Networking Compendium | Installment 12
In the realm of data transmission, two key aspects were highlighted in the GATE CS 2009 exam: the importance of CRC error detection and the efficiency of network transmission.
Firstly, let's delve into CRC error detection. The condition for a generator polynomial to detect all errors consisting of an odd number of bits is that must be a factor of . This condition ensures that the CRC code can detect any error pattern where an odd number of bits are inverted.
In binary terms, the factor corresponds to detecting odd parity errors. Errors of odd weight (odd number of bit errors) will produce a non-zero syndrome if includes this factor. This is a widely accepted and established result in CRC error detection theory.
In the scenario described, frames of 1000 bits are sent over a 10^6 bps duplex link between two hosts, with a propagation time of 25ms. To maximally pack these frames in transit, the minimum number of bits required to represent the sequence numbers distinctly is 5.
Moving on to network transmission efficiency, the transmission time for a single frame of size 1000 bits is given. To fully utilize the channel, we need to send 1000 frames per second, as each frame is 1000 bits.
The waiting time for the sender before starting transmission of the next frame was calculated, assuming the sender was not waiting during the time it was transmitting. In this case, the minimum time the sender will have to wait is approximately 18ms.
Moreover, the exam also emphasized the use of the sliding window protocol. With the sender window size equal to the number of bits identified in the previous question, after sending 2^i frames, the minimum time the sender will have to wait before starting transmission of the next frame is still 18ms.
Lastly, the Round Trip Time (RTT) was defined. RTT is the sum of Propagation time for frame, Transmission time for frame, Propagation time for ACK, and Transmission time for ACK. With the propagation time of 25ms, to fully pack the link we need to send at least 25 frames. ACK (Acknowledgement) is piggybacked and assumes the same frame size for piggybacking (1000 bits).
In conclusion, the GATE CS 2009 exam shed light on the importance of CRC error detection and the efficiency of network transmission. By understanding these concepts, we can ensure reliable and efficient data transmission in modern communication networks.
References: [1] LeGall, E. (2005). Error Detection and Correction Codes. Springer Science & Business Media. [2] Lin, D. S. (1983). A Survey of Cyclic Redundancy Check Codes. IEEE Transactions on Communications, 31(12), 1656-1665.
Math plays a significant role in determining the efficiency of network transmission, as calculating the minimum number of bits required to represent sequence numbers distinctly is a mathematical problem.
In the context of data-and-cloud-computing, technology like the sliding window protocol, which optimizes the use of network resources by sending frames in a controlled manner, is crucial for efficient data transmission.
Moreover, CRC error detection, a fundamental concept in networking, relies on mathematical principles such as polynomial mathematics for designing error-detecting codes. This theory is well-documented in works like "Error Detection and Correction Codes" by LeGall and "A Survey of Cyclic Redundancy Check Codes" by Lin.
