Error Control Coding, Second Edition
Error Control Coding, Second Edition
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Efficient decoding of Reed-Solomon codes beyond half the minimum distance
IEEE Transactions on Information Theory
Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes
IEEE Transactions on Information Theory
Algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
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Reed Solomon (RS) forward error correction (FEC) coding in conjunction with M-ary hyper phase-shift keying (MHPSK) and soft decision decoding is considered in order to improve the robustness of a high spectral efficiency, non-linear satellite communications link. In this paper, a system that utilizes RS encoding of the information symbols which are then transmitted with MHPSK is evaluated in terms of probability of bit error and spectral efficiency. Using standard RS hard decision decoding, the receiver either correctly decodes the received block or returns a decoding failure. In the event of a decoding failure, soft decision reliability information is used to identify received code symbols with a low probability of being correctly received and to generate new code symbol estimates that are used in the traditional RS decoding algorithm. Because the majority of decoding failures are caused when the total number of code symbol errors exceeds the error correction capability t of the RS code by only a few symbols, only a few code symbols must be corrected in order to successfully decode the received block. The performance of this system is compared to a two-subcarrier OFDM system with either 8-PSK or 8- QAM on each subcarrier and single carrier 8-PSK where the data bits are encoded with the Digital Video Broadcast (DVB) standard rate 0.83 low density parity check (LDPC) code. The MHPSK system with RS encoding and soft decision decoding, the two-subcarrier OFDM system with either 8-QAM or 8-PSK on each subcarrier with LDPC encoding, and single carrier 8-PSK with LDPC encoding are compared in terms of probability of bit error, peak-to-average power ratio, amplifier backoff, and spectral efficiency for very long block lengths.