{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

7 - ECE 562 Advanced Digital Communication Lecture 7...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 562: Advanced Digital Communication Lecture 7: Capacity of the AWGN Channel Introduction In the last two lectures we have seen that it is possible to communicate rate efficiently and reliably. In this lecture we will see what the fundamental limit to the largest rate of such a reliable communication strategy is. This fundamental limit is called the capacity . Examples We can see what the fundamental limits to reliable communication are in the context of the scenarios in the last two lectures: 1. AWGN channel : With binary modulation and random linear coding at the transmit- ter and ML decoding at the receiver, we have seen that the largest rate of reliable communication is R * = 1 - log 2 1 + e - SNR 2 . (1) This is the capacity of the AWGN channel when the transmitter is restricted to do linear coding and binary modulation. 2. Erasure channel : We developed this model in Lecture 6 in the context of simplifying the receiver structure. But it is a very useful abstract model on its own right and widely used to model large packet networks (such as the Internet). The basic model is the following: the transmitter transmits one bit at a time (you could replace the word “bit” by ”packet”). The receiver either receives the bit correctly or it is told that the bit got erased . There is only a single parameter in this channel and that is the rate of erasures (the chance that any single transmit bit will get erased before reaching the receiver): p . What is the largest data rate at which we can hope to communicate reliably? Well, since only a single bit is sent at any time, the data rate cannot be more than 1 bit per unit time. This is rather trivial and we can tighten our argument as follows: the receiver receives only a fraction 1 - p of the total bits sent (the remaining p fraction of the total bits sent got erased). So, the data rate for reliable communication could not have been any more than the fraction of bits that the receiver got without erasures.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern