulting in improved resistance to burst and random errors. To address the coding aspect, this paper designs a coding table using RS coding as the underlying logic, enabling efficient coding. For decoding, a decoding scheme based on the minimum Euclidean distance criterion is devised, enabling high-performance decoding. Simulation results demonstrate that the proposed LDPC-RS concatenated coding scheme significantly enhances the performance of the communication system, thereby offering considerable potential for application in UAV video transmission systems.