Material de lectura 14 - WCRL Seminar Series LDPC Codes An...

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WCRL Seminar Series LDPC Codes An Introduction to Low Density Parity Check (LDPC) Codes Jian Sun [email protected] Wireless Communication Research Laboratory Lane Dept. of Comp. Sci. and Elec. Engr. West Virginia University June 3, 2003 West Virginia University 1
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WCRL Seminar Series LDPC Codes Outline 1. History of LDPC codes 2. Properties of LDPC codes 3. Basics of LDPC codes Encoding of LDPC codes Iterative decoding of LDPC codes Simplified approximations of LDPC decoders 4. Applications of LDPC codes June 3, 2003 West Virginia University 2
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WCRL Seminar Series LDPC Codes Features of LDPC Codes Approaching Shannon capacity For example, 0.3 dB from Shannon limit Irregular LDPC code with code length 1 million. (Richardson:1999) An closer design from (Chung:2001), 0.0045 dB away from capapcity Good block error correcting performance Low error floor The minimum distance is proportional to code length Linear decoding complexity in time Suitable for parallel implementation June 3, 2003 West Virginia University 3
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WCRL Seminar Series LDPC Codes History of LDPC Codes Invented by Robert Gallager in his 1960 MIT Ph. D. dissertation. Long time being ignored due to 1. Requirement of high complexity computation 2. Introduction of Reed-Solomon codes 3. The concatenated RS and convolutional codes were considered perfectly suitable for error control coding. Rediscovered by MacKay(1999) and Richardson/Urbanke(1998). June 3, 2003 West Virginia University 4
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WCRL Seminar Series LDPC Codes Foundamentals of Linear Block Codes The structure of a code is completely described by the generator matrix G or the parity check matrix H . The capacity of correcting symbol errors in a codeword is determined by the minimum distance ( d min ). d min is the least weight of the rows in G . d min is the least number of columns in H that sum up to 0 . Example: (7, 4) Hamming code G = 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 H = 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 June 3, 2003 West Virginia University 5
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WCRL Seminar Series LDPC Codes Properties of LDPC Codes H is sparse. Very few 1’s in each row and column. Expected large minimum distance. Regular LDPC codes – H contains exactly W c 1’s per column and exactly W r = W c ( n/m ) 1’s per row, where W c << m . The above definition implies that W r << n . W c 3 is necessary for good codes.
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