Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel

Yu, Yun William; Chen, Wen; Wei, Lili

doi:10.1109/wcl.2012.050112.120297

Cited by 7 publications

(12 citation statements)

References 8 publications

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“…for the purpose of reducing the computational complexity [14], [15], [20]. Especially in certain cases, when the receiver receives a non-binary codeword from the binary input channels and only limited computational resources are available, the consideration of using binary decoders is natural and practical for a fast and correct information recovery.…”

Section: A Related Workmentioning

confidence: 99%

“…Especially in certain cases, when the receiver receives a non-binary codeword from the binary input channels and only limited computational resources are available, the consideration of using binary decoders is natural and practical for a fast and correct information recovery. However, the binary representation of a non-binary parity check matrix has numerous bit-level cycles, even if there is no symbol-level cycle [14], [20] in the non-binary parity check matrix. Thus, in [14], [15], the authors introduce the (punctured) extended binary representation for the non-binary LDPC code to solve this issue.…”

Section: A Related Workmentioning

confidence: 99%

“…When there is no symbol-level cycle, this representation will also be cycle-free. In [20], the authors propose a hybrid hard decision decoder particularly for the BEC which eliminates the local decoding cycles by introducing matrix inverse operations.…”

Section: A Related Workmentioning

confidence: 99%

“…The non-binary LDPC code C is a particular case ofC in the sense that F q ∼ = F p 2 and the non-zero entries in H can be represented by the powers of the companion matrix over F q [20], [22]- [24]. With a little abuse of the notation, in the following, we denote any binary parity check matrix over F 2 byH and any non-binary parity check matrix over F q by H. We also define diag(B 1 , B 2 , .…”

Section: A Binary Images For Non-binary Ldpc Codesmentioning

confidence: 99%

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Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

Chen

et al. 2014

IEEE Trans. Commun.

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In this paper, we consider the performance-optimized nonbinary low-density parity check code over general linear group, i.e.,C. A new methodology for constructing the binary representation [generalized binary representation (GBR)] ofC is proposed, which can be optimized with regard to both degree distributions and girth. As to the decoding of the GBR, we develop a low-complexity hybrid parallel decoding process. It is shown that the decoding performance of the GBR under the proposed binary decoding process could closely approach the decoding performance of its mother codeC under nonbinary belief propagation decoding. A simple code optimization algorithm for the GBR is also provided. Simulations show the comparative results and justify the advantages of the proposed constructions.Index Terms-Non-binary LDPC code, binary image, binary Gaussian channel, binary symmetric channel.

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Section: A Related Workmentioning

confidence: 99%

Section: A Related Workmentioning

confidence: 99%

Section: A Related Workmentioning

confidence: 99%

Section: A Binary Images For Non-binary Ldpc Codesmentioning

confidence: 99%

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Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

Chen

et al. 2014

IEEE Trans. Commun.

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“…Recently, their counterpart, non-binary LDPC codes constructed over Galois field (GF) of size q, have shown their potential in improving the coding gain especially at small or moderate codeword lengths, or when higher order modulation is employed. By now, a great deal of research efforts have been done on non-binary LDPC codes defined over GF(q) [4]- [7], for some q > 0.…”

Section: Introductionmentioning

confidence: 99%

Informed dynamic scheduling strategies for novel majority-logic decoding of non-binary LDPC codes

Jamalipour

2015

2015 9th International Conference on Signal Processing and Communication Systems (ICSPCS)

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Recent studies show that dynamic scheduling using the latest available information is superior to the flooding scheduling. While the existing works on informed dynamic scheduling focus on belief propagation (BP) based algorithm for binary LDPC codes, in this paper we devise novel methods which are appropriate for majority-logic decoding of non-binary LDPC codes. Firstly we propose a low complexity extrinsic message based decoding algorithm for non-binary LDPC codes. The novelty of this decoding algorithm lies in that we compute extrinsic messages and iteratively update the messages in every iteration. Then we propose a dynamic scheduling schemes specifically designed for majority-logic decoding of non-binary LDPC codes. The proposed scheduling method, named informed dynamic scheduling, can achieve better performance compared with the layered and the flooding schemes.Index Terms-LDPC; Non-binary LDPC; Informed dynamic scheduling; Majority logic decoding. I. INTRODUCTIONLow-Density-Parity-Check (LDPC) codes were firstly invented in early 1960s by Gallagar [1] and rediscovered by Mackay [2] in 1996. It has been proved that binary LDPC codes can achieve rates close to channel capacity when codeword length is long enough [3], and LDPC codes have become candidate communication protocols (WiFi, WiMax, etc). Recently, their counterpart, non-binary LDPC codes constructed over Galois field (GF) of size q, have shown their potential in improving the coding gain especially at small or moderate codeword lengths, or when higher order modulation is employed. By now, a great deal of research efforts have been done on non-binary LDPC codes defined over GF(q) [4]-[7], for some q > 0.Although non-binary LDPC codes have shown significant improvement in performance, the decoding process is much more complicated than binary LDPC codes. A straight-forward implementation of belief-propagation (BP) decoder requires O(q 2 ) complexity. Mackay [8] devised a fast Fourier transform (FFT) based q-ary sum-product algorithm (QSPA) to reduce the complexity from O(q 2 ) to O(q log q). Declercq [9] proposed the extended min-sum (EMS) algorithm where only a subset of the n m most significant messages in GF(q) is utilized. This decoding technique can reduce the computational complexity because n m is usually much smaller than q. In addition, the min-max algorithm [10] further reduces the complexity by replacing the sum operation with max operation in check node update. Unfortunately, these algorithms are still too complicated for some practical applications.

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Cooperative decoder design for non-binary LDPC code with coefficients selection

Chen

et al. 2013

2013 IEEE Global Communications Conference (GLOBECOM)

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Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel

Cited by 7 publications

References 8 publications

Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

Informed dynamic scheduling strategies for novel majority-logic decoding of non-binary LDPC codes

Cooperative decoder design for non-binary LDPC code with coefficients selection

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