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At least 55 records · Page 3

Prioritized LT Codes

The original Luby Transform (LT) coding scheme is extended to account for data transmissions where some information symbols in a message block are more important than others. Prioritized LT codes provide unequal error protection (UEP) of data on an erasure channel by modifying the original LT encoder. The prioritized algorithm improves high-priority data protection without penalizing low-priority data recovery. Moreover, low-latency decoding is also obtained for high-priority data due to fast encoding. Prioritized LT codes only require a slight change in the original encoding algorithm, and no changes at all at the decoder. Hence, with a small complexity increase in the LT encoder, an improved UEP and low-decoding latency performance for high-priority data can be achieved. LT encoding partitions a data stream into fixed-sized message blocks each with a constant number of information symbols. To generate a code symbol from the information symbols in a message, the Robust-Soliton probability distribution is first applied in order to determine the number of information symbols to be used to compute the code symbol. Then, the specific information symbols are chosen uniform randomly from the message block. Finally, the selected information symbols are XORed to form the code symbol. The Prioritized LT code construction includes an additional restriction that code symbols formed by a relatively small number of XORed information symbols select some of these information symbols from the pool of high-priority data. Once high-priority data are fully covered, encoding continues with the conventional LT approach where code symbols are generated by selecting information symbols from the entire message block including all different priorities. Therefore, if code symbols derived from high-priority data experience an unusual high number of erasures, Prioritized LT codes can still reliably recover both high- and low-priority data. This hybrid approach decides not only "how to encode" but also "what to encode" to achieve UEP. Another advantage of the priority encoding process is that the majority of high-priority data can be decoded sooner since only a small number of code symbols are required to reconstruct high-priority data. This approach increases the likelihood that high-priority data is decoded first over low-priority data. The Prioritized LT code scheme achieves an improvement in high-priority data decoding performance as well as overall information recovery without penalizing the decoding of low-priority data, assuming high-priority data is no more than half of a message block. The cost is in the additional complexity required in the encoder. If extra computation resource is available at the transmitter, image, voice, and video transmission quality in terrestrial and space communications can benefit from accurate use of redundancy in protecting data with varying priorities.

Woo, Simon S.↗

Intelligibility and Space-based Voice with Relaxed Delay Constraints

The inherent aspects and flaws surrounding space based communication is technically described and the math surrounding encoding and decoding LT Codes is examined. Utilizing LT codes as a means of reducing packet erasures due to corrupted packets on an RF link can result in higher voice quality. PESQ-MOS measure was used to analyze voice degradation over space links tested for LT codec size and number of 10ms per packet.Extensions utilizing LT codes to improve the packet erasure performance and combining the use of ASR could provide for a solid means of identifying the benefit in terms of intelligibility of voice communications in space-based networks

space communications↗

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

quantum error correction↗

A decoding failure test for the transform decoder of Reed-Solomon code

Using a finite field transform, a transform decoding algorithm is able to correct erasures as well as errors of any (n,k,d) Reed-Solomon code over the finite field GF(q). A pitfall of transform decoding and how to avoid it are discussed. A simple test is given so that the decoder fails to decode instead of introducing additional errors, whenever the received word contains too many errors and erasures.

Miller, R. L.↗

On decoding BCH codes.

Extension, modification and analysis of Gorenstein-Zierler decoding algorithm for binary codes of Bose, Ray-Chaudhuri and Hocquenghem /BCH/ correcting erasures and errors

BINARY CODE↗

Prioritized LT Codes

It is common in data transmissions that some information is more important than others. This is especially true in space communications where mission critical information or science data are high priority. In this work, we propose a simple yet constructive scheme to send high priority data reliably and efficiently using Luby Transform (LT) codes. The new proposed scheme modifies the conventional LT encoder to send high priority data as a degree 1 and 2 so that high priority data can be quickly resolved and very likely recovered before a decoder stops. Preliminary results show that a carefully designed degree distribution of high priority data increases the likelihood of receiving high priority information while having negligible performance impact on data with lower priority. The performance of the proposed scheme is evaluated and compared with the conventional LT approach with the same parameters under a range of erasure error rates.

priority coding↗

Enhanced decoding for the Galileo S-band mission

A coding system under consideration for the Galileo S-band low-gain antenna mission is a concatenated system using a variable redundancy Reed-Solomon outer code and a (14,1/4) convolutional inner code. The 8-bit Reed-Solomon symbols are interleaved to depth 8, and the eight 255-symbol codewords in each interleaved block have redundancies 64, 20, 20, 20, 64, 20, 20, and 20, respectively (or equivalently, the codewords have 191, 235, 235, 235, 191, 235, 235, and 235 8-bit information symbols, respectively). This concatenated code is to be decoded by an enhanced decoder that utilizes a maximum likelihood (Viterbi) convolutional decoder; a Reed Solomon decoder capable of processing erasures; an algorithm for declaring erasures in undecoded codewords based on known erroneous symbols in neighboring decodable words; a second Viterbi decoding operation (redecoding) constrained to follow only paths consistent with the known symbols from previously decodable Reed-Solomon codewords; and a second Reed-Solomon decoding operation using the output from the Viterbi redecoder and additional erasure declarations to the extent possible. It is estimated that this code and decoder can achieve a decoded bit error rate of 1 x 10(exp 7) at a concatenated code signal-to-noise ratio of 0.76 dB. By comparison, a threshold of 1.17 dB is required for a baseline coding system consisting of the same (14,1/4) convolutional code, a (255,223) Reed-Solomon code with constant redundancy 32 also interleaved to depth 8, a one-pass Viterbi decoder, and a Reed Solomon decoder incapable of declaring or utilizing erasures. The relative gain of the enhanced system is thus 0.41 dB. It is predicted from analysis based on an assumption of infinite interleaving that the coding gain could be further improved by approximately 0.2 dB if four stages of Viterbi decoding and four levels of Reed-Solomon redundancy are permitted. Confirmation of this effect and specification of the optimum four-level redundancy profile for depth-8 interleaving is currently being done.

Dolinar, S.↗

Fast transform decoding of nonsystematic Reed-Solomon codes

A Reed-Solomon (RS) code is considered to be a special case of a redundant residue polynomial (RRP) code, and a fast transform decoding algorithm to correct both errors and erasures is presented. This decoding scheme is an improvement of the decoding algorithm for the RRP code suggested by Shiozaki and Nishida, and can be realized readily on very large scale integration chips.

Truong, T. K.↗

Custom CMOS Reed Solomon coder for the Hubble Space Telescope

A VLSI coder is presented that can function either as an encoder or decoder for Reed-Solomon codes. VLSI is one approach to implementing high-performance Reed-Solomon decoders. There are three VLSI technologies that could be used: gate arrays, standard cells, and full custom. The first two approaches are relatively easy to implement, but are limited in both performance and density. Full-custom VLSI is used to achieve both circuit density and speed, and allows control of the amount of interconnect. Speed, which is a function of capacitance, which is a function of interconnect, is an important parameter in high-performance VLSI. A single 8.2 mm x 8.4 mm, 200,000 transistor CMOS chip implementation of the Reed-Solomon code required by the Hubble Space Telescope is reported. The chip features a 10-MHz sustained byte rate independent of error pattern. The 1.6-micron CMOS integrated circuit has complete decoder and encoder functions and uses a single data/system clock. Block lengths up to 255 bytes and shortened codes are supported with no external buffering. Erasure corrections and random error corrections are supported with programmable correction of up to 10 symbol errors. Correction time is independent of error pattern and the number of errors in the incoming message.

Whitaker, S.↗

Reed Solomon error correction for the space telescope

This paper reports a single 8.2mm by 8.4mm, 200,000 transistor CMOS chip implementation of the Reed Solomon code required by the Space Telescope. The chip features a 10 MHz sustained byte rate independent of error pattern. The 1.6 micron CMOS integrated circuit has complete decoder and encoder functions and uses a single data/system clock. Block lengths up to 255 bytes as well as shortened codes are supported with no external buffering. Erasure corrections as well as random error corrections are supported with programmable corrections of up to 10 symbol errors. Correction time is independent of error pattern and the number of errors.

Whitaker, S.↗

High rate concatenated coding systems using bandwidth efficient trellis inner codes

High-rate concatenated coding systems with bandwidth-efficient trellis inner codes and Reed-Solomon (RS) outer codes are investigated for application in high-speed satellite communication systems. Two concatenated coding schemes are proposed. In one the inner code is decoded with soft-decision Viterbi decoding, and the outer RS code performs error-correction-only decoding (decoding without side information). In the other, the inner code is decoded with a modified Viterbi algorithm, which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, whereas branch metrics are used to provide reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. The two schemes have been proposed for high-speed data communication on NASA satellite channels. The rates considered are at least double those used in current NASA systems, and the results indicate that high system reliability can still be achieved.

Deng, Robert H.↗

Error control techniques for satellite and space communications

High rate concatenated coding systems with trellis inner codes and Reed-Solomon (RS) outer codes for application in satellite communication systems are considered. Two types of inner codes are studied: high rate punctured binary convolutional codes which result in overall effective information rates between 1/2 and 1 bit per channel use; and bandwidth efficient signal space trellis codes which can achieve overall effective information rates greater than 1 bit per channel use. Channel capacity calculations with and without side information performed for the concatenated coding system. Concatenated coding schemes are investigated. In Scheme 1, the inner code is decoded with the Viterbi algorithm and the outer RS code performs error-correction only (decoding without side information). In scheme 2, the inner code is decoded with a modified Viterbi algorithm which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, while branch metrics are used to provide the reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. These two schemes are proposed for use on NASA satellite channels. Results indicate that high system reliability can be achieved with little or no bandwidth expansion.

Costello, D. J., Jr.↗

PPM demodulation for Reed-Solomon decoding for the optical space channel

The use of Reed-Solomon (RS) block codes over the pulse position modulated (PPM) frames to obtain the largest degree of error correction is considered. Since RS codes can correct both symbol errors and symbol erasures, a question arises as to the best way to demodulate the PPM laser fields in order to generate the input symbols for the RS decoder. The method selected for demodulating (converting the received laser field to digital symbols) defines the erasure and transmitted symbols of the laser link, and therefore determines the work error probabilities of the system. Several demodulating schemes are considered, and the effect of each on RS decoding performance computed. This computation was carried out for various optical receiver models. It is shown that simple threshold decisioning of pulse slots produces performance that degrades as the background noise increases. This is caused by the generation of too many erasures for the RS decoder to handle. A decision scheme, delta-max demodulation which offers improvement over threshold decisioning by redefining the generation of an erasure is proposed.

Divsalar, D.↗

Encoders for block-circulant LDPC codes

In this paper, we present two encoding methods for block-circulant LDPC codes. The first is an iterative encoding method based on the erasure decoding algorithm, and the computations required are well organized due to the block-circulant structure of the parity check matrix. The second method uses block-circulant generator matrices, and the encoders are very similar to those for recursive convolutional codes. Some encoders of the second type have been implemented in a small Field Programmable Gate Array (FPGA) and operate at 100 Msymbols/second.

encoders↗

Leveraging Qubit Loss Detection in Fault-Tolerant Quantum Algorithms

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral-atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault-tolerant quantum computation in systems with loss error detection.

atoms↗

Erasure declaring Viterbi decoders

Several methods for realizing erasure declaring Viterbi decoders for the (7,1/2) NASA code are discussed. Only bit oriented algorithms are considered. When such decoders are used in a concatenated system with a (255,223) Reed-Solomon decoder, improvements on the probability of word error of at most 0.1 dB were obtained.

Pollara, F.↗