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Keywords
(10)
Automorphism Group
Bch Code
Binary Erasure Channel
Block Codes
Cyclic Code
Hamming Code
Iterative Decoding
Lower and Upper Bound
Message Passing
Maximum Likelihood
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Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes,10.1109/TIT.2008.2006456,IEEE Transactions on Informati
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Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes
(
Citations: 7
)
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Thorsten Hehn
,
Olgica Milenkovic
,
Stefan Laendner
,
Johannes B. Huber
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the tradeoff between performance and complexity of
iterative decoding
for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovasz's local lemma (LLL) and Bonferronitype inequalities, and specialize them for codes with cyclic paritycheck matrices. Based on the observed properties of paritycheck matrices with good stopping redundancy characteristics, we develop a novel decoding technique, termed
automorphism group
decoding, that combines iterative
message passing
and permutation decoding. We also present bounds on the smallest number of permutations of an
automorphism group
decoder needed to correct any set of erasures up to a prescribed size. Simulation results demonstrate that for a large number of algebraic codes, the performance of the new decoding method is close to that of maximumlikelihood (ML) decoding.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 54, no. 12, pp. 53085331, 2008
DOI:
10.1109/TIT.2008.2006456
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Citation Context
(3)
...Another closely related approach was described in [11], where a simple simulationbased study was performed using randomly chosen paritycheck matrices of the [24,
12
, 8] extended Golay code...
...The approach followed in this paper draws upon the prior work of the authors on BEC decoding [
12
] and introduces a novel decoding method that operates in parallel and iterative fashion on a collection of paritycheck matrices...
...For cyclic algebraic codes, we proved in a companion paper [
12
] that paritycheck matrices that consist of cyclic shifts of carefully chosen cogs offer excellent stopping set properties...
...illustrate our findings only on the [24,
12
, 8] extended Golay...
...We use �� to denote the number of parallel BP decoders in the MBBP architecture. A. The [24,
12
, 8] Extended Golay Code...
...The [24,
12
, 8]extended Golay code is self dual and contains 759 codewords of minimum weight 8. This set of codewords can be partitioned into 33 cyclic orbits...
...For the 24th row of the paritycheck matrix, we use the allone codeword: this codeword preserves the stopping set distribution of the 23 × 24 matrix, and is the only reasonable parity check of the [24,
12
, 8] extended Golay code invariant under all affine permutations...
...Fig. 2. Performance comparison for the [24,
12
, 8] extended Golay code using �� ℓ, ℓ ∈ℱ 1, ℱ2, ℱ3...
...NUMBER OF STOPPING SETS FOR THE [24,
12
, 8] EXTENDED GOLAY CODE, �� ℓ, cog ℓ ∈ℱ �� , �� =1 ,..., 3...
Thorsten Hehn
,
et al.
Multiplebases beliefpropagation decoding of highdensity cyclic code...
...In order to mitigate this problem, one may resort to the use of redundant paritycheck matrices, i.e., matrices that contain more than n − k rows, although they have rowrank equal to n − k. Examples of the use of redundant paritycheck matrices for signaling over the binary erasure channel can be found in [6], [4], [17], [
18
]...
Stefan Laendner
,
et al.
The Trapping Redundancy of Linear Block Codes
...Several authors [2], [3], [4], [5], [
6
] presen ted pioneering work on the binary erasure channel (BEC) and provided results on the number of redundant paritycheck equations required to prevent certain decoder failures...
Thorsten Hehn
,
et al.
MBBP for improved iterative channel decoding in 802.16e WiMAX systems
References
(23)
The Stopping Redundancy Hierarchy of Cyclic Codes
(
Citations: 10
)
Thorsten Hehn
,
Stefan Laendner
,
Olgica Milenkovic
,
Johannes B. Huber
Published in 2006.
Stopping and dead  end se t enumerators for binary Hamming codes
(
Citations: 6
)
J. Weber
,
K. Abdel Ghaffar
Published in 2005.
On the hardness of approximating stopping and trapping sets
(
Citations: 7
)
Andrew McGregor
,
Olgica Milenkovic
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 56, no. 4, pp. 16401650, 2010
Finitelength analysis of lowdensity paritycheck codes on the binary erasure channel
(
Citations: 375
)
Changyan Di
,
David Proietti
,
Ì. Emre Telatar
,
Thomas J. Richardson
,
Rüdiger L. Urbanke
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 48, no. 6, pp. 15701579, 2002
On decoding of lowdensity paritycheck codes over the binary erasure channel
(
Citations: 62
)
Hossein Pishronik
,
Faramarz Fekri
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 20, no. 3, pp. 439454, 2004
Sort by:
Citations
(7)
Stopping Set Distributions of Some Reed–Muller Codes
Yong Jiang
,
ShuTao Xia
,
FangWei Fu
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 57, no. 9, pp. 60786088, 2011
Multiplebases beliefpropagation decoding of highdensity cyclic codes
(
Citations: 3
)
Thorsten Hehn
,
Johannes B. Huber
,
Olgica Milenkovic
,
Stefan Laendner
Journal:
IEEE Transactions on Communications  TCOM
, vol. 58, no. 1, pp. 18, 2010
Stopping Set Distributions of Some Linear Codes
(
Citations: 1
)
Yong Jiang
,
ShuTao Xia
,
FangWei Fu
Journal:
Computing Research Repository  CORR
, vol. abs/1003.0, 2010
Improved iterative decoding of LDPC codes from the IEEE WiMAX standard
Thorsten Hehn
,
Johannes B. Huber
,
Stefan Laendner
Published in 2010.
MultipleBases BeliefPropagation Decoding of HighDensity Cyclic Codes
(
Citations: 8
)
Thorsten Hehn
,
Johannes B. Huber
,
Olgica Milenkovic
,
Stefan Laendner
Journal:
Computing Research Repository  CORR
, vol. abs/0905.0, 2009