### 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 language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 6 |

Publication status | Published - 1 Dec 2000 |

Externally published | Yes |

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### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*6*, 1-11.