Question

Let us consider convolutional code with k = 1, n = 2, l = 3 That is, in each step, one bit is read, a window of last 3 bits is considered (including the current bit), and 2 coded bits are produced. Let the stream of bits be denoted by $x[i]$ (index $i$ goes over all bits in the message). When we read in each bit $x[i]$, we compute two parity bits $p[i]$ and $q[i]$ as follows, $p[i] = x[i] + x[i - 1] + x[i - 2]$ $q[i] = x[i] + x[i - 1]$ For the first bit ($i = 0$), assume $x[i - 1] = x[i - 2] = 0$. (a) What is the rate of this convolutional code? (b) If the message = 1101, compute the coded bits by using convolutional code. (c) If the message = 0110, compute the coded bits by using convolutional code.

          Let us consider convolutional code with
k = 1, n = 2, l = 3
That is, in each step, one bit is read, a window of last 3 bits is considered (including the
current bit), and 2 coded bits are produced. Let the stream of bits be denoted by $x[i]$
(index $i$ goes over all bits in the message). When we read in each bit $x[i]$, we compute
two parity bits $p[i]$ and $q[i]$ as follows,
$p[i] = x[i] + x[i - 1] + x[i - 2]$
$q[i] = x[i] + x[i - 1]$
For the first bit ($i = 0$), assume $x[i - 1] = x[i - 2] = 0$.
(a) What is the rate of this convolutional code?
(b) If the message = 1101, compute the coded bits by using convolutional code.
(c) If the message = 0110, compute the coded bits by using convolutional code.

Let us consider convolutional code with
k = 1, n = 2, l = 3
That is, in each step, one bit is read, a window of last 3 bits is considered (including the
current bit), and 2 coded bits are produced. Let the stream of bits be denoted by x[i]
(index i goes over all bits in the message). When we read in each bit x[i], we compute
two parity bits p[i] and q[i] as follows,
p[i] = x[i] + x[i - 1] + x[i - 2]
q[i] = x[i] + x[i - 1]
For the first bit (i = 0), assume x[i - 1] = x[i - 2] = 0.
(a) What is the rate of this convolutional code?
(b) If the message = 1101, compute the coded bits by using convolutional code.
(c) If the message = 0110, compute the coded bits by using convolutional code.

Added by Patricia L.

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