Simulation Results for Algebraic Soft-Decision Decoding of Reed-Solomon Codes
Warren J. Gross, Frank R. Kschischang, R. Koetter, P. Glenn Gulak · 2002
The Koetter-Vardy algorithm is an algebraic softdecision decoder for Reed-Solomon codes. The algorithm is based on an extension to the Guruswami-Sudan list-decoding algorithm with variable multiplicities that are assigned proportional to the reliabilities of the received symbols. There are three steps: (1) multiplicity calculation, (2) interpolation of a bivariate polynomial, and (3) finding the y-roots of this polynomial. A low-complexity algorithm for calculating the multiplicities is proposed. Simulation results indicate that the coding gain is dependent on the code rate and ranges from 0.25 dB to 4.25 dB with a practical upper limit of 1 1.5 dB, assuming binary phase shift keying and additive white Gaussian noise. Higher coding gains of between 2 dB and 6.8 dB can be achieved over a Rayleigh fading channel. The KV algorithm exhibits a performance-complexity tradeoff which is tunable by the choice of m max , n and k. The code parameters should be chosen carefully to take advantage of the "sweet spots" in the performance-complexity profile.