Serial concatenated convolutional codes

Serial Concatenated Convolutional Codes

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

SCCC's typically include an inner code, an outer code, and a linking interleaver. A distinguishing feature of SCCC's is the use of a recursive systematic convolutional code (RSC code) as the inner code. RSC codes are also part of classic turbo codes. The RSC inner code provides the 'interleaver gain' for the SCCC, which is the source of the excellent performance of these codes.

Prior forms of serial concatenated codes typically did not use recursive inner codes. Additionally, the constituent codes used in prior forms of serial concatenated codes were generally too complex for reasonable soft-in-soft-out (SISO) decoding. SISO decoding is considered essential for turbo decoding.

Serial concatenated convolutional codes have not found wide spread commercial use, although they were proposed for communications standards such as DVB-S2. Nonetheless, the analysis of SCCC's has provided insight into the performance and bounds of all types of iterative decodable codes including turbo codes and LDPC codes.

US patent 6,023,783 covers some forms of SCCC's. This patent will expire on May 15, 2016.

History

Serial concatenated convolutional codes were first analyzed view 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. 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 "the use of a recursive convolutional inner encoder always yields an interleaver gain." 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. This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive systematic 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". 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

Fig 1 is an example of a SCCC.

• 
  Rate 1/2 SCCC Encoder

The encoder is comprised of a 16-state outer code and a 2-state inner code linked by an interleaver. The codes may be punctured to rates of 2/3 for the inner code and 3/4 for the outer code to give an overall SCCC rate of 1/2.

Example Decoder

An example of an interative SCCC decoder.

• 
  SCCC Turbo Decoder

The SCCC decoder includes two SISO decoders and an interleaver. The SISO decoding may be done is serial or parallel fashion, or some combination thereof.

Performance

SCCCs provide performance comparable to other iteratively decodable codes including turbo codes and LDPC codes. They are noted for having slightly worse performance at low SNR environments (i.e. worse waterfall region), but slightly better performance at higher SNR environments (i.e. lower error floor).

See also

• Convolutional code
• Viterbi algorithm
• Soft-decision decoding
• Interleaver
• BCJR algorithm
• Low-density parity-check code
• Turbo equalizer

External links

"Concatenated codes", Scholarpedia

"Concatenated Convolutional Codes and Iterative Decoding", Willian E. Ryan