Ideal-Based Code Construction and Low-Complexity Hybrid Decoding over Gaussian Integer Rings

In this paper, a novel ideal-based linear code family defined over Gaussian integer rings and compatible with restricted error models is proposed. The algebraic construction of the proposed codes allows for the exact correction of specific error patterns. At the receiver side, as an alternative to the computational complexity caused by the traditional Maximum Likelihood (ML) rule at large constellation sizes, an S-Search algorithm that restricts the search space solely to a fixed-element error set is presented. Furthermore, a hybrid decoding architecture utilizing a dynamic reliability threshold has been developed to autonomously adapt to channel quality and preserve error performance for risky symbols near the decision boundaries. Simulation results obtained under the AWGN channel demonstrate that the proposed hybrid algorithm exhibits an error performance close to that of the ML algorithm, while significantly reducing the computational load by making it completely independent of the constellation size.