Complexity Analysis of Reed-Solomon Decoding over GF(2^m) Without Using Syndromes

For the majority of the applications of Reed-Solomon (RS) codes, hard decision decoding is based on syndromes. Recently, there has been renewed interest in decoding RS codes without using syndromes. In this paper, we investigate the complexity of syndromeless decoding for RS codes, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis differs in several aspects from existing asymptotic complexity analysis, which is typically based on multiplicative fast Fourier transform (FFT) techniques and is usually in big O notation. First, we focus on RS codes over characteristic-2 fields, over which some multiplicative FFT techniques are not applicable. Secondly, due to moderate block lengths of RS codes in practice, our analysis is complete since all terms in the complexities are accounted for. Finally, in addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. Comparing the complexities of both syndromeless and syndrome-based decoding algorithms based on direct and fast implementations, we show that syndromeless decoding algorithms have higher complexities than syndrome-based ones for high rate RS codes regardless of the implementation. Both errors-only and errors-and-erasures decoding are considered in this paper. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.Comment: 11 pages, submitted to EURASIP Journal on Wireless Communications and Networkin

Phonetic Temporal Neural Model for Language Identification

Deep neural models, particularly the LSTM-RNN model, have shown great potential for language identification (LID). However, the use of phonetic information has been largely overlooked by most existing neural LID methods, although this information has been used very successfully in conventional phonetic LID systems. We present a phonetic temporal neural model for LID, which is an LSTM-RNN LID system that accepts phonetic features produced by a phone-discriminative DNN as the input, rather than raw acoustic features. This new model is similar to traditional phonetic LID methods, but the phonetic knowledge here is much richer: it is at the frame level and involves compacted information of all phones. Our experiments conducted on the Babel database and the AP16-OLR database demonstrate that the temporal phonetic neural approach is very effective, and significantly outperforms existing acoustic neural models. It also outperforms the conventional i-vector approach on short utterances and in noisy conditions.Comment: Submitted to TASL

Phone-aware Neural Language Identification

Pure acoustic neural models, particularly the LSTM-RNN model, have shown great potential in language identification (LID). However, the phonetic information has been largely overlooked by most of existing neural LID models, although this information has been used in the conventional phonetic LID systems with a great success. We present a phone-aware neural LID architecture, which is a deep LSTM-RNN LID system but accepts output from an RNN-based ASR system. By utilizing the phonetic knowledge, the LID performance can be significantly improved. Interestingly, even if the test language is not involved in the ASR training, the phonetic knowledge still presents a large contribution. Our experiments conducted on four languages within the Babel corpus demonstrated that the phone-aware approach is highly effective.Comment: arXiv admin note: text overlap with arXiv:1705.0315