The mapping is a one-to-one (i.e., unique) and this transformation is linear. This means code
words outside the 2n code words cannot be created by the addition of valid code words.
The input bit rate is the uncoded rate, denoted above as Rb (bits/sec). The encoder output-coded bit
rate is n/k times the input bit rate. This ratio is inversely related to what is commonly called the code rate.
Pictorially speaking, there are 2n code words, of which 2k are used. The set of all n-tuple code words
is typically called a vector space. The entire coded vector space is denoted as circles in Fig. 5.13. In
fact, each circle represented an n-tuple codeword. The encoder input-to-output mapping rule selects a
subset of the vector space to use as its code-word pool. This subset (or sometimes called subspace providing
some criteria are met) is shown in Fig. 5.13 by the black circles [1].
PERFORMANCE IMPROVEMENT TECHNIQUES 231
FEC Encoder
(n, k)
Rb = Input Bit Rate Rc = (n/k)Rb = Output Bit Rate
k bits n bits
2k Distinct Words 2n Distinct Code Words
FIGURE 5.12 FEC encoder notation.
FIGURE 5.13 n-tuple code word vector space.
Prior to moving into the linear block code encoding rules, let us discuss various coding definitions.
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