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Also known as: RS Code
An algebraic block code over finite fields that corrects burst errors and erasures using polynomial encoding and decoding.
DESCRIPTION
Reed–Solomon codes are nonbinary block codes defined over finite fields, excellent at correcting burst errors and erasures. Their algebraic structure enables powerful decoding algorithms like Berlekamp–Massey and Euclidean methods. They protect CDs, DVDs, QR codes, satellite links, and distributed storage. Parameters determine correction capability via the designed distance. Implementations often exploit lookup tables and field arithmetic for efficiency. While modern iterative codes may outperform at long lengths, Reed–Solomon remains unmatched for erasures and short to moderate block sizes.
ALTERNATIVE DEFINITIONS
Wikipedia
Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.
Historical origin and classification as error-correcting codes.
Wolfram MathWorld
A Reed–Solomon code is a nonbinary BCH code over a finite field capable of correcting multiple symbol errors and erasures.
Emphasizes nonbinary nature and erasure capability.
RELATED TERMS
Galois Field Error-Correcting Code Erasure Coding Polynomial Codes Lagrange Interpolation QR Code RAID 6 ECC Memory
COMPETING TERMS
Bose–Chaudhuri–Hocquenghem Code LDPC Code Turbo Codes
KNOWLEDGE AREAS
Data Storage & Operations IoT & Edge Data Infrastructure Mathematics
TARGET AUDIENCE
Hardware Engineer Software Developer Cloud Architect Data Engineer
EXTERNAL SOURCES
- Wikipedia - Reed–Solomon error correction
- IETF - Reed–Solomon FEC schemes for RTP
- CCSDS - Space link Reed–Solomon channel coding
- Apache Hadoop - HDFS erasure coding with Reed–Solomon
TOP QUESTIONS
Where are Reed–Solomon Codes commonly used?
They are used in CDs/DVDs, QR codes, satellite links, and distributed storage for burst-error and erasure protection.
Category: Application
How do Reed–Solomon Codes correct erasures?
Knowing error locations reduces unknowns, allowing correction of more symbol losses via polynomial interpolation.
Category: HowTo
What determines the correction capability of a Reed–Solomon Code?
The designed minimum distance, set by code parameters, determines how many symbol errors or erasures can be corrected.
Category: Concept
Which decoding algorithms are used for Reed–Solomon Codes?
Common methods include Berlekamp–Massey, Euclidean algorithm, and Forney’s formula for error evaluation.
Category: Overview
How do Reed–Solomon Codes compare to LDPC Codes?
RS excel at erasures and shorter blocks; LDPC often outperform on long blocks with near-capacity iterative decoding.
Category: Comparison
What is a common implementation pitfall?
Incorrect finite field arithmetic or generator polynomial selection can compromise correction performance.
Category: Mistakes
Can Reed–Solomon Codes be shortened or punctured?
Yes, shortening adapts block size; puncturing adjusts rate, offering flexibility for system integration.
Category: HowTo
Do Reed–Solomon Codes protect against burst errors?
Yes, as symbol-oriented codes, they are robust against bursts spanning multiple bits within symbols.
Category: Relevancy
What parameters define a Reed–Solomon Code?
Defined over GF(q) with block length n, dimension k, and distance d = n − k + 1 for Reed–Solomon codes.
Category: Concept