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Unformatted text preview: 1 EE522 Communications Theory Spring 2010 Instructor: Hwang Soo Lee Lecture #16 – Block Codes: Performance Evaluation and Tradeoffs 2 Announcements ¡ Handout: Lecture #16 Notes 3 Error Correction Codes ¡ Names: ¢ Error Correction Coding ¢ Channel Coding ¢ Forward Error Correction ¡ Channel coding provides a practical way to achieve performance which more nearly approaches theoretical capacity. ¡ Channel coding trades bandwidth efficiency for energy efficiency. 4 Encoding and Decoding of Error Correction Codes ¡ Encoding operation usually easy ¢ can be thought of in terms of parity checks. ¡ Decoding operation is usually complex. ¡ Many good practical codes have been developed for use in communication systems. We focus on block codes first. 5 Terminology for Block Codes ¡ k = number of input symbols (usually bits). ¡ n = number of output symbols (usually bits). ¡ is the code rate. ¡ is the minimum distance. ¡ is the error correcting capability. ¡ Codes can be classified as linear, systematic, and cyclic. 6 Encoding of Block Codes ¡ Encoding can be viewed in terms of adding parity bits to the information bits. ¡ This operation can be described in terms of matrix multiplication: where = vector of k input data bits = codeword of n output data bits = k x n Generator Matrix ¡ Only required kn multiplies and additions. 7 The Generator Matrix G ¡ Let the message bits by a vector ¡ Then any linear code can be represented by a Generator Matrix ¡ The row vectors gform a linearly independent basis for the code C 8 Encoding with a Generator Matrix ¡ The transmitted codeword is generated by the equation ¢ C=mG , where ¢ m is a k element row vector ¢ c is an n element row vector ¢ note that c can be expressed as a linear combination of row vectors 9 Systematic Representation of...
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This note was uploaded on 11/23/2010 for the course EE EE522 taught by Professor Eeehwangsoo during the Spring '10 term at Korea Advanced Institute of Science and Technology.
 Spring '10
 EeeHwangsoo

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