Serial concatenated convolutional codes - Revision history

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	== External links ==		== External links ==
	*{{cite journal \|first=Dave \|last=Forney \|date=2009 \|journal=Scholarpedia \|volume=4 \|issue=2 \|page=8374 \|title=Concatenated codes\|doi=10.4249/scholarpedia.8374 ~~\|doi-broken-date=2024-06-12~~ \|bibcode=2009SchpJ...4.8374F \|doi-access=free }}		*{{cite journal \|first=Dave \|last=Forney \|date=2009 \|journal=Scholarpedia \|volume=4 \|issue=2 \|page=8374 \|title=Concatenated codes\|doi=10.4249/scholarpedia.8374 \|bibcode=2009SchpJ...4.8374F \|doi-access=free }}
	*{{cite web \|url=http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf \|title=Concatenated Convolutional Codes and Iterative Decoding \|first=Willian E. \|last=Ryan \|publisher=Department of Electrical & Computer Engineering, University of Arizona \|date=2001}}		*{{cite web \|url=http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf \|title=Concatenated Convolutional Codes and Iterative Decoding \|first=Willian E. \|last=Ryan \|publisher=Department of Electrical & Computer Engineering, University of Arizona \|date=2001}}

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	== External links ==		== External links ==
	*{{cite journal \|first=Dave \|last=Forney \|date=2009 \|journal=Scholarpedia \|volume=4 \|issue=2 \|page=8374 \|title=Concatenated codes\|doi=10.4249/scholarpedia.8374 \|bibcode=2009SchpJ...4.8374F \|doi-access=free }}		*{{cite journal \|first=Dave \|last=Forney \|date=2009 \|journal=Scholarpedia \|volume=4 \|issue=2 \|page=8374 \|title=Concatenated codes\|doi=10.4249/scholarpedia.8374 \|doi-broken-date=2024-06-12 \|bibcode=2009SchpJ...4.8374F \|doi-access=free }}
	*{{cite web \|url=http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf \|title=Concatenated Convolutional Codes and Iterative Decoding \|first=Willian E. \|last=Ryan \|publisher=Department of Electrical & Computer Engineering, University of Arizona \|date=2001}}		*{{cite web \|url=http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf \|title=Concatenated Convolutional Codes and Iterative Decoding \|first=Willian E. \|last=Ryan \|publisher=Department of Electrical & Computer Engineering, University of Arizona \|date=2001}}

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← Previous revision		Revision as of 03:38, 23 September 2023
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	'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (iterative) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment\|url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008~~-12-18~~\|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern\|url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009~~-09-17~~\|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.		'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (iterative) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment \|chapter=5 Error Correction Techniques §5.1.4 Turbo Codes \|chapter-url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008 \|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern \|chapter=7.3 Serial-Concatenated Convolutional Codes \|chapter-url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009 \|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.

	SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.		SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.
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	Serial concatenated convolutional codes have not found widespread commercial use, although they were proposed for communications standards such as [[DVB-S2]]. Nonetheless, the analysis of SCCCs has provided insight into the performance and bounds of all types of iterative decodable codes including [[turbo codes]] and [[LDPC]] codes.{{Citation needed\|date = June 2014}}		Serial concatenated convolutional codes have not found widespread commercial use, although they were proposed for communications standards such as [[DVB-S2]]. Nonetheless, the analysis of SCCCs has provided insight into the performance and bounds of all types of iterative decodable codes including [[turbo codes]] and [[LDPC]] codes.{{Citation needed\|date = June 2014}}

	US patent 6,023,783 covers some forms of SCCCs. The patent expired on May 15, 2016.<ref>{{cite ~~web~~\|url=https://www.google.com/patents/US6023783 \|~~title~~=~~Patent~~ ~~US6023783~~ - Hybrid concatenated codes and iterative decoding ~~- Google Patents \|date=~~ \|~~accessdate~~=~~2014~~-06-04}}</ref>		US patent 6,023,783 covers some forms of SCCCs. The patent expired on May 15, 2016.<ref>{{cite patent \|url=https://www.google.com/patents/US6023783 \|country=US \|number=6023783 \|invent1=Dariush Divsalar \|invent2=Fabrizio Pollara \|status=Expired \|title=Hybrid concatenated codes and iterative decoding \|gdate=2000-02-08}}</ref>

	== History ==		== History ==

	Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>{{Cite web \|url=http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|title=~~Archived~~ ~~copy~~ \|access-date=2014-04-02 \|archive-date=2017-08-13 \|archive-url=https://web.archive.org/web/20170813054421/http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|url-status=dead }}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.		Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>{{Cite web \|url=http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|id=TDA Progress Report 42-126 \|date=August 15, 1996
			\|title=Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding \|first1=S. \|last1=Benedetto \|first2=D. \|last2=Divsalar \|first3=G. \|last3=Montorsi \|first4=F. \|last4=Pollara \|access-date=2014-04-02 \|archive-date=2017-08-13 \|archive-url=https://web.archive.org/web/20170813054421/http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|url-status=dead }}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.

	Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=~~Allerton98~~.~~tex~~ \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.		Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Coding Theorems for "Turbo-Like" Codes
			\|first1=Dariush \|last1=Divsalar \|first2=Hui \|last2=Jin \|first3=Robert J. \|last3=McEliece \|publisher=Jet Propulsion Laboratory, California Institute of Technology \|date=1998 \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.

	SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>[https://web.archive.org/web/20100529020555/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf ~~NASA.gov]~~</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.		SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>{{cite conference \|url=http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf \|title=Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code \|first1=D. \|last1=Divsalar \|first2=S. \|last2=Dolinar \|first3=E \|last3=Pollara \|book-title=Globecom '00 - IEEE. Global Telecommunications Conference \|date=2000 \|doi=10.1109/GLOCOM.2000.891245 \|isbn=0-7803-6451-1 \|archive-url=https://web.archive.org/web/20100529020555/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf \|archive-date=2010-05-29 }}</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.

	== Example Encoder ==		== Example Encoder ==
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	== External links ==		== External links ==
			*{{cite journal \|first=Dave \|last=Forney \|date=2009 \|journal=Scholarpedia \|volume=4 \|issue=2 \|page=8374 \|title=Concatenated codes\|doi=10.4249/scholarpedia.8374 \|bibcode=2009SchpJ...4.8374F \|doi-access=free }}
	*[http://www.scholarpedia.org/article/Concatenated_codes "Concatenated codes", Scholarpedia]
	*[http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf "Concatenated Convolutional Codes and Iterative Decoding", Willian E. Ryan]		*{{cite web \|url=http://www.mif.vu.lt/~skersys/vsd/turbo/ryan_chapter.pdf \|title=Concatenated Convolutional Codes and Iterative Decoding \|first=Willian E. \|last=Ryan \|publisher=Department of Electrical & Computer Engineering, University of Arizona \|date=2001}}

	[[Category:Data]]		[[Category:Data]]

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2022-08-21T07:46:26Z

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← Previous revision		Revision as of 07:46, 21 August 2022
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	Serial concatenated convolutional codes have not found widespread commercial use, although they were proposed for communications standards such as [[DVB-S2]]. Nonetheless, the analysis of SCCCs has provided insight into the performance and bounds of all types of iterative decodable codes including [[turbo codes]] and [[LDPC]] codes.{{Citation needed\|date = June 2014}}		Serial concatenated convolutional codes have not found widespread commercial use, although they were proposed for communications standards such as [[DVB-S2]]. Nonetheless, the analysis of SCCCs has provided insight into the performance and bounds of all types of iterative decodable codes including [[turbo codes]] and [[LDPC]] codes.{{Citation needed\|date = June 2014}}

	US patent 6,023,783 covers some forms of SCCCs. The patent expired on May 15, 2016.<ref>{{cite web\|url=https://www.google.com/patents/US6023783 \|title=Patent US6023783 - Hybrid concatenated codes and iterative decoding - Google Patents ~~\|publisher=Google.com~~ \|date= \|accessdate=2014-06-04}}</ref>		US patent 6,023,783 covers some forms of SCCCs. The patent expired on May 15, 2016.<ref>{{cite web\|url=https://www.google.com/patents/US6023783 \|title=Patent US6023783 - Hybrid concatenated codes and iterative decoding - Google Patents \|date= \|accessdate=2014-06-04}}</ref>

	== History ==		== History ==
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	Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>{{Cite web \|url=http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|title=Archived copy \|access-date=2014-04-02 \|archive-date=2017-08-13 \|archive-url=https://web.archive.org/web/20170813054421/http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|url-status=dead }}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.		Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>{{Cite web \|url=http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|title=Archived copy \|access-date=2014-04-02 \|archive-date=2017-08-13 \|archive-url=https://web.archive.org/web/20170813054421/http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|url-status=dead }}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.

	Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex ~~\|format=PDF~~ \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.		Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.

	SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>[https://web.archive.org/web/20100529020555/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf NASA.gov]</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.		SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>[https://web.archive.org/web/20100529020555/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf NASA.gov]</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.

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← Previous revision		Revision as of 15:43, 17 February 2022
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	== History ==		== History ==

	Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf ~~{{Dead~~ ~~link~~\|date=~~February~~ ~~2022~~}}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.		Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>{{Cite web \|url=http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|title=Archived copy \|access-date=2014-04-02 \|archive-date=2017-08-13 \|archive-url=https://web.archive.org/web/20170813054421/http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf \|url-status=dead }}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.

	Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.		Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.

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← Previous revision		Revision as of 19:38, 9 February 2022
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	== History ==		== History ==

	Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.		Serial concatenated convolutional codes were first analyzed with a view toward turbo decoding in "Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding" by S. Benedetto, D. Divsalar, G. Montorsi and F. Pollara.<ref>http://www.systems.caltech.edu/EE/Courses/EE127/EE127C/handout/serial.pdf {{Dead link\|date=February 2022}}</ref> This analysis yielded a set of observations for designing high performance, turbo decodable serial concatenated codes that resembled [[turbo codes]]. One of these observations was that "the use of a recursive convolutional inner encoder always yields an interleaver gain."{{Clarify\|date=June 2014}} This is in contrast to the use of block codes or non-recursive convolutional codes, which do not provide comparable interleaver gain.

	Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.		Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.

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← Previous revision		Revision as of 23:55, 29 June 2021
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	Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.		Additional analysis of SCCCs was done in "Coding Theorems for 'Turbo-Like' Codes" by D. Divsalar, Hui Jin, and Robert J. McEliece.<ref>{{cite web\|url=http://www.mif.vu.lt/~skersys/vsd/turbo/Allerton98.pdf \|title=Allerton98.tex \|format=PDF \|date= \|accessdate=2014-06-04}}</ref> This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver. The performance of the RA codes is quite good considering the simplicity of the constituent codes themselves.

	SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.		SCCC codes were further analyzed in "Serial Turbo Trellis Coded Modulation with Rate-1 Inner Code".<ref>[https://web.archive.org/web/20100529020555/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/18647/1/99-2030.pdf NASA.gov]</ref> In this paper SCCCs were designed for use with higher order modulation schemes. Excellent performing codes with inner and outer constituent convolutional codes of only two or four states were presented.

	== Example Encoder ==		== Example Encoder ==

131.176.243.9: fixed typo, iteractive -> iterative

2021-03-16T12:23:49Z

fixed typo, iteractive -> iterative

← Previous revision		Revision as of 12:23, 16 March 2021
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	'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (~~iteractive~~) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment\|url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008-12-18\|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern\|url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009-09-17\|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.		'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (iterative) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment\|url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008-12-18\|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern\|url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009-09-17\|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.

	SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.		SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.

Uziel302: interative -> iterative - Fix a typo in one click

2019-10-07T18:14:46Z

interative -> iterative - Fix a typo in one click

← Previous revision		Revision as of 18:14, 7 October 2019
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	== Example Decoder ==		== Example Decoder ==

	An example of an ~~interative~~ SCCC decoder.		An example of an iterative SCCC decoder.

	[[File:SCCC Decoder.png\|thumb\|none\|500px\|Fig. 2. SCCC Decoder]]		[[File:SCCC Decoder.png\|thumb\|none\|500px\|Fig. 2. SCCC Decoder]]

Possibly: typo

2019-08-05T19:26:02Z

typo

← Previous revision		Revision as of 19:26, 5 August 2019
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	'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (~~iterative~~) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment\|url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008-12-18\|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern\|url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009-09-17\|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.		'''Serial concatenated convolutional codes''' ('''SCCC''') are a class of [[forward error correction]] (FEC) codes highly suitable for [[Turbo code\|turbo]] (iteractive) decoding.<ref name="Minoli2008">{{cite book\|last=Minoli\|first=Daniel\|title=Satellite Systems Engineering in an IPv6 Environment\|url=https://books.google.com/books?id=4yJi1UQDPp8C&pg=PA152\|accessdate=4 June 2014\|date=2008-12-18\|publisher=CRC Press\|isbn=9781420078695\|pages=152–}}</ref><ref name="RyanLin2009">{{cite book\|last1=Ryan\|first1=William\|last2=Lin\|first2=Shu\|title=Channel Codes: Classical and Modern\|url=https://books.google.com/books?id=0gwqxBU_t-QC&pg=PA320\|accessdate=4 June 2014\|date=2009-09-17\|publisher=Cambridge University Press\|isbn=9781139483018\|pages=320–}}</ref> Data to be transmitted over a noisy channel may first be encoded using an SCCC. Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols.

	SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.		SCCCs typically include an [[inner code]], an [[outer code]], and a linking interleaver. A distinguishing feature of SCCCs is the use of a recursive [[convolutional code]] as the inner code. The recursive inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.