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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. Outline. Introduction Block-LDPC Code Construction

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block ldpc a practical ldpc coding system design approach

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

outline
Outline
  • Introduction
  • Block-LDPC Code Construction
  • Block-LDPC Encoder Design
  • LDPC Decoder Design
  • Conclusion
introduction
Introduction
  • LDPC coding system implementation
    • Conventional: code-to-encoder/decoder design

 Not appropriate

    • Block-LDPC: joint code-encoder-decoder design
introduction4
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?
introduction5
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.
introduction6
Introduction
  • Block-LDPC code system
    • Semi-random implementation-oriented code construction approach.
    • Low-complexity encoding process and pipelined partially parallel encoder hardware architecture.
    • Partially parallel decoder hardware architecture.
block ldpc code construction
Block-LDPC Code Construction
  • Implementation-Oriented Constraints
    • Decoder-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.

block ldpc code construction8
Block-LDPC Code Construction
  • Performance-Oriented Constraints
    • Large code length (Determined by applications)
    • Carefully designed node degree distribution

 Obtained by a standard technique, i.e, density evolution

    • Not too many small cycles

 Set a constraint on the girth and the degree of a cycle

    • Widespread bipartite graph connectivity

 Reached by randomness in the overall construction

block ldpc code construction9
Block-LDPC Code Construction
  • The degree of a cycle :

The sum of degrees of all variable nodes found along the path of a cycle.

block ldpc code construction10
Block-LDPC Code Construction
  • Block-LDPC Code Construction

1) 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.

block ldpc code construction11
Block-LDPC Code Construction
  • Code selection is based on a metric called cycle effect metric.

Ni : the number of cycles with the length of i

a : a value chosen for the sum to converge.

  • The code with smaller value of cycle effect tends to have less small cycles.
block ldpc code construction12
Block-LDPC Code Construction
  • Parity check matrix subject to implementation-oriented constraints
block ldpc encoder design
Block-LDPC Encoder Design
  • Encoding process

* H =

Since

And let x=(s,p1,p2), s : systematic part, p1and p2 : parity part

We get

then

block ldpc encoder design17
Block-LDPC Encoder Design
  • Block Structured Matrix-Vector Multiplication
    • inter-vector-parallel/intra-vector-serial computational style
block ldpc encoder design19
Block-LDPC Encoder Design
  • Hardware architecture for block structured sparse matrix-vector multiplication
block ldpc encoder design20
Block-LDPC Encoder Design
  • Pipelined Block-LDPC encoder structure
ldpc decoder design
LDPC Decoder Design
  • Decoder architecture
conclusion
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.