Serial concatenated convolutional codes: Difference between revisions

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'''Serial concatenated convolutional codes (SCCC)''' were analyzed in the 1990's inare a seriesclass of publications from NASA's [[Jetforward Propulsionerror Laboratorycorrection]] (JPLFEC). codes Thishighly researchsuitable yieldedfor aturbo form(iterative) ofdecoding. turbo-like serialData concatenatedto codesbe thattransmitted 1)over werea iterativelynoisy ('turbo')channel decodablemay withfirst reasonablebe complexity,encoded andusing 2)an gaveSCCC errorand correctionupon performancereception comparableerrors withintroduced theduring [[turbotransmission codes]].may be Thecorrected analysisvia ofrepeated SCCCsdecoding wasand spawned[de]interleaving in part byof the earlierreceived discoverysymbols. of [[turbo codes]] in 1993.

SCCC's were analyzed in the 1990's in a series of publications from NASA's [[Jet Propulsion Laboratory]] (JPL). This research yielded a form of turbo-like serial concatenated codes that 1) were iteratively ('turbo') decodable with reasonable complexity, and 2) gave error correction performance comparable with the [[turbo codes]]. The analysis of SCCCs was spawned in part by the earlier discovery of [[turbo codes]] in 1993.

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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The SCCC decoder includes two soft-in-soft-out (SISO) decoders and an interleaver. While shown as separate units, the two SISO decoders may share all or part of their circuitry. The SISO decoding may be done is serial or parallel fashion, or some combination thereof. The SISO decoding is typically done using [[Maximum a posteriori]] (MAP) decoders using the [[BCJR]] algorithm.

== RSC Codes ==

[[File:Two-state_RSC_code.png|thumb|340px|none|Img. 3. Two-state recursive systematic convolutional (RSC) code. Also called an 'accumulator.' Useful for LDPC codes and inner constituent code for serial concatenated convolutional codes (SCCCs).]]

[[File:Four-state_RSC_code.png|thumb|340px|none|Img. 4. Four-state RSC code. Useful for SCCCs.]]

[[File:Sixteen-state_RSC_code.png|thumb|340px|none|Img. 5. Sixteen-state RSC code. Useful for low error rate turbo codes for applications such as satellite links. Suitable as outer code for SCCCs.]]

== Performance ==