Consider a three layer protocol in which Layer 3 encapsulates
Layer 2 and Layer 2 encapsulates Layer 1. Assume minimalist headers
with fixed length packets. Assume the following characteristics of the
layers: Layer 1, 6 octet address length, 512 octet payload; Layer 2, 4
octet address length , 256 octet payload; Layer 3, 8 octet address length,
1024 octet payload. Note that in the minimalist header arrangement,
no error detection or correction will be used; however, there must be a
scheme (that you must devise) to allow a multipacket datagram at each
separate layer. You may assume that there is some sort of routing or other
address translation protocol that will identify which addresses are to be
used. Assume that the data communications channel in use do form a
data communications network. (Hint: do recall what is needed for a data
communications network as contrasted with an arbitrary graph.)
1.1. For each of the three layers, separately calculated, how many items
(nodes) can be addressed? Do not simply show an answer, but explain
your reasoning (hint: combinatorics).
1.2. We have discussed functors as a formal, theoretical description between
layers of a network. In terms of these three layers, illustrate
the functors between the layers, and explain how functors address
the differences in topology and relevant information content at the
1.3. Assume that the datagram has 5 layer 1 packets. How does this
datagram encapsulate in layer 2?
1.4. Taking the above result, or a made-up one of your choosing if you
cannot calculate such a result, how does this data from layer 2 encapsulating
layer 1 data then encapsulate in layer 3?
1.5. Assuming that the only information of interest is the payload of layer
1, what is the overall efficiency of the final encapsulated data stream
in layer 3 for the layer 1 datagram described above?
1.6. Assuming that only the information in the starting layer 1 datagram
payload is the signal, and the rest of all packets at all layers is noise
with respect to this very restricted view of the information content
of a channel, what is the effective Shannon-Hartley theorem relation
between “channel capacity” and “bandwidth” for this specific datagram