Prioritized Luby Transform (LT) Codes
This viewgraph presentation describes a prioritized Luby Transform coding scheme that seeks to decode high priority data with high reliability, when decoders fail.
Luby Transform (LT) codes↗
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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↗
Protograph LDPC Codes Over Burst Erasure Channels
In this paper we design high rate protograph based LDPC codes suitable for binary erasure channels. To simplify the encoder and decoder implementation for high data rate transmission, the structure of codes are based on protographs and circulants. These LDPC codes can improve data link and network layer protocols in support of communication networks. Two classes of codes were designed. One class is designed for large block sizes with an iterative decoding threshold that approaches capacity of binary erasure channels. The other class is designed for short block sizes based on maximizing minimum stopping set size. For high code rates and short blocks the second class outperforms the first class.
protgraph based codes↗
Constructing LDPC Codes from Loop-Free Encoding Modules
A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.
Divsalar, Dariush↗
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↗
Optimal Codes for the Burst Erasure Channel
Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure protection. As can be seen, the simple interleaved RS codes have substantially lower inefficiency over a wide range of transmission lengths.
Hamkins, Jon↗
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.↗
Multiplexed Holographic Data Storage in Bacteriorhodopsin
High density optical data storage, driven by the information revolution, remains at the forefront of current research areas. Much of the current research has focused on photorefractive materials (SBN and LiNbO3) and polymers, despite various problems with expense, durability, response time and retention periods. Photon echo techniques, though promising, are questionable due to the need for cryogenic conditions. Bacteriorhodopsin (BR) films are an attractive alternative recording medium. Great strides have been made in refining BR, and materials with storage lifetimes as long as 100 days have recently become available. The ability to deposit this robust polycrystalline material as high quality optical films suggests the use of BR as a recording medium for commercial optical disks. Our own recent research has demonstrated the suitability of BR films for real time spatial filtering and holography. We propose to fully investigate the feasibility of performing holographic mass data storage in BR. Important aspects of the problem to be investigated include various data multiplexing techniques (e.g. angle- amplitude- and phase-encoded multiplexing, and in particular shift-multiplexing), multilayer recording techniques, SLM selection and data readout using crossed polarizers for noise rejection. Systems evaluations of storage parameters, including access times, memory refresh constraints, erasure, signal-to-noise ratios and bit error rates, will be included in our investigations.
Mehrl, David J.↗
Erasure information for a Reed-Solomon decoder
Many Reed-Solomon decoders, including the one decoding the outer code for Voyager data from Uranus, assume that all symbols have the same chance of being correct or incorrect. Insome cases, like in a burst of incorrect symbols, this is not the case, and a Reed-Solomon decoder could make use of this. The use of information about bit quality sent to the Reed-Solomon from an (inner) Viterbi decoder is examined, as well as information about the error status of adjacent symbols in decoding interleaved Reed-Solomon encoded symbols. It is discovered that, in a region of interest, only about 0.04 dB can gained.
Pitt, G. H., III↗
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↗