563489578934

Sec. 1–11 Coding 25
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Path A
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Figure 1–7 Code tree for convolutional encoder of Fig. 1–6.
x 1 = 0000
y 1 = 00000000
x 2 = 0001
y 2 = 00000011
x 3 = 0010
y 3 = 00001101
x 4 = 0011
y 4 = 00001110
x 5 = 0100
y 5 = 00110111
x 6 = 0101
y 6 = 00110100
x 7 = 0110
y 7 = 00111010
x 8 = 0111
y 8 = 00111001
x 9 = 1000
y 9 = 11011100
x 10 = 1001
y 10 = 11011111
x 11 = 1010
y 11 = 11010001
x 12 = 1011
y 12 = 11010010
x 13 = 1100
y 13 = 11101011
x 14 = 1101
y 14 = 11101000
x 15 = 1110
y 15 = 11100110
x 16 = 1111
y 16 = 11100101
decision output is known, and it is not known if the decision was almost “too close to call”
(because the test value was almost equal to the threshold value). The soft-decision
technique can translate into a 2-dB improvement (decrease) in the required receiver input
E b /N 0 [Clark and Cain, 1981]. E b is the received signal energy over a 1-bit time interval,
and N 0 /2 is the power spectral density (PSD) of the channel noise at the receiver input.
Both E b and N 0 will be defined in detail in later chapters. [E.g. see Eq. (7–24b) or
Eq. (8–44).]