Exploiting the Cannibalistic Traits of Reed-Solomon Codes

O Collins

Home/Archive/NASA NTRS

NASA NTRS · 19940009905

Exploiting the Cannibalistic Traits of Reed-Solomon Codes

O Collins

View original source ↗Export metadata ↓

Abstract

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many communications or storage systems cannot easily accommodate an increased symbol size, e.g., M-ary frequency shift keying (FSK) and photon-counting pulse-position modulation demand a fixed symbol size. A technique for sharing redundancy among many different Reed-Solomon codewords to achieve the efficiency attainable in long Reed-Solomon codes without increasing the symbol size is described. Techniques both for calculating the performance of these new codes and for determining their encoder and decoder complexities is presented. These complexities are usually found to be substantially lower than conventional Reed-Solomon codes of similar performance.

Keep this discovery

BibTeX RIS

O Collins. 1993-08-15. Exploiting the Cannibalistic Traits of Reed-Solomon Codes. https://ntrs.nasa.gov/citations/19940009905

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

NASA NTRS1993

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 -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.

S Dolinar↗

DOE OSTI2026

Full ribosomal operon sequencing of anaerobic gut fungi (phylum Neocallimastigomycota ): insights on its markers and phylogenetic resolution

The phylogenetic affiliations of anaerobic gut fungi (Neocallimastigomycota) are typically evaluated using single-gene markers. However, this approach often fails to resolve relationships between closely related lineages. To address this issue and identify alternative markers, we created a curated database comprising the complete ribosomal operon sequences of 156 isolates, representing 20 of the 22 recognized genera and two new genus-level clades. Using long-read sequencing, we obtained ~9 kbp operon sequences and developed a robust analysis pipeline. Incorporating both coding genes and non-coding regions (excluding IGS1) improved phylogenetic resolution. This phylogenetic approach successfully resolved the Cyllamyces and Caecomyces clades (hard-to-distinguish genetically), as well as seven analysed Piromyces species. We also scanned the operon for markers that are suitable for short-read sequencing platforms, with the aim of enhancing biodiversity and phylogenetic studies. Notably, the ETS1 genetic region also enabled the distinction between these lineages, indicating its phylogenetic value within the ribosomal operon. The resulting database is a valuable resource for expanding and strengthening phylogenetic frameworks.

High-throughput sequencing↗

DOE OSTI2026

Divergent trait controls on soluble sugars and starch underlie global strategies of tree carbohydrate storage

Nonstructural carbohydrate (NSC) stores buffer tree metabolism, osmotic regulation, and defense, thereby mediating tolerance and survival under climate extremes. Yet, the functional and evolutionary determinants of interspecific variation in NSC remain elusive, limiting understanding and prediction of forest carbon allocation and mortality under global change. Here, we present a cross-species synthesis of NSC concentrations across multiple organs for 281 woody species from 102 mixed forest communities worldwide, where we quantified species-specific deviations from community means to disentangle intrinsic trait effects from environmental and methodological variation. We found phylogenetic signals in NSC deviations, with coniferous gymnosperms and evergreen species consistently maintaining lower stem soluble sugars and starch concentrations than co-occurring angiosperms and deciduous species, respectively. A global pattern emerged where greater stomatal sensitivity to leaf water potential was associated with declines in the relative concentrations of both sugars and starch. In contrast, xylem hydraulic safety traits showed weak and organ-dependent relationships with NSC concentrations. Sugars increased with photosynthetic capacity and declined with wood density, whereas starch showed the reverse pattern, which aligned with the distinct functional-metabolic roles of sugars and starch. By integrating trait-based ecology with a community-centered framework, our study provides global evidence that stomatal regulation, photosynthetic capacity, specific leaf area, and wood density jointly govern interspecific NSC variation, through contrasting effects on sugars and starch. These are among the most broadly measured traits globally, thus the emergent carbohydrate–trait relationships can have broad applications toward understanding and predicting forest growth and survival under climate change.

tropic system↗