A short tutorial to assist in obtaining
an understanding of Reed-Solomon Coding
A.A.R.Townsend
Introduction
Digital Television Terrestrial
Broadcasting (DTTB) uses Coded Orthogonal Frequency-Division Multiplex (COFDM)
which is a multi-carrier modulation method in which many closely spaced
carriers occupy a given channel bandwidth. The letters FDM corresponds to
Frequency-division multiplex and refers to the set of evenly spaced carriers.
The letter “C” refers to Coded which in turn refers to the use of
channel coding to combat frequency-dependent fading and degradation of the
symbol or bit error rate. Finally, “O” refers to Orthogonal which
refers to the relationship between the multiple carriers.
What is considered in this
tutorial is the “C” or coded component, more specifically, the outer code that
is known as the “Reed-Solomon” code. This outer code is a block code that is
effective in coping with large consecutive losses of data, such as might occur
with analogue television co-channel interference or impulse noise. In contrast, the inner code in a COFDM system
is a “Viterbi “or trellis code. The trellis code is most effective
for coping with random errors such as those caused by white noise. When the
trellis code capacity is exceeded, a burst error is generated at the output. It
is because of this burst error and also to deal with the occurrence of any
impulse noise entering the receiver that the Reed-Solomon outer block decoder
is concatenated after de-interleaving and trellis decoding. This permits a more
robust system to be obtained.
This tutorial comprises 278 power point slides that
have been converted into pdf format, so that it can be read by adobe reader 6.0
and above and downloaded by anyone wishing to complete the tutorial off-line.
It has been called “Galois fields” as it
requires a brief introduction to the mathematics of finite fields for a proper
understanding of the Reed-Solomon encoding and decoding process. The tutorial
can be opened by clicking on “Galois fields”