Performance Limits of Compound Codes with Symbol-Based Iterative Decoding

H. Sawaya, S. Vialle, Joseph Boutros, G. Zémor

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study the performance limit of concatenated codes based on binary constituent codes, under symbol-based iterative decoding. Although the results exposed herein are valid for any compound code built from both block and convolutional codes, we mainly focus on parallel turbo codes based on binary convolutional codes. The performance limit is found by evaluating the probability density function of the APP decoder output via a general propagation formula governing the density law through iterations. We propose also a second method to estimate the signal-to-noise ratio limit where the a priori density is assumed to be gaussian distributed. The results show that a gain in performance is achieved when bit nodes are combined into quaternary symbol nodes. For example, with a rate 1/2 Turbo code and a rate 2/3 binary RSC constituent, the minimal attainable signal-to-noise ratio per bit is 0.31 dB which is 0.13 dB away from the capacity of the AWGN channel with BPSK modulation.

Original languageEnglish
Pages (from-to)433-443
Number of pages11
JournalElectronic Notes in Discrete Mathematics
Volume6
DOIs
Publication statusPublished - 1 Apr 2001
Externally publishedYes

Fingerprint

Iterative Decoding
Iterative decoding
Turbo codes
Convolutional codes
Turbo Codes
Signal to noise ratio
Convolutional Codes
Binary Code
Concatenated codes
Binary codes
Block codes
Probability density function
Block Codes
Modulation
Vertex of a graph
Valid
Propagation
Binary
Iteration
Output

Keywords

  • Belief propagation
  • Concatenated codes
  • Soft-input soft-output decoding
  • Turbo codes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Performance Limits of Compound Codes with Symbol-Based Iterative Decoding. / Sawaya, H.; Vialle, S.; Boutros, Joseph; Zémor, G.

In: Electronic Notes in Discrete Mathematics, Vol. 6, 01.04.2001, p. 433-443.

Research output: Contribution to journalArticle

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