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Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. C H A P T E R 15 ERROR CORRECTING CODES.

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Presentation on theme: "Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. C H A P T E R 15 ERROR CORRECTING CODES."— Presentation transcript:

1 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. C H A P T E R 15 ERROR CORRECTING CODES

2 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.1 Encoder for linear block codes.

3 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.2 Encoder for systematic cyclic code.

4 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.3 Performance comparison of coded (doshed) and uncoded (solid) systems.

5 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.4 Burst error detection.

6 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.5 Convolutional encoder.

7 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.6 Code tree for the encoder in Fig

8 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.7 (a) State and (b) state transition diagram of the encoder in Fig

9 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.8 Trellis diagram for the encoder in Fig

10 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure 15.9 A recursive systematic convolutional (RSC) encoder.

11 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Viterbi decoding example in Fig. 15.5: (a) stage 1 and 2; (b) stage 3; (c) stage 4; (d) stage 5; (e) stage 6.

12 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Continued

13 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Continued

14 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Convolutional encoder.

15 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Code tree for the encoder in Fig

16 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Setting the threshold in sequential decoding.

17 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Trellis diagram of a Hamming (7, 4, 3) code with parity check matrix of Eq. (15.34).

18 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure A block (nonrandom) interleaver for correcting random and burst errors.

19 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Product code formed by two encoders separated by a block interleaver.

20 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Concatenated code with a nonbinary outer code and a binary inner code.

21 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Block diagram of Chase soft-decoding algorithms.

22 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Block diagram of Chase soft decoding algorithms.

23 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Parallel concatenated turbo code: (a) rate 1/3 turbo encoder; (b) Implementation of recursive systematic convolutional (RSC) encoder g 1 (D)=1+D+D 4, g 2 (D)=1+ D 2 +D 3 +D 4.

24 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Exchange of extrinsic information between two component CJR decoders for iterative turbo decoding.

25 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure The decoding performance of a rate 1/2 Turbo code is shown to be very close to the theoretical limit. (Reproduced with copyright permission from IEEE from Ref. 14.)

26 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Tanner graph of the (7, 4, 3) Hamming code.

27 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Message passing in the sum-product algorithm.

28 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure Comparison of bit error rates of uncoded polar signaling transmission and polar signaling transmission of Hamming (7, 4) encoded [(dashed) and uncoded (solid) message bits.

29 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P

30 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P

31 Modern Digital and Analog Communication Systems Lathi Copyright © 2009 by Oxford University Press, Inc. Figure P


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