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Design of Low-Density Parity-Check Code Pair for Joint Source-Channel Coding Systems Based on Graph Theory.

Yijie Lv1, Jiguang He2,3, Weikai Xu1

  • 1Department of Information and Communication Engineering, Xiamen University, Xiamen 361005, China.

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|August 26, 2023
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Summary
This summary is machine-generated.

This study introduces a novel graph-theoretic method for constructing double low-density parity-check (D-LDPC) codes in joint source-channel coding systems. The new D-LDPC codes offer improved performance and flexible frame length adaptability.

Keywords:
graph theoryjoint source-channel codinglow-density parity-check code

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Area of Science:

  • Coding Theory
  • Information Theory
  • Graph Theory

Background:

  • Joint Source-Channel Coding (JSCC) systems require efficient error correction codes.
  • Low-Density Parity-Check (LDPC) codes are widely used due to their performance near the Shannon limit.
  • Designing LDPC code pairs (D-LDPC) for JSCC presents unique challenges in optimizing performance and flexibility.

Purpose of the Study:

  • To develop a novel graph-theoretic method for constructing D-LDPC codes.
  • To enhance the performance and frame length flexibility of LDPC code pairs in JSCC systems.
  • To pre-set the girth of parity-check matrices for jointly designed LDPC codes.

Main Methods:

  • Application of a graph-theoretic approach utilizing constraints among sets associated with parity-check matrices.
  • Joint design of two LDPC codes by pre-setting the girth of their parity-check matrices.
  • Construction of parity-check matrices with an identity submatrix and an additional submatrix of pre-settable column weights.

Main Results:

  • The constructed D-LDPC codes demonstrate significant performance improvements compared to benchmark code pairs.
  • The D-LDPC codes exhibit enhanced flexible frame length, adapting better to various channel conditions.
  • The graph-theoretic method allows for precise control over code properties like girth and column weights.

Conclusions:

  • The proposed graph-theoretic method is effective for constructing high-performance D-LDPC codes for JSCC.
  • The developed D-LDPC codes offer a valuable trade-off between performance and adaptability.
  • This approach provides a flexible framework for designing LDPC code pairs tailored to specific communication requirements.