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

Block-LDPC Encoder Design

LDPC Decoder Design

Conclusion

Introduction

LDPC coding system implementationConventional: code-to-encoder/decoder design

Not appropriate

Block-LDPC: joint code-encoder-decoder design

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?

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.

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.

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.

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

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 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.

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.

Block-LDPC Code Construction

Parity check matrix subject to implementation-oriented constraints

Simulation Result

Simulation Result

Block-LDPC Encoder DesignEncoding process

* H =

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

Since

then

Block-LDPC Encoder Design

Block-LDPC Encoder Design

Block Structured Matrix-Vector Multiplication

inter-vector-parallel/intra-vector-serial computational style

Block-LDPC Encoder Design

Block-LDPC Encoder DesignHardware architecture for block structured sparse matrix-vector multiplication

Block-LDPC Encoder DesignPipelined Block-LDPC encoder structure

LDPC Decoder Design

Decoder architecture

LDPC Decoder Design

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.

Thank you~