Serial concatenated convolutional codes: Difference between revisions

Revision as of 15:43, 17 February 2022

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}}

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>

== 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.

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>[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.