By Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
ISBN-10: 3319511025
ISBN-13: 9783319511023
ISBN-10: 3319511033
ISBN-13: 9783319511030
This e-book discusses either the idea and functional purposes of self-correcting info, generally called error-correcting codes. The functions integrated display the significance of those codes in a variety of daily applied sciences, from smartphones to safe communications and transactions. Written in a without difficulty comprehensible sort, the e-book provides the authors’ twenty-five years of analysis equipped into 5 parts:
Part I is worried with the theoretical functionality possible through the use of mistakes correcting codes to accomplish communications potency in electronic communications systems.
Part II explores the development of error-correcting codes and explains different households of codes and the way they're designed. strategies are defined for generating the superior codes.
Part III addresses the research of low-density parity-check (LDPC) codes, essentially to calculate their preventing units and low-weight codeword spectrum which determines the functionality of those codes.
Part IV bargains with decoders designed to gain optimal performance.
Part V describes purposes which come with mixed blunders correction and detection, public key cryptography utilizing Goppa codes, correcting mistakes in passwords and watermarking.
This publication is a important source for somebody attracted to error-correcting codes and their purposes, starting from non-experts to pros on the vanguard of analysis of their field.
This e-book is open entry below a CC via 4.0 license.
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Extra info for Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Example text
In order to use a standard array, the coset leaders of all the cosets of a code must be known. We illustrate complete decoding with an example. 2 Hard Decision Performance 27 Coset Leaders 0000000 1000111 0101011 0011101 1101100 0110110 1011010 1110001 0000001 0000010 0000100 0001000 0010000 0100000 1000000 1000110 1000101 1000011 1001111 1010111 1100111 0000111 0101010 0101001 0101111 0100011 0111011 0001011 1101011 0011100 0011111 0011001 0010101 0001101 0111101 1011101 1101101 1101110 1101000 1100100 1111100 1001100 0101100 0110111 0110100 0110010 0111110 0111110 0010110 1110110 1011011 1011000 1011110 1010010 1001010 1111010 0011010 1110000 1110011 1110101 1111001 1100001 1010001 0110001 0000011 0000110 0001100 0011000 0001010 0010100 0010010 0001110 1000100 1000001 1001011 1011111 1001101 1010011 1010101 1001001 0101000 0101101 0100111 0110011 0100001 0111111 0111001 0100101 0011110 0011011 0010001 0000101 0010111 0001001 0001111 0010011 1101111 1101010 1100000 1110100 1100110 1111000 1111110 1100010 0110101 0110000 0111010 0101110 0111100 0100010 0100100 0111000 1011001 1011100 1010110 1000010 1010000 1001110 1001000 1010100 1110010 1110111 1111101 1101001 1111011 1100101 1100011 1111111 Fig.
25) The evaluation of the average probability of decoder error for quantised soft decisions, pC Q is given, as before by averaging over all codes and rearranging the order of summation pC Q < 1 2n2k 2n2 k n i=1 d=0 n! d! 26) Simplifying n pC Q < d=0 n! d! 30) giving n pC Q < d=0 n! d! 32) and poverall Q < 2k 2n n d=0 n! d! 33) When three-level quantisation is used for the received signal plus noise, a threshold, vthr esh is defined, whereby, if the magnitude of the received signal plus noise is less than vthr esh , an erasure is declared otherwise a hard decision is made.
A simple derivation of the coding theorem and some applications. IEEE Trans. Inf. Theory 11(1), 459–470 (1960) 5. : Code Tables: Bounds on the parameters of various types of codes, http://www. de (2007) 6. : Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2003). ISBN 0 521 78280 5 7. : On spectra of BCH codes. IEEE Trans. Inf. Theory 41(3), 786–788 (1995) 8. : On the accuracy of the binomial approximation to the distance distribution of codes. IEEE Trans. Inf. Theory 41(5), 1472–1474 (1995) 9.
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications by Martin Tomlinson, Cen Jung Tjhai, Marcel A. Ambroze, Mohammed Ahmed, Mubarak Jibril
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