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

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.