Q. How much do we need to know about polynomial arithmetic as used in CRCs?
A. You are expected to appreciate that CRCs are stronger than simple checksums in several respects (short burst errors especially). Also that the same mechanisms can be extended for error correction based on Hamming distance. But the lectured material, where the remainder mod 5 was stored in a 3-bit field was explicitly described as an over-simplification (eg not all code points would be used, which is wasteful), and no familiarity with real-world GF2 arithmetic is required for this course.
In Topic 03b lecture regarding the possibility of slotted CSMA I said I would post a clarification on the web page.
In a simple Aloha system, where a station just transmits without carrier sense or any other form of MAC: adding slots helps. Slots have the advantage that a collision will only interfere with other transmissions in that slot, which is half as many as in an unrestricted system, where a transmission could hit the end of transmission already in progress and then the start of a subsequent one.
Additionally, whether the system is slotted (the medium is formatted into fixed-length intervals with all stations being synchronised) or not, we may casually use the term 'slot time' to devote the time needed to convey one packet, or the smallest supported packet if they can be of variable length. An example of this use is in the exponential, binary back-off specification.
Once we add carrier sense to multiple access (giving CSMA), but if we have no hidden terminal problem and we can consider 'slots' of length equal to the shortest packet duration. A simple mechanism would be for one station to 'format' the medium, sending a regular burst of carrier or specially-modulated carrier, to denote a slot boundry. Stations would randomly contend to send after this. This would have the downside of all slotted systems, in that latency is increased by having to wait for the next slot start and some capacity is used up with the slot synchronisation method. But under heavy load, performance may be better, since the vulnerability period for a collision is shortened. This is nicely developed in
Enhancing LoRaWAN scalability with Longest First Slotted CSMA. The details of that particular protocol are beyond the scope of this course, but you should appreciate why slotting can help in general.
Q. On slide 24 of topic 3a, you mentioned that for OFDM modulation, the FFT is performed at the transmitter and the IFFT at the receiver in wireless systems. As I was curious to learn more about OFDM, I looked at several resources online, including the reference below. In these sources, I noticed that the IFFT is typically applied at the transmitter, while the FFT is used at the receiver. [Springer, Advanced Optical and Wireless Communications Systems Chapter 7: OFDM for Wireless and Optical Communications https://link.springer.com/chapter/10.1007/978-3-319-63151-6_7 ] I would greatly appreciate it if you could clarify which implementation is correct.
A. In reality, the Fourier Transform (and hence the FFT) is a self-inverse except for a sign change; doing it four times becomes the identity function. So the distinction is ultimately a matter of convention. Given the common definition/concept of the Fourier Transform as converting from time domain to frequency domain, you are right to point out that I should have labelled the boxes the other way around. I shall update the slide.
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