152,994 research outputs found
Efficient dot product over word-size finite fields
We want to achieve efficiency for the exact computation of the dot product of
two vectors over word-size finite fields. We therefore compare the practical
behaviors of a wide range of implementation techniques using different
representations. The techniques used include oating point representations,
discrete logarithms, tabulations, Montgomery reduction, delayed modulus
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
On Galois-Division Multiple Access Systems: Figures of Merit and Performance Evaluation
A new approach to multiple access based on finite field transforms is
investigated. These schemes, termed Galois-Division Multiple Access (GDMA),
offer compact bandwidth requirements. A new digital transform, the Finite Field
Hartley Transform (FFHT) requires to deal with fields of characteristic p, p
\neq 2. A binary-to-p-ary (p \neq 2) mapping based on the opportunistic
secondary channel is introduced. This allows the use of GDMA in conjunction
with available digital systems. The performance of GDMA is also evaluated.Comment: 6 pages, 4 figures. In: XIX Simposio Brasileiro de Telecomunicacoes,
2001, Fortaleza, CE, Brazi
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