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冗余余數(shù)系統(tǒng)低復雜度快速糾錯算法設計

肖翰珅,  胡劍浩,  馬上

肖翰珅, 胡劍浩, 馬上. 冗余余數(shù)系統(tǒng)低復雜度快速糾錯算法設計[J]. 電子與信息學報, 2015, 37(8): 1944-1949. doi: 10.11999/JEIT141454
引用本文: 肖翰珅, 胡劍浩, 馬上. 冗余余數(shù)系統(tǒng)低復雜度快速糾錯算法設計[J]. 電子與信息學報, 2015, 37(8): 1944-1949. doi: 10.11999/JEIT141454
Xiao Han-shen, Hu Jian-hao, Ma Shang. Low-complexity Error Correction Algorithms for Redundant Residue Number Systems[J]. Journal of Electronics & Information Technology, 2015, 37(8): 1944-1949. doi: 10.11999/JEIT141454
Citation: Xiao Han-shen, Hu Jian-hao, Ma Shang. Low-complexity Error Correction Algorithms for Redundant Residue Number Systems[J]. Journal of Electronics & Information Technology, 2015, 37(8): 1944-1949. doi: 10.11999/JEIT141454

冗余余數(shù)系統(tǒng)低復雜度快速糾錯算法設計

doi: 10.11999/JEIT141454 cstr: 32379.14.JEIT141454
  • 1.

    (清華大學數(shù)學科學系 北京 100084) ②(電子科技大學通信抗干擾技術國家級重點實驗室 成都 611731)

基金項目: 

國家自然科學基金(61101033, 61076096)，國家863計劃項目(2011AA010201)，清華大學自主科研計劃(20141081231)和國家高科技中央高校基本科研業(yè)務費(ZYGX 2011J118)

Low-complexity Error Correction Algorithms for Redundant Residue Number Systems

  • 1.

    (Department of Mathematics, Tsinghua University, Beijing 100084, China)

  • 2.

    (National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • 摘要: 余數(shù)系統(tǒng)由于具有增強傳輸信息在并行系統(tǒng)中魯棒性的優(yōu)勢，已被廣泛應用在無線局域網(wǎng)(WLAN)以及碼分多址通信技術(CDMA)等領域。而余數(shù)系統(tǒng)中的糾錯檢錯是保證傳輸數(shù)據(jù)可靠性和高效性的關鍵問題。該文根據(jù)有限環(huán)上剩余類的性質提出溢出判定定理，不重復判斷定理和唯一性區(qū)間搜索定理，并在此基礎上進一步提出采用模運算代替?zhèn)鹘y(tǒng)中國剩余定理進行快速恢復的單錯誤糾錯算法，將復雜度降低為O(k,r)；提出不重復判定糾錯算法；并對于一般錯誤情形，設計通過比較算子實現(xiàn)的搜索糾錯算法。其中搜索糾錯算法能直接實現(xiàn)系統(tǒng)最大糾錯能力，且避免依靠復雜模運算算子實現(xiàn)，系統(tǒng)吞吐率得以提高；與傳統(tǒng)算法相比，計算復雜度由多項式級降低至對數(shù)級。
    Abstract: Redundant Residue Number System (RRNS) is widely used in communication systems for WLAN (Wireless LAN) and CDMA (Code Division Multiple Access) etc. due to its strong ability to enhance robustness of information in parallel processing environments. Error detection and correction of RRNS is an important guarantee for information reliability in communication systems. The overflow detection theorem, the unique theorem, and the searching theorem are proposed and proved in the paper based on properties of residue classes in finite rings. With the theorems, a single-error-correction algorithm using modular operations with reduced complexityO(k,r) is proposed. The uniqueness test algorithm is proposed. Furthermore, for any general types of errors, the searching multiple-error-correction algorithm is proposed. The computational complexity of the searching multiple-error- correction algorithm is reduced from polynomial order to logarithmic order according to the analysis, and the method can reach the extreme correction capability efficiently with only comparison operations instead of complex modular arithmetic.
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出版歷程
  • 收稿日期:  2014-11-20
  • 修回日期:  2015-04-08
  • 刊出日期:  2015-08-19

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