TS-LDPC Codes: Turbo-Structured Codes With Large Girth

Lu, Jin; Moura, J.M.F.

doi:10.1109/tit.2006.890690

Cited by 14 publications

(7 citation statements)

References 33 publications

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“…This scheme was found to be very efficient in terms of speed, exhibiting low delay even for long keys. The proposed contribution of this work is that a variation of LDPC (Low Density Parity Check) error correction codes [18], [21][22][23][24]. LDPC is an error correcting code that constructs a parity check matrix M, which is multiplied with the original data words, d to provide a list of code words, c. If the original data word consists of 8 bits, then LDPC (8,16) parity check matrix is generated.…”

Section: Literature Surveymentioning

confidence: 99%

Error Detection and Correction for Distributed Group Key Agreement Protocol

Vijayakumar¹,

Bose²,

Kannan³

2011

IJNSA

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Integrating an efficient Error detection and correction scheme with less encoding and decoding complexity to support the distribution of keying material in a secure group communication is an important issue, since the amount of information carried out in the wireless channel is high which produces more errors due to noise available in the communication channel. Moreover, the key must be sent securely to the group members. In this paper, we propose a new efficient group key computation protocol that provides more security and also integrates an encoding method in sender side and decoding method in the receiver side. To achieve security in key computation process, we propose Euler's totient function based Diffie-hellman key distribution protocol. To provide efficient error detection and correction method while distributing the Keying and re-keying information, we introduce tanner graph based encoding stopping set construction algorithm in sender and receiver side of the group communication. Two major operations in this scheme are joining and leaving operations for managing group memberships. The encoding and decoding complexity of this approach is computed in this paper and it is proved that this proposed approach takes less decoding time complexity.

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Section: Literature Surveymentioning

confidence: 99%

Error Detection and Correction for Distributed Group Key Agreement Protocol

Vijayakumar¹,

Bose²,

Kannan³

2011

IJNSA

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“…Note that references [27], [28] have also proposed other LDPC code construction methods based on interleaver design utilizing different code structure representations. Reference [27] designed the edge-interleaver for an arbitrary LDPC code whereas reference [28] designed an LDPC code with its Tanner graph compromising of an upper tree and a lower tree which are connected through an interleaver. We could utilize Theorems 1, 2, 3 and 4 to construct nonbinary regular cycle codes.…”

Section: A the Proposed Code Structure Designmentioning

confidence: 99%

Structure, property, and design of nonbinary regular cycle codes

Huang

Zhou

Willett

2010

IEEE Trans. Commun.

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Abstract-In this paper, we study nonbinary regular LDPC cycle codes whose parity check matrix H has fixed column weight j = 2 and fixed row weight d. Through graph analysis, we show that the parity check matrix H of a regular cycle code can be put into an equivalent structure in the form of concatenation of row-permuted block-diagonal matrices if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. This equivalent structure of H enables: i) parallel processing in lineartime encoding; ii) considerable resource reduction on the code storage for encoding and decoding; and iii) parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. On the code's structure design, we propose a novel design methodology based on the equivalent structure of H. Finally, we present various numerical results on the code performance and the decoding complexity.

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“…Recompute the values of x γ and x δ from C α and C β by equations (7) to (9); Find a check node C * such that E ∫ \C * does not contain any encoding stopping set.…”

Section: Encodingmentioning

confidence: 99%

“…In [6], an efficient encoding approach is proposed for Reed-Solomon-type array codes. Reference [7] shows that there exists a linear time encoder for turbo-structured LDPC codes. Reference [8] constructs LDPC codes based on finite geometries and proves that this type of structured LDPC codes can be encoded in linear time.…”

Section: Introductionmentioning

confidence: 99%

Linear Time Encoding of LDPC Codes

Moura

2010

IEEE Trans. Inform. Theory

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Abstract-In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method "label-and-decide." We prove that the "label-and-decide" method is applicable to Tanner graphs with a hierarchical structure-pseudo-trees-and that the resulting encoding complexity is linear with the code block length. Next, we define a second type of Tanner graphs-the encoding stopping set. The encoding stopping set is encoded in linear complexity by a revised label-and-decide algorithm-the "label-decide-recompute." Finally, we prove that any Tanner graph can be partitioned into encoding stopping sets and pseudo-trees. By encoding each encoding stopping set or pseudo-tree sequentially, we develop a linear complexity encoding method for general low-density parity-check (LDPC) codes where the encoding complexity is proved to be less than 4 1 M 1 ( k 0 1), where M is the number of independent rows in the parity-check matrix and k represents the mean row weight of the parity-check matrix.

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TS-LDPC Codes: Turbo-Structured Codes With Large Girth

Cited by 14 publications

References 33 publications

Error Detection and Correction for Distributed Group Key Agreement Protocol

Error Detection and Correction for Distributed Group Key Agreement Protocol

Structure, property, and design of nonbinary regular cycle codes

Linear Time Encoding of LDPC Codes

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