Reduced List-Decoding of Reed--Solomon Codes Using Reliability Information

Abstract: We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating the output of the EEA at the least reliable positions of the received word. We refer to this decoding method as reduced list-decoding, since not all received positions are used in the interpolation as in other list-decoding methods, such as the Guruswami-Sudan and Wu algorithms. Consequently the complexity of the interpolation step is reduced considerably. The probability of failure can be minimised by adjusting certain parameters, making it comparable with the K\"otter-Vardy algorithm but having a much lower complexity.