M.Sc Thesis | |

M.Sc Student | Assaf Uri |
---|---|

Subject | Aspects in Soft Decision Decoding of Reed-Solomon Codes |

Department | Department of Electrical and Computer Engineering |

Supervisor | DR. Shraga Bross |

- Turbo Product Codes received some attention in recent papers, and were applied mainly for binary codes and binary signaling.

Kaneko Algorithm

- If utilized for decoding low-rate codes, The performance of Kaneko algorithm greatly depends on the practical limit of test patterns. Therefore, for complexity reasons, Kaneko algorithm is relevant mainly for high-rate codes.

- We propose a sub-optimal symbol reliability which utilizes a predetermined parameter instead of the noise variance, with minimal impairment to the decoder’s performance.

- In order to avoid useless decoding iterations, we suggest to maintain a storage of all the decoded codewords. We discuss the complexity of such procedure and the situations at which it may be beneficial.

Koetter-Vardy Algorithm

- The complexity of K-V algorithm is found to be *O*(*cost*^{3}).
Since the complexity is independent of the code rate, K-V algorithm is
attractive mainly for low-rate codes.

- We prove a surprising flaw in K-V algorithm, i.e. at low SNR and high-rate codes K-V algorithm may fail to output the transmitted codeword even if there are no errors in the received codeword at all.

- We discuss
choice of decoding parameters, mainly *cost*. The lack of monotony with
respect to *cost* is discussed.

Turbo Product Codes

- Turbo product codes decoding algorithm is adjusted for RS codes and MPSK signaling.

- Turbo product code (TPC) with RS code as component codes and MPSK modulation outperforms standard Kaneko algorithm with similar code rate and complexity with only two full iterations.