| Reed-Solomon (RS) codes have been widely used in a variety of communication systems on both transmission and storage channels, and are expected to be included in several new standards for wireless communications.;After reviewing the previous work on the decoding of RS codes, in this dissertation, we propose a symbol-based adaptive belief propagation (ABP) algorithm for iterative soft-decision decoding of RS codes. Complexity reduction is achieved by using a fast Fourier transform (FFT)-based belief propagation (BP) algorithm. Parity-check matrix adaptation based on the reliability of the codeword symbols is an essential step to make the BP algorithm effective on high-density parity-check matrices characteristic of RS codes. The matrix adaptation and all other operations are performed at symbol level such that bit-to-symbol and symbol-to-bit conversions are avoided. Although the symbol-based algorithm exhibits some loss in terms of frame error rate compared to its bit-based version, there is a moderate coding gain over algebraic hard-decision decoding on additive white Gaussian noise and Rayleigh fading channels. The algorithm addresses the main weakness of the bit-based ABP algorithm, namely its prohibitively high complexity, for practical applications that use long codes and large finite fields, and require short decoding latency. |
