以孫子定理碼構成的乘積碼之性能

Abstract

孫子定理碼(Chinese Remainder Theorem Codes)的發展是源自孫子定理(Chinese Remainder Theorem)，故命名之。本論文主旨在探討以孫子定理碼構成的乘積碼的性能。因孫子定理(n, k)碼和RS碼一樣，擁有最遠的最小距離碼(maximum-minimum distance code)的性質，所以，其更錯能力為 。 孫子定理碼本來就有可任意調整長度的特性，因為這個優點，所以嘗試以孫子定理碼構成乘積碼(product codes)，並探討其特性。又因孫子定理碼的性質，我們考慮兩種不同的編碼方式，即系統碼(systematic code)和非系統碼(nonsystematic code)。為了提升性能，我們也利用刪去解碼法(erasure control)。我們分別探討孫子定理乘積碼在白色高斯雜訊(AWGN)通道及瑞雷縗衰褪(flat Rayleigh fading)通道下的效能。我們模擬不同的解碼法的效能並同時和和部分的理論值作比較，最後我們提出一種實際可行的解碼設計建議。

Residue number systems and redundant residue number systems (RRNS) codes are derived and developed from the the Chinese Remainder Theorem (CRT). RRNS codes are thus also known as CRT codes. The purpose of this thesis is to examine the performance of product codes based on CRT codes. An (n,k) RRNS code is a maximum-minimum distance block code therefore possesses the same distance property as that of Reed-Solomom (RS) codes, yielding a t=(n-k)/2 error-correcting capability. As the code length of an RRNS code can be adaptively adjusted, it is suitable for use in applications that require incremental redundancy. We investigate some issues concerning the design of RRNS-based product codes. Because of the nature of RRNS codes, two different symbol mapping methods are considered, resulting in systematic and nonsystematic RRNS codes. To improve the performance, erasure decoding is also investigated in this thesis. The performance of product RRNS codes is evaluated by computer simulation under AWGN and flat Rayleigh fading. Some analytic performance bounds are also computed and compared with the simulated results. Finally we suggest some practical and efficient decoder design rules based on our findings.