Comparisons of Verification-based Decodings for Nonbinary Codes in Error and Error-Erasure Channels

Recently, new algorithms on verification-based decoding for codes with nonbinary symbols have been proposed. Namely, there are 1) Vector Symbol Decoding (VSD) that corrects only the data part, 2) hard-decision Message Passing (hMP) that uses a group common idea and 3) limited complexity VSD for partial retransmission ARQ. This paper compares them in terms of their decoding time and decoding performance in various error channels and an error-erasure channel. Symbol error rates (SER) for these channels are necessary and are reported for the 32-bit symbol case. Results show that while VSD: correct data only has the best performance in all channels, hMP group common has the least decoding time and better performance than limited complexity VSD in error channels. The idea of converting erasures to errors is investigated in comparison with the previous idea of converting errors to erasures. Results show that VSD: correct data only is still the best for any overhead. Other methods give good performance for different ranges of overhead.