🤖 AI Summary
This work addresses the challenge of constructing low-density parity-check (LDPC) codes at short block lengths, where asymptotic design methods fail due to finite-length effects and structural constraints of the underlying Tanner graph. The problem is formulated as a constrained binary combinatorial optimization task. To tackle it, the authors propose a novel global search strategy based on tunneling-enhanced simulated annealing (TASA), combined with local refinement and penalty mechanisms targeting short cycles and harmful trapping set substructures to effectively manage multiple design constraints. Simulation results over the AWGN channel for code lengths ranging from 64 to 128 demonstrate that the constructed codes achieve an average coding gain of 0.45 dB over randomly generated LDPC codes and perform within 0.6 dB of progressive-edge-growth (PEG) codes, thereby overcoming limitations inherent in conventional greedy algorithms.
📝 Abstract
Designing high-performance error-correcting codes at short blocklengths is critical for low-latency communication systems, where decoding is governed by finite-length and graph-structural effects rather than asymptotic properties. This paper presents a global discrete optimization framework for constructing short-block linear codes by directly optimizing parity-check matrices. Code design is formulated as a constrained binary optimization problem with penalties for short cycles, trapping-set-correlated substructures, and degree violations. We employ a hybrid strategy combining tunneling-augmented simulated annealing (TASA) with classical local refinement to explore the resulting non-convex space. Experiments at blocklengths 64-128 over the AWGN channel show 0.1-1.3 dB SNR gains over random LDPC codes (average 0.45 dB) and performance within 0.6 dB of Progressive Edge Growth. In constrained regimes, the method enables design tradeoffs unavailable to greedy approaches. However, structural improvements do not always yield decoding gains: eliminating 1906 trapping set patterns yields only +0.08 dB improvement. These results position annealing-based global optimization as a complementary tool for application-specific code design under multi-objective constraints.