Soft-decision decoding of linear block codes based on ordered statistics

@article{Fossorier1995SoftdecisionDO,
  title={Soft-decision decoding of linear block codes based on ordered statistics},
  author={Marc P. C. Fossorier and Shu Lin},
  journal={IEEE Trans. Inf. Theory},
  year={1995},
  volume={41},
  pages={1379-1396}
}
Presents a novel approach to soft decision decoding for binary linear block codes. The basic idea is to achieve a desired error performance progressively in a number of stages. For each decoding stage, the error performance is tightly bounded and the decoding is terminated at the stage where either near-optimum error performance or a desired level of error performance is achieved. As a result, more flexibility in the tradeoff between performance and decoding complexity is provided. The decoding… 

Figures from this paper

Computationally efficient soft-decision decoding of linear block codes based on ordered statistics
TLDR
It is shown that two-stage decoding with the algorithm of Fossorier and Lin offers a large variety of choices, since the reprocessing order of each stage can be determined independently.
Fast Soft Decision Decoding of Linear Block Codes Using Partial Syndrome Search
Ordered statistics-based decoding (OSD) is a soft decision decoding algorithm for linear block codes, yielding near maximum likelihood decoding performance. The OSD algorithm first sorts the received
New Approach to Order Statistics Decoding of Long Linear Block Codes
TLDR
The ALMLT algorithm outperforms the OSD(2) algorithm as illustrated by decoding the binary image of the (255, 239,17) RS code and has a lower mean number of tests, while using the same stopping criterion.
Ordered statistics-based list decoding techniques for linear binary block codes
TLDR
Numerical examples show that, in some cases, the proposed decoding schemes are superior to the original OSD in terms of both the bit error rate performance as well as the decoding complexity.
On the reliability-order-based decoding algorithms for binary linear block codes
TLDR
It is shown that any bounded-distance ROBDA is asymptotically optimal: the ratio between the probability of decoding error of a bounded- distance ROBDA and that of the maximum-likelihood (ML) decoding approaches 1 when the signal-to-noise ratio (SNR) approaches infinity.
Title On the reliability-order-based decoding algorithms for binary linear block codes
TLDR
It is shown that any bounded-distance ROBDA is asymptotically optimal: the ratio between the probability of decoding error of a bounded- distance ROBDA and that of the maximum-likelihood (ML) decoding approaches 1 when the signal-to-noise ratio (SNR) approaches infinity.
Iterative soft-decision decoding of linear block codes
TLDR
The authors show that for linear block codes defined over extensions of GF(2) a variant of the sub-optimal soft-decision Dorsch (1974) algorithm offers very good performance with low complexity and is exploited in an iterative decoding scheme for product codes.
NOMA Joint Decoding based on Soft-Output Ordered-Statistics Decoder for Short Block Codes
TLDR
A low-complexity soft-output ordered-statistics decoding (LC-SOSD) based on a decoding stopping condition, derived from approximations of the a-posterior probabilities of codeword estimates, which has the similar mutual information transform property to the original SOSD with a significantly reduced complexity.
Efficient decoding of block turbo codes
TLDR
The proposed algorithm can avoid a number of unnecessary hard-decision decoding operations by imposing two conditions on the Chase algorithm and provide a trade-off between the performance and the computational complexity of BTCs by properly selecting a decoding parameter.
Low-Complexity Decoding of Block Turbo Codes Based on the Chase Algorithm
TLDR
A low-complexity decoding algorithm for BTCs that first checks whether an algebraic hard-decision decoder outputs a codeword for a given decoder input vector, and then adaptively applies one of the two estimation rules.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 29 REFERENCES
Soft decision decoding of linear block codes based on ordered statistics
  • M. Fossorier, Shu Lin
  • Computer Science
    Proceedings of 1994 IEEE International Symposium on Information Theory
  • 1994
TLDR
The ordered statistics of the noise after ordering are derived and a simple algorithm based on these ordered statistics is developed that applies to any linear block code, does not require any data storage and is well suitable for parallel processing.
First-order approximation of the ordered binary-symmetric channel
TLDR
A tight approximation of Pe(i; N), the probability that the hard decision associated with the ith symbol of the ordered sequence is in error, is derived and the fully connected 2/sup N/-state BSC representing the channel after ordering is simplified by N independent time-shared 2- state BSCss.
Soft-decision decoding of binary linear block codes based on an iterative search algorithm
TLDR
Numerical results show that the proposed decoding scheme achieves either practically optimal performance or a performance only a fraction of a decibel away from the optimal maximum-likelihood decoding with a significant reduction in decoding complexity compared with the Viterbi decoding based on the full trellis diagram of the codes.
Efficient priority-first search maximum-likelihood soft-decision decoding of linear block codes
The authors present a novel and efficient maximum-likelihood soft-decision decoding algorithm for linear block codes. The approach used here converts the decoding problem into a search problem
Class of algorithms for decoding block codes with channel measurement information
  • D. Chase
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1972
TLDR
It is shown that as the signal-to-noise ratio (SNR) increases, the asymptotic behavior of these decoding algorithms cannot be improved, and computer simulations indicate that even for SNR the performance of a correlation decoder can be approached by relatively simple decoding procedures.
Simplified correlation decoding by selecting possible codewords using erasure information
TLDR
A new algorithm for soft-decision decoding is presented, simplifying the correlation scheme by selecting certain codewords and decreasing decoding complexity by using erasure information.
Maximum likelihood soft decoding of binary block codes and decoders for the Golay codes
TLDR
A binary multiple-check generalization of the Wagner rule is presented, and two methods for its implementation, one of which resembles the suboptimal Forney-Chase algorithms, are described.
Closest coset decoding of |u|u+v| codes
  • F. Hemmati
  • Computer Science
    IEEE J. Sel. Areas Commun.
  • 1989
TLDR
The algorithm is a suboptimum decoding scheme and, in the range of signal-to-noise-power-density ratios of interest, its BER performance is only a few tenths of a dB inferior to the performance of the MLD for the codes examined.
An efficient maximum-likelihood-decoding algorithm for linear block codes with algebraic decoder
TLDR
Computer simulation results indicate, for some signal-to-noise ratios (SNR), that the proposed soft decoding algorithm requires less average complexity than those of the other two algorithms, but the performance of the algorithm is always superior to those ofthe other two.
Efficient maximum likelihood decoding of linear block codes using a trellis
  • J. Wolf
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1978
It is shown that soft decision maximum likelihood decoding of any (n,k) linear block code over GF(q) can be accomplished using the Viterbi algorithm applied to a trellis with no more than q^{(n-k)}
...
1
2
3
...