# Part ONE. a. Assuming each of the four bases occurs with equal probability, how many bits of information does a nucleotide contain?

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1 Networked Systems, COMPGZ01, 2012 Answer TWO questions from Part ONE on the answer booklet containing lined writing paper, and answer ALL questions in Part TWO on the multiple-choice question answer sheet. Marks for each part of each question are indicated in square brackets Calculators are permitted Part ONE 1. Error-Control Coding and Framing with DNA In this question we ll explore the error correcting code and framing mechanism that cells use to synthesize amino acids from DNA, the molecule that carries information in most living things. In order to focus on the information-theoretic aspects, we ll slightly simplify our description. A strand of DNA is made of an ordered sequence of nucleotides. A nucleotide contains one of four possible bases: cytosine (C), guanine (G), adenine (A), and thymine (T). Consequently, each nucleotide conveys information. a. Assuming each of the four bases occurs with equal probability, how many bits of information does a nucleotide contain? [4 marks] A strand of DNA is turned into a sequence of amino acids (which in turn are the building blocks of proteins) through the process of synthesis, which we focus on here. In synthesis, groups of three nucleotides (called codons) are mapped to one of 20 possible amino acids according to Table 1. b. What is the rate of this code? [6 marks] To understand the error correcting and framing properties of this code, let s define the nucleotide error rate (NER) as the probability that any single nucleotide is errored. Assume that when a nucleotide error occurs, the nucleotide in question changes to one of the other three nucleotides at random and with equal probability of changing to each. For the following questions, assume an NER of 10%. c. What is the probability that a codon coding for the amino acid Thr has at least one nucleotide error? d. What is the probability that a codon coding for the amino acid Thr is synthesised to a different amino acid or (stop)? [6 marks] COMPGZ01 1 TURN OVER

2 First nucleotide base of DNA codon T TTT = Phe TTC = Phe TTA = Leu TTG = Leu Second nucleotide base of DNA codon T C A G TC = Ser C CT = Leu CC = Pro A ATT = Ile ATC = Ile ATA = Ile ATG = Met AC = Thr G GT = Val GC = Ala TAT = Tyr TAC = Tyr TAA = (stop) TAG = (stop) CAT = His CAC = His CAA = Gln CAG = Gln AAT = Asn AAC = Asn AAA = Lys AAG = Lys GAT = Asp GAC = Asp GAA = Glu GAG = Glu TGT = Cys TGC = Cys TGA = (stop) TGG = Trp CG = Arg AGT = Ser AGC = Ser AGA = Arg AGG = Arg CG = Gly Table 1: Codon to three-letter amino acid abbreviation mapping for the DNA code. An en-dash ( ) indicates any nucleotide base. (stop) indicates a codon that frames the end of the protein instead of translating to an amino acid. e. What is the probability that the codon GAT coding for the amino acid Asp is synthesised to a different amino acid or (stop)? [6 marks] f. Which is/are the codon(s) that is/are most likely to be mistaken for (stop) and what is the likelihood of those codons being confused for (stop)? How does the framing error you have just computed compare with the NER? [8 marks] [Question 1: Total 33 marks] COMPGZ01 2 CONTINUED

3 2. TCP and Time-Sequence Plots Below follows a series of Transmission Control Protocol (TCP) time-sequence plots taken at the TCP sender, as discussed in lecture. In the plots, data packets are shown as solid rectangles and ACKs are shown as hollow rectangles. Answer the following questions about these plots. a. Time-sequence plot A: i. In plot A above, what is the approximate packet size used by the sender? ii. In plot A above, what is the approximate round-trip time (RTT) for the first exchange in the 3-way TCP handshake? iii. In plot A above, what is the approximate RTT for data packets once the connection is established? iv. In plot A above, what, measured in number of packets, is the value of the congestion window just before time = 6 seconds? v. In plot A above, does the receiver use delayed ACKs? Justify your answer with evidence from the plot. COMPGZ01 3 TURN OVER

4 b. Time-sequence plot B: i. In plot B above (again, recorded at the sender), what, measured in number of packets, is the value of the congestion window after the arrival of the ACK recorded just before time = 4.5 seconds? ii. In plot B above, there is a retransmitted packet. What is the approximate highest sequence number contained in the retransmitted packet? iii. For the same retransmitted packet in plot B above, was this packet retransmitted using a retransmit timeout or fast retransmit? Give specific evidence from the plot to support your answer. iv. For the same retransmitted packet in plot B above, was only that one packet lost, or were others in flight at the same time also lost? Give specific evidence from the plot to support your answer. v. After the same retransmitted packet in plot B above has been acknowledged, what, in number of packets is the congestion window size? COMPGZ01 4 CONTINUED

5 vi. Assuming no further packet loss after the retransmission in plot B above, how many round-trip times will it take for the sender s congestion window size to return to its value before the retransmission? Justify your answer by referring to relevant details of the TCP protocol. [Question 2: Total 33 marks] COMPGZ01 5 TURN OVER

7 Suppose that John determines using dig that the firewall indeed does allow nonpaying clients to send DNS queries directly to the Internet, and receive replies to them. John excitedly hypothesizes that to obtain free Internet access through this WiFi service, he can simply tunnel IP within UDP to get through the firewall. Before leaving home, John wrote a UDP tunnel endpoint server and left it running on a host elsewhere on the Internet. John hopes that the firewall only inspects the UDP header, and not the payload of the UDP packets. ii. Assuming the firewall doesn t inspect the payload of these UDP packets, but only their headers, what header values will outbound and inbound UDP packets need to have in order to appear to the firewall as DNS-like traffic? [2 marks] iii. What does it mean to tunnel IP within UDP? Describe specifically what actions John s laptop would need to take to tunnel IP within UDP, and what actions the UDP tunnel endpoint server John runs elsewhere on the Internet would need to take to serve as the remote endpoint of that tunnel. [5 marks] b. Suppose that when John attempts to tunnel IP over UDP, he finds that the firewall does not allow these packets through: neither outbound nor inbound. Yet tests with dig reveal that the firewall does consistently allow through DNS queries and responses sent directly to/from all nameservers John tries elsewhere on the Internet. i. Based on the behavior John observes in this part of this question, what additional step(s) apart from looking at the header is the firewall most likely using to decide whether to block or forward UDP packets? COMPGZ01 7 TURN OVER

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