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Error control coding for wireless communication technologies

Error control coding for wireless communication technologies. Background material for Hamming codes. EU-USA Atlantis Programme. FIT & Budapest University of Technology and Economics. An intuitive approach to coding gain. Given a BSC with . a nd a required level of QoS.

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Error control coding for wireless communication technologies

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  1. Errorcontrolcodingforwireless communicationtechnologies Backgroundmaterialfor Hamming codes EU-USA Atlantis Programme FIT & Budapest University of Technology and Economics

  2. An intuitiveapproachtocodinggain Given a BSC with and a required level of QoS , design a code which can achieve 1. Evaluate if n-k is too large or if then there is no solution with correcting only single errors (then you need a more powerful code capable of correcting more than a single error) 2. Construct the parity check matrix obeying the rules: (i) each column vector is different; (ii) none of the column vector is the all-zero vector; (iii) the code is systematic 3. Implement the coding scheme Array of matchingsystemsor LUT u H G Trunc BSC with

  3. Designing an errorcorrectingcodefor a BSC (BER=0.001) toachieve BER’=0.00001 Step 1: indetifying the code parameters n=7, k=4

  4. inlogarithmicscale BER vs. SNR This gain – manifesting itself as a virtual increase in signal power - has been achieved by algorithmic means !!! Instead of real signal power increase, QoS was achieved by error control coding. Original BER BER’ achieved by coding Coding gain 2 db

  5. Correcting every double error ?

  6. Error detection with matching systems Mathcing system Mathcing system e u v s Mathcing system H G BSC with e Mathcing system u c Trunc Mathcing system Mathcing system Mathcing system

  7. Homeworkassignment Design thecodingscheme of a linearbinarycodewithgeneratormatrix Determinethecodewords GivetheparitycheckmatrixH Determinetheerrorgroups (givethe Standard Array of thecode) Determinethesyndromedecodingtable Evaluatetheprobability of theerrorvectorsoccuringinthesyndromedecodingtable Givethescheme of thesystem Describeallthebinaryvectorsintheschemewhensendingallthepossiblemessagevectors (ineachcaseslettheerrorvectorhave 1 inthefirstcomponent and rest of thecomponentsarezeros).

  8. Helpforthehomework

  9. Helpforthehomework Pick areknown

  10. Suggestedreadings D. Costello: Errorcontrolcodes, Wiley, 2005, Chapter 3

  11. ExpectedQuizquestion Given a generator matrix of a linear binary systematic code, determine the error group belonging to a given error vector Give the parity check matrix of the C(15,11) Hamming code

  12. Thank you for your attention !

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