پديد آورنده :
زارعي، مينا
عنوان :
كد گشايي سريع دسته اي از كدهاي باقي مانده مربعي بدون تشخيص سيندروم هاي ناشناخته
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده، [۷۶]ص.: مصور
استاد راهنما :
مرتضي اسماعيلي
واژه نامه :
انگليسي به فارسي
توصيفگر ها :
كد باقي مانده مربعي , كد گشايي تصميم سخت , سيندرم , سيندرم ناشناخته , آستانه
استاد داور :
علي زاغيان، رضا سبحاني
تاريخ ورود اطلاعات :
1397/02/26
چكيده انگليسي :
Fast Decoding of some of the Quadratic Residue Codes Without Determining the Unkonwn Syndromes Mina Zarei Mina zarei@math iut ac ir 2018 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mortaza Esmaeili emorteza@cc iut ac ir 2018 MSC 05C15 53C42 Keywords Quadratic residue hard desision decoding unkown syndrome threshold Abstract This thesis is an extension and generalization of the work done by Zhang Pengwei Li Yong Chang Hsin Chiu Liu Hongqing and Truon Trieu Kien In this thesis a hard decision HD scheme is presented to facilitate faster decoding of the quadratic residue codes with a code length lessthan or equal 71 In the new HD algorithm for any code the required known syndromes are calculated rst then using the Newton identities for each error cases error locator polynomials are written Sincefor 7 4 3 QR code and 17 9 5 QR code there are su ciently consecutive syndromes so the error locator polynomial is directly written For 23 12 7 QR code and 31 16 7 QR code for up to twoerrors there are su ciently consecutive syndromes so the error locator polynomial is directly written but corrects three errors with new di erent method The reliability based shift search algorithm can beutilized to decode weight 3 error patterns In other words a three error case can be decoded in termsof a two error case after inverting an incorrect bit of the received word The 41 21 9 QR code di res In this code for up to two errors there are su ciently consecutive syndromes so the error locatorpolynomial is directly written but corrects three and four errors with new di erent methods In thethree error case the new algorithm directly determines the coe cients of the error locator polynomialby eliminating unknown syndromes in Newton identities Subsequently the reliability based shift search algorithm can be utilized to decode weight 4 error patterns In other words a four error casecan be decoded in terms of a three error case after inverting an incorrect bit of the received word Inthe 47 24 11 QR code and 71 36 11 QR code for up to three errors there are su ciently consecutive
استاد راهنما :
مرتضي اسماعيلي
استاد داور :
علي زاغيان، رضا سبحاني
