Wavelet-Based Error-Correcting Codes: Performance Comparison with BCH in Modern Channels

Reliable data transmission over noisy channels requires effective error-correcting codes. While classical algebraic constructions, such as Bose–Chaudhuri–Hocquenghem (BCH) codes, remain industry standards, structured alternatives based on discrete wavelet transforms offer potential benefits in terms of implementation complexity and error resilience. This study presents a comparative analysis of BCH and wavelet-based linear block codes, focusing on their error-correction capability and overall performance under realistic wireless channel conditions. This work evaluates both coding schemes across five channel models: additive white Gaussian noise (AWGN), Rayleigh fading, sinusoidal attenuation, multiplicative Gaussian noise, and a composite Rayleigh-plus-sinusoid channel. Performance is assessed using bit error rate (BER), frame error rate (FER), and decoding reliability across a range of signal-to-noise ratios. Results show that wavelet codes achieve error-correction performance comparable to or slightly better than BCH in most channels. Notably, they demonstrate a consistent advantage in scenarios with periodic or slow-varying interference, outperforming BCH starting from the 1.5 dB SNR threshold where the wavelet code achieves a BER reduction of up to 48% and a 37.5% improvement in FER, significantly enhancing decoding reliability in structured noise environments. These findings indicate that wavelet-based codes are not only viable but, in specific practical environments characterized by structured noise, represent a superior alternative for robust and reliable communication systems.