Transcript chapte r 15 - Oxford University Press

C H A P T E R
15
ERROR CORRECTING CODES
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Figure 15.1 Encoder for linear block codes.
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Figure 15.2 Encoder for systematic cyclic code.
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Figure 15.3 Performance comparison of coded (doshed) and uncoded (solid) systems
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Figure 15.4 Burst error detection.
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Figure 15.5 Convolutional encoder.
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Figure 15.6 Code tree for the encoder in Fig. 15.5.
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Figure 15.7 (a) State and (b) state transition diagram of the encoder in Fig. 15.5.
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Figure 15.8 Trellis diagram for the encoder in Fig. 15.5.
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Figure 15.9 A recursive systematic convolutional (RSC) encoder.
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Figure 15.10 Viterbi decoding example in Fig. 15.5: (a) stage 1 and
2; (b) stage 3; (c) stage 4; (d) stage 5; (e) stage 6.
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Figure 15.10 Continued
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Figure 15.10 Continued
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Figure 15.11 Convolutional encoder.
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Figure 15.12 Code tree for the encoder in Fig. 15.11.
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Figure 15.13 Setting the threshold in sequential decoding
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Figure 15.14 Trellis diagram of a Hamming (7, 4, 3) code with
parity check matrix of Eq. (15.34).
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Figure 15.15 A block (nonrandom) interleaver for correcting random and burst errors.
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Figure 15.16 Product code formed by two encoders separated by a block interleaver.
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Figure 15.17 Concatenated code with a nonbinary outer code and a binary inner code.
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Figure 15.18 Block diagram of Chase soft-decoding algorithms.
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Figure 15.19 Block diagram of Chase soft decoding algorithms.
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Figure 15.20 Parallel concatenated turbo code: (a) rate 1/3 turbo encoder;
(b) Implementation of recursive systematic convolutional (RSC) encoder
g1(D)=1+D+D4, g2(D)=1+ D2+D3+D4.
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Figure 15.21 Exchange of extrinsic information between two component CJR
decoders for iterative turbo decoding.
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Figure 15.22 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.)
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Figure 15.23 Tanner graph of the (7, 4, 3) Hamming code.
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Figure 15.24 Message passing in the sum-product algorithm.
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Figure 15.25 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.
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Figure P.15.5-2
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Figure P.15.5-3
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Figure P.15.5-5
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