Exjobbspresentation: Increasing the Rate of GLDPC Codes: Single Parity-Check Versus Multiple Parity-Check Components

Generalized low-density parity-check (GLDPC) codes improve the error-correction capability of conventional low-density parity-check (LDPC) codes by replacing single parity-check (SPC) constraints with more powerful component codes. However, stronger local constraints introduce additional redundancy and may reduce the overall code rate. This thesis investigates how the rate of Hamming-based GLDPC codes can be increased while retaining useful local decoding capability.

Two rate-adaptation methods are studied. In Method 1, Hamming generalized check nodes and SPC check nodes are mixed in adjustable proportions. The mixing ratio provides direct control over the balance between redundancy and local recovery strength. In Method 2, the standard Hamming parity-check matrix is extended by periodically repeating its nonzero columns. This construction increases the component-code length and the design rate without adding new parity-check equations. A hybrid extension scheme that combines these two mechanisms is also investigated for the binary erasure channel (BEC).

Overall, the results show that no single configuration is optimal across all rate regions. Instead, Hamming/SPC mixing and repeated-column extension provide complementary mechanisms for adapting GLDPC codes to different requirements on rate, reliability, and decoding complexity.

Handledare: Michael Lentmaier

Examinator: Thomas Johansson