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![Page 1: Block-LDPC: A Practical LDPC Coding System Design Approach Hao Zhong and Tong Zhang, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e4e5503460f94b44998/html5/thumbnails/1.jpg)
Block-LDPC: A Practical LDPC Coding System Design Approach
Hao Zhong and Tong Zhang, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 52, no. 4, pp. 766–775, April 2005
2005 / 8 / 16 Chia-Yu Lin
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Outline
Introduction
Block-LDPC Code Construction
Block-LDPC Encoder Design
LDPC Decoder Design
Conclusion
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Introduction
LDPC coding system implementationConventional: code-to-encoder/decoder design
Not appropriate
Block-LDPC: joint code-encoder-decoder design
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Introduction
Questions of a complete joint design solution
What constraints should be used in code construction to facilitate the hardware implementation?
How to preserve the good error-correcting performance under those code construction constraints?
What are the appropriate encoder and decoder architectures?
![Page 5: Block-LDPC: A Practical LDPC Coding System Design Approach Hao Zhong and Tong Zhang, IEEE Transactions on Circuits and Systems I: Regular Papers, vol.](https://reader031.fdocuments.in/reader031/viewer/2022032313/56649e4e5503460f94b44998/html5/thumbnails/5.jpg)
Introduction
Weaknesses of the state-of-the-art LDPC coding system design solutions
Only consider decoder design and left encoder design unconsidered.
Did not address how to further optimize the code error-correcting performance under these constraints.
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Introduction
Block-LDPC code systemSemi-random implementation-oriented code construction approach.Low-complexity encoding process and pipelined partially parallel encoder hardware architecture.Partially parallel decoder hardware architecture.
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Block-LDPC Code Construction
Implementation-Oriented ConstraintsDecoder-oriented constraint
The parity check matrix should be block structured with circular block matrices.
Encoder-oriented constraint
The parity check matrix should be lower macro-block triangular.
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Block-LDPC Code Construction
Performance-Oriented ConstraintsLarge code length (Determined by applications)Carefully designed node degree distribution Obtained by a standard technique, i.e, density evolutionNot too many small cycles Set a constraint on the girth and the degree of a cycleWidespread bipartite graph connectivity Reached by randomness in the overall construction
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Block-LDPC Code Construction
The degree of a cycle :
The sum of degrees of all variable nodes found along the path of a cycle.
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Block-LDPC Code Construction
Block-LDPC Code Construction1) Determine the code parity check
matrix parameters.2) Construct a group of code parity
check matrices.3) Select one code from the code group for real application.
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Block-LDPC Code Construction
Code selection is based on a metric called cycle effect metric.
Ni : the number of cycles with the length of ia : a value chosen for the sum to converge.The code with smaller value of cycle effect tends to have less small cycles.
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Block-LDPC Code Construction
Parity check matrix subject to implementation-oriented constraints
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Simulation Result
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Simulation Result
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Block-LDPC Encoder DesignEncoding process
* H =
And let x=(s,p1,p2), s : systematic part, p1and p2 : parity partWe get
Since
then
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Block-LDPC Encoder Design
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Block-LDPC Encoder Design
Block Structured Matrix-Vector Multiplication
inter-vector-parallel/intra-vector-serial computational style
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Block-LDPC Encoder Design
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Block-LDPC Encoder DesignHardware architecture for block structured sparse matrix-vector multiplication
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Block-LDPC Encoder DesignPipelined Block-LDPC encoder structure
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LDPC Decoder Design
Decoder architecture
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LDPC Decoder Design
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Conclusion
Present a joint code-encoder-decoder design solution, called Block-LDPC, for practical LDPC coding system implementations.
Present code construction constraints and develop a semi-random approach for Block-LDPC code construction.
Develop a pipelined partially parallel Block-LDPC code encoder and a partially parallel Block-LDPC code decoder.
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Thank you~