(7,4) Hamming Code: MATLAB Simulations for Hard-Decision, Maximum Likelihood, and Sum-Product Algorithm (SPA) Decoding
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This article presents three distinct decoding methodologies: Hard-Decision Decoding, Maximum Likelihood Decoding, and the Sum-Product Algorithm (SPA). We provide accompanying MATLAB simulation programs to facilitate deeper understanding of these decoding principles. The MATLAB implementations include key functions for encoding parity-check matrices, calculating syndrome patterns for hard-decision decoding, implementing log-likelihood ratio computations for maximum likelihood approaches, and message-passing iterations for SPA. These methods find extensive applications, particularly in (7,4) Hamming Code implementations where they demonstrate varying computational complexity and error-correction performance. The attached resources aim to support your learning and research endeavors by providing practical code examples that illustrate algorithm initialization, iteration processes, and termination conditions for each decoding technique.
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