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

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

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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

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).

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.

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.

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.

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

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

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.

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.

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.)

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

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

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.

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

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

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