Editing Reed–Solomon error correction (section)

===Space transmission===

[[File:DeepSpaceFEC.png|350px|right|thumb| Deep-space concatenated coding system.<ref>{{cite book |first1=J. |last1=Hagenauer |first2=E. |last2=Offer |first3=L. |last3=Papke |chapter=11. Matching Viterbi Decoders and Reed-Solomon Decoders in a Concatenated System |title=Reed Solomon Codes and Their Applications |publisher=IEEE Press |date=1994 |page=433 |oclc=557445046 |isbn=9780470546345}}</ref> Notation: RS(255, 223) + [[convolutional codes|CC]] ("constraint length" = 7, code rate = 1/2).]]

One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the [[Voyager program]].

Voyager introduced Reed–Solomon coding [[concatenated code|concatenated]] with [[convolutional code]]s, a practice that has since become very widespread in deep space and satellite (e.g., direct digital broadcasting) communications.
<!-- Unsourced image removed: [[Image:NASA ECC Codes-imperfection.png|thumb|600px|none|NASA's Deep Space Missions ECC Codes (code imperfectness) {{Deletable image-caption|date=March 2012}}]] -->

[[Viterbi decoder]]s tend to produce errors in short bursts. Correcting these burst errors is a job best done by short or simplified Reed–Solomon codes.

Modern versions of concatenated Reed–Solomon/Viterbi-decoded convolutional coding were and are used on the [[Mars Pathfinder]], [[Galileo probe|Galileo]], [[Mars Exploration Rover]] and [[Cassini probe|Cassini]] missions, where they perform within about 1–1.5 [[decibel|dB]] of the ultimate limit, the [[Channel capacity|Shannon capacity]].

These concatenated codes are now being replaced by more powerful [[turbo code]]s:
{| class="wikitable"
|+ Channel coding schemes used by NASA missions<ref name="Andrews, 2007">{{cite journal |last1=Andrews |first1=K.S. |last2=Divsalar |first2=D. |last3=Dolinar |first3=S. |last4=Hamkins |first4=J. |last5=Jones |first5=C.R. |last6=Pollara |first6=F. |title=The development of turbo and LDPC codes for deep-space applications. |journal=Proceedings of the IEEE |volume=95 |issue=11 |pages=2142–56 |date=2007 |doi=10.1109/JPROC.2007.905132 |s2cid=9289140 |url=https://scholar.archive.org/work/shkuo6oxabbklkfz4d6v4gero4/access/wayback/http://coding.jpl.nasa.gov/~hamkins/publications/journals/2007_11_turbo_LDPC.pdf}}</ref>
|-
! Years  !! Code !! Mission(s)
|-
| 1958–present || Uncoded || Explorer, Mariner, many others
|-
| 1968–1978 || [[convolutional codes]] (CC) (25, 1/2) || Pioneer, Venus
|-
| 1969–1975 || [[Reed–Muller code]] (32, 6) || Mariner, Viking
|-
| 1977–present || [[Binary Golay code]] || Voyager
|-
| 1977–present || RS(255, 223) + CC(7, 1/2) || Voyager, Galileo, many others
|-
| 1989–2003 || RS(255, 223) + CC(7, 1/3) || Voyager
|-
| 1989–2003 || RS(255, 223) + CC(14, 1/4) || Galileo
|-
| 1996–present || RS + CC (15, 1/6) || Cassini, Mars Pathfinder, others	
|-
| 2004–present || [[Turbo codes]]{{refn|group=nb| Authors in Andrews et al. (2007), provide simulation results which show that for the same code rate (1/6) turbo codes outperform Reed-Solomon concatenated codes up to 2 dB ([[bit error rate]]).<ref name="Andrews, 2007"/>}}
|| Messenger, Stereo, MRO, MSL,others
|-
| est. 2009 || [[LDPC codes]] || Constellation, M2020, MAVEN
|}