Erasure Information Research Articles

Fault-Tolerant Postselection for Low-Overhead Magic State Preparation

We introduce a framework for fault-tolerant postselection (FTPS) of fault-tolerant codes and channels—such as those based on surface codes—using soft-information metrics based on visible syndrome and erasure information. We introduce several metrics for ranking configurations of syndromes and erasures. In particular, we introduce the (and variants thereof) as a powerful soft-information metric for predicting logical error rates of fault-tolerant channels based on topological error-correcting codes. The logical gap is roughly the unsigned weight difference between inequivalent logical corrections and is adaptable to any tailored noise model or decoder. We deploy this framework to prepare high-quality surface-code magic states with low overhead under a model of independent and identically distributed (IID) Pauli and erasure errors. Postselection strategies based on the logical gap can suppress the encoding error rate (EER) of a magic state preparation channel to the level of the physical error rate with low overhead. For example, when operating at 60% of the bulk threshold of the corresponding surface code, an overall reduction of the EER by a factor of 15 is achievable with a relative overhead factor of <2 (approximately 23 times less than that of simple syndrome-counting rules). We analyze a schematic buffer architecture for implementing postselection rules on magic state factories in the context of magic state distillation. The FTPS framework can be utilized for mitigating errors in more general fault-tolerant logical channels. Published by the American Physical Society 2024

Video Person Re-Identification with Frame Sampling-Random Erasure and Mutual Information-Temporal Weight Aggregation.

Partial occlusion and background clutter in camera video surveillance affect the accuracy of video-based person re-identification (re-ID). To address these problems, we propose a person re-ID method based on random erasure of frame sampling and temporal weight aggregation of mutual information of partial and global features. First, for the case in which the target person is interfered or partially occluded, the frame sampling–random erasure (FSE) method is used for data enhancement to effectively alleviate the occlusion problem, improve the generalization ability of the model, and match persons more accurately. Second, to further improve the re-ID accuracy of video-based persons and learn more discriminative feature representations, we use a ResNet-50 network to extract global and partial features and fuse these features to obtain frame-level features. In the time dimension, based on a mutual information–temporal weight aggregation (MI–TWA) module, the partial features are added according to different weights and the global features are added according to equal weights and connected to output sequence features. The proposed method is extensively experimented on three public video datasets, MARS, DukeMTMC-VideoReID, and PRID-2011; the mean average precision (mAP) values are 82.4%, 94.1%, and 95.3% and Rank-1 values are 86.4%, 94.8%, and 95.2%, respectively.

Optimizing quantum codes with an application to the loss channel with partial erasure information

Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no universal approach to finding new or optimal codes for a certain task and subject to specific experimental constraints. In particular, once found, a QECC is typically used in very diverse contexts, while its resilience against errors is captured in a single figure of merit, the distance of the code. This does not necessarily give rise to the most efficient protection possible given a certain known error or a particular application for which the code is employed.In this paper, we investigate the loss channel, which plays a key role in quantum communication, and in particular in quantum key distribution over long distances. We develop a numerical set of tools that allows to optimize an encoding specifically for recovering lost particles both deterministically and probabilistically, where some knowledge about what was lost is available, and demonstrate its capabilities. This allows us to arrive at new codes ideal for the distribution of entangled states in this particular setting, and also to investigate if encoding in qudits or allowing for non-deterministic correction proves advantageous compared to known QECCs. While we here focus on the case of losses, our methodology is applicable whenever the errors in a system can be characterized by a known linear map.

Efficient and Reliable Three-dimensional Reed-solomon Codes for Holographic Data Storage

The three-dimensional Reed-solomon (RS) code with erasures-and-errors decoding (3DRS-E) can be utilized to efiectively correct burst errors in Holographic Data Storage (HDS), a considerable application in multimedia storage. However, the RS codes have two drawbacks: 1) Received erroneous codewords may not be detected by the RS decoders; 2) The RS decoders may produce a codeword that difiers from the transmitted codeword. In the implementation of erasures-and-errors decoding, such drawbacks may cause the RS codes to provide incorrect erasure information to other RS codes, resulting in unreliable burst-error correction performance of the HDS. In order to combat the drawbacks, we propose a new three-dimensional code in which Cyclic Redundancy Check (CRC) codes are applied; we call this new code as the 3DRS-E and CRC code (3DRS-EC). Experimental results show that the 3DRSEC can signiflcantly decrease the probability of the drawbacks, thereby improving the error-correction performance of HDS systems.

Error Correction Schemes with Erasure Information for Fast Memories

Two error correction schemes are proposed for word-oriented binary memories that can be affected by erasures, i.e. errors with known location but unknown value. The erasures considered here are due to the drifting of the electrical parameter used to encode information outside the normal ranges associated to a logic 0 or a logic 1 value. For example, a dielectric breakdown in a magnetic memory cell may reduce its electrical resistance sensibly below the levels which correspond to logic 0 and logic 1 values stored in healthy memory cells. Such deviations can be sensed during memory read operations and the acquired information can be used to boost the correction capability of an error-correcting code (ECC). The proposed schemes enable the correction of double-bit errors based on the combination of erasure information with single-bit error correction and double-bit error detection (SEC-DED) codes or shortened (SEC) codes. The correction of single-bit errors is always guaranteed. Ways to increase the number of double-bit and triple-bit errors that can be detected by shortened SEC and SEC-DED codes are considered in order to augment the error correction capability of the proposed solutions.

A new error correction technique for BD systems

Two-dimensional error correction codes (2DECCs) have been the cornerstone of all three generations of optical recording-CD, DVD and BD. Research into powerful error correction methods is paramount for the development of high-capacity optical recording systems. A picket code for BD systems performs an error and erasure decoding by giving and taking erasure information between two ECCs. However, the method is possible to generate and utilize incorrect erasure information with non-ignorable probability by each ECC. This paper will present a new error correction strategy for BD systems that performs error and erasure decoding using the only erasure information supplied from a modulation code decoder - more specifically, the 17 parity-preserving (PP) code for BD systems. We will evaluate the decoding efficiency of the new error correction technique under a channel model with various error types as well as real optical storage system.

An efficient decoding strategy of 2D-ECC for optical recording systems

Two-dimensional error correction codes (2DECCs) have been the cornerstone of all three generations of optical recording - CD, DVD and BD. Research into powerful error correction methods is paramount for the development of high-capacity optical recording systems. A Reed-Solomon product-code (RS-PC) for DVD systems performs error and erasure decoding by giving and taking erasure information between two ECCs. In this paper, we will present a new error correction method that performs erasure decoding using the only erasure information supplied from a modulation code decoder - more specifically, the EFMPlus code for DVD systems. We will evaluate the decoding efficiency of the new error correction method under a channel environment with various error types.

The Performance Analysis of MPE-FEC Decoding Methods at the DVB-H Link Layer for Efficient IP Packet Retrieval

DVB-H is a new broadcasting standard, which offers reliable high data rate reception of IP packets for mobile handheld battery-powered devices. A link layer with multiprotocol encapsulation (MPE), including Reed-Solomon forward error correction (FEC) combined with a cyclic redundancy check (CRC), is defined in the standard to work on top of the DVB-T physical layer. For error correction in the receiver the DVB-H standard suggests to use erasure decoding based on the CRC information. Yet, the decoding method is not strictly determined in the standard. This paper investigates the performance of five different Reed-Solomon decoding schemes for the DVB-H link layer forward error correction called MPE-FEC. They differ on utilization strategy of existing erasure information. The performance of different decoding methods are evaluated analytically in an binary symmetric channel (BSC) and with simulations in the additive white Gaussian noise (AWGN) and a mobile fading channel. For the simulations in the fading channel a packet channel model based on actual measurements is designed. It is shown that more sophisticated decoding methods than the one suggested in the standard are required for efficient retrieval of IP packets

Performance analysis of coded M-ary orthogonal signaling using errors-and-erasures decoding over frequency-selective fading channels

The performance of M-ary orthogonal signaling schemes employing Reed-Solomon (RS) codes and redundant residue number system (RRNS) codes is investigated over frequency-selective Rayleigh fading channels. Errors-and-erasures decoding is considered, where erasures are judged based on two low-complexity, low-delay erasure insertion schemes-Viterbi's ratio threshold test (RTT) and the proposed output threshold test (OTT). The probability density functions (PDF) of the ratio associated with the RTT and that of the demodulation output in the OTT conditioned on both the correct detection and erroneous detection of M-ary signals are derived, and the characteristics of the RTT and OTT are investigated. Furthermore, expressions are derived for computing the codeword decoding error probability of RS codes or RRNS codes based on the above PDFs, The OTT technique is compared to Viterbi's RTT, and both of these are compared to receivers using error-correction only decoding over frequency-selective Rayleigh-fading channels. The numerical results show that by using errors-and-erasures decoding, RS or RRNS codes of a given code rate can achieve higher coding gain than that without erasure information, and that the OTT technique outperforms the RTT, provided that both schemes are operated at the optimum decision thresholds.

A Reed-Solomon coded DS-CDMA system using noncoherent M-ary orthogonal modulation over multipath fading channels

The performance of Reed-Solomon (RS) coded direct-sequence code division multiple-access (DS-CDMA) systems using noncoherent M-ary orthogonal modulation is investigated over multipath Rayleigh fading channels. Diversity reception techniques with equal gain combining (EGC) or selection combining (SC) are invoked and the related performance is evaluated for both uncoded and coded DS-CDMA systems. "Errors-and-erasures" decoding is considered, where the erasures are based on Viterbi's (1982) so-called ratio threshold test (RTT). The probability density functions (PDF) of the ratio associated with the RTT conditioned on both the correct detection and erroneous detection of the M-ary signals are derived. These PDFs are then used for computing the codeword decoding error probability of the RS coded DS-CDMA system using "errors-and-erasures" decoding. Furthermore, the performance of the "errors-and-erasures" decoding technique employing the RTT is compared to that of "error-correction-only" decoding refraining from using side-information over multipath Rayleigh fading channels. As expected, the numerical results show that when using "errors-and-erasures" decoding, RS codes of a given code rate can achieve a higher coding gain than without erasure information.

Improved frame synchronization performance for CCITT algorithms using bit erasures

For the CCITT recommendations on frame synchronization (as enhanced in Jones and Al-Subbagh, 1985), the performance in the presence of jamming, interference or other disturbance is improved by using bit erasure information. The acquisition time and misalignment detection times are reduced and the false exit time is increased, with only a minor reduction in the already large false entry time. >

Letter: Impact of RFI Detection in DRS Links on the Performance of Coding Schemes

AbstractThis paper deals with Data Relay Satellite systems operating in the S‐band environment and using Binary Phase Shift Keying modulation with concatenated Forward Error Correction data protection. One of the major sources of their performance degradation is radar generated Radio Frequency Interference in the same band. Transmission channel performance would certainly be improved if RFI positions (called erasures) were detected and passed to the decoders. By allowing the codes to handle about twice as many erasures as errors, this information would significantly reduce the effects of RFI deterioration.A novel technique for RFI detection is developed. It is based on a bank of simple “moving windows” associated with a detection algorithm and a method for the removal of ambiguous RFI detections. The use of this erasure information in the Viterbi decoding process is then illustrated and a new rule for updating the decoding metric is proposed.The residual correlation on the errors at the Viterbi decoder output makes the outer code useless, unless a further interleaving is introduced.Extensive simulation results highlighting the good performance of the joint RFI detection and modified Viterbi decoding schemes are presented. Simulation is also used to assess the outer code behavior.

Performance evaluation of a minimum bit error decoding algorithm of convolutional codes and its application

AbstractBasic decoding characteristics of a minimum bit error decoding (MBED), originally proposed by Bahl et al., is investigated. It is shown that MBED can predict the bit error rate of each decoded bit with good precision. Then MBED is applied to the convolutional/Reed‐Solomon (RS) concatenated coding scheme. The outer RS codes are decoded by an erasure decoding using the symbol erasure information provided from the MBED results of inner convolutional codes. Simulation results show that the overall bit error rate is reduced one‐half to one‐third more than the conventional nonerasure decoding.

Performance of frame synchronization in packet transmission using bit erasure information

The probability of successful frame sync in packet transmission using bit erasure information is compared to the same probability when erasure information is ignored. For a given bound on the false alarms, a significant improvement is found on additive white Gaussian noise (AWGN) channels if an erasure zone is added to the receiver. An improvement is also found for channels in which the presence of jamming or other interference is detected and erased by the receiver. An expression for the probability of frame synchronization in packet transmission is derived as a function of the bit error and erasure probability, the amount of overlap, and the number of bit errors/erasures which are tolerated in the frame sync word.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frame synchronisation with errors and erasures

The probability of successful frame synchronisation in the presence of jamming or interference may be increased by using bit erasure information without also increasing the total probability of simulated alignment Pt,sim in an incorrect position in the overlap region. An expression for Pt,sim is obtained as a function of the bit error and erasure probability, the specified frame alignment pattern, the amount of overlap and the number of bit errors and erasures which are tolerated in the frame sync word.

Forward Error Correction Coding for Fading Compensation in Mobile Satellite Channels

Fading in mobile satellite communications severely degrades the performance of data transmission. The channel is modeled with nonfrequency selective Rice and Rayleigh fading. Also, stored channel simulation is used for hardware data transmission. FEC coding with Viterbi decoding of convolutional codes, and Berlekamp-Massey decoding of Reed-Solomon codes, are used to compensate for the fading. In addition to interleaving, channel state and erasure information improve the performance of the decoder. The BER after decoding is calculated for specific codes on several channels and for different transmission schemes. Using very simple channel state and erasure information gives 2-7 dB additional coding gain. These gains have been verified by hardware data transmission on synthetic fading channels and stored mobile satellite channels.

Simplified correlation decoding by selecting possible codewords using erasure information (Corresp.)

Correlation decoding is an optimal scheme of soft-decision decoding for error-correcting codes in the sense of minimum block-error probability. However, it is very difficult to apply the scheme when the number of information digits is large because of decoding complexity. A new algorithm for soft-decision decoding is presented, simplifying the correlation scheme by selecting certain codewords and decreasing decoding complexity by using erasure information. Any desired block-error probability between the error Probabilities of correlation and hard-decision decoding can be realized by setting up a suitable threshold value 0 for erasure decision. Computer simulation has been performed for Golay (23,12,7) code and BCH (15,7,5) code.