What is the corresponding sequence of bits in the AWGN channel?

Assume a codeword w = (w1, w2, . . . , wN ) is transmitted over an AWGN channel with zero mean and variance N0/2 using BPSK signaling and let y = (y1, y2, . . . , yN ) be the corresponding received sequence.

What is the number of decoders that are used to decode the rows?

After both row (column) decoders finish decoding all the rows (columns), the most reliable parts of them are combined and the resulting extrinsic matrix for the next iteration is transmitted to both column (row) decoders.

Open AccessJournal Article10.1109/TCOMM.2004.841982

Shuffled iterative decoding

Juntan Zhang, +1 more

- 07 Mar 2005

- IEEE Transactions on Communications

- Vol. 53, Iss: 2, pp 209-213

396

TL;DR: Simulations show that the new schedules of iterative decoding of low-density parity-check codes and turbo codes offer better performance/complexity tradeoffs, especially when the maximum number of iterations has to remain small.

Abstract: Shuffled versions of iterative decoding of low-density parity-check codes and turbo codes are presented. The proposed schemes have about the same computational complexity as the standard versions, and converge faster. Simulations show that the new schedules offer better performance/complexity tradeoffs, especially when the maximum number of iterations has to remain small.

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1. What are the contributions in "Replica shuffled iterative decoding" ?

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2. What is the disadvantage of the parallel turbo decoding?

Although the parallel turbo decoding reduces the decoding delay of serial decoding by half, the extrinsic messages are not taken advantage of as soon as they become available, because the extrinsic messages are delivered to component decoders only after each iteration is completed.

3. What is the disadvantage of the parallel turbo decoding scheme?

The decoding approach proposed in [3] operates in serial mode, i.e., the component decoders take turns generating the extrinsic values of the estimated information symbols, and each component decoder uses the extrinsic messages delivered by the last component decoder as the a priori values of the information symbols.

4. What is the simplest way to decode a two-dimension turbo product code?

ITERATIVE DECODING OF TURBO PRODUCT CODESA two-dimension turbo product code (TPC) can be denoted as C1 ⊗ C2, where C1 and C2 are two linear block codes.

Fig. 4. Replica parallel decoder (one iteration)

Fig. 1. Bit error performance of 2-component turbo code with interleaver size 16384, for standard parallel, plain shuffled and replica shuffled decodings.

Fig. 5. Procedure of replica parallel decoder

Fig. 3. Error performance for iterative decoding of the (16200, 7200) irregular LDPC code.

Fig. 6. Performance of TPC (64, 57, 4)2 with parallel and replica parallel decoders.

Fig. 2. Error performance for iterative decoding of the (8000, 4000)(3, 6) LDPC code with group shuffled BP algorithm, for G = 1, 2, 8, 100, 8000 and at most 10 iterations.

Citations

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References

•Book

Low-Density Parity-Check Codes

Robert G. Gallager

- 01 Jan 1963

TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.

...read moreread less

12.7K

•Journal Article

Optimal decoding of linear codes for minimizing symbol error rate

L. R. Bahl

- 01 Jan 1974

- IEEE Transactions on Information Theory

TL;DR: The general problem of estimating the a posteriori probabilities of the states and transitions of Markov source observed through a discrete memoryless channel is considered.

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6.8K

Journal Article•10.1109/TIT.1974.1055186

Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)

Lalit R. Bahl, +3 more

- 01 Mar 1974

- IEEE Transactions on Information Theory

TL;DR: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered and an optimal decoding algorithm is derived.

...read moreread less

5.1K

Journal Article•10.1109/18.748992

Good error-correcting codes based on very sparse matrices

David J. C. MacKay

- 29 Jun 1997

TL;DR: It is proved that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit, and experimental results for binary-symmetric channels and Gaussian channels demonstrate that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved.

...read moreread less

4.1K

Journal Article•10.1109/26.539767

Near optimum error correcting coding and decoding: turbo-codes

Claude Berrou, +1 more

- 01 Oct 1996

- IEEE Transactions on Communications

TL;DR: A new family of convolutional codes, nicknamed turbo-codes, built from a particular concatenation of two recursive systematic codes, linked together by nonuniform interleaving appears to be close to the theoretical limit predicted by Shannon.

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3.1K

Shuffled iterative decoding

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Most frequently asked questions

1. What are the contributions in "Replica shuffled iterative decoding" ?

2. What is the disadvantage of the parallel turbo decoding?

3. What is the disadvantage of the parallel turbo decoding scheme?

4. What is the simplest way to decode a two-dimension turbo product code?

5. What is the corresponding sequence of bits in the AWGN channel?

6. What is the number of decoders that are used to decode the rows?

Figures

Citations

Suppressing quantum errors by scaling a surface code logical qubit

Low-complexity decoding for non-binary LDPC codes in high order fields

Low density parity check decoder for regular LDPC codes

Experimental quantum key distribution certified by Bell's theorem

A Survey on FEC Codes for 100 G and Beyond Optical Networks

References

Low-Density Parity-Check Codes

Optimal decoding of linear codes for minimizing symbol error rate

Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)

Good error-correcting codes based on very sparse matrices

Near optimum error correcting coding and decoding: turbo-codes

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