Principles of Digital Communications


Instructor Rudiger Urbanke
Office INR 116
Phone +4121 6937692
Office Hours By appointment
Teaching Assistant Hamed Hassani
Phone +4121 6937516
Office INR 031
Office Hours 24/7
Teaching Assistant Saeid Haghighatsoar
Phone +4121 6936654
Office INR030
Office Hours 24/7


Student Assistant Yannick Messerli
Student Assistant Johan Paratte
Student Assistant Paul Landry


Lectures:   Wednesday 15:15 – 18:00 (room:INM 202)
    Friday 9:15 – 12:00 (room:INM 202)


Language: English Coefficient/Crédits: 6 ECTS

link to the official course description


30% midterm + 50% final + 20% project;
You can collect bonus: The first person who emails me a typo, error, etc. in the course notes gets a bonus point. If you sent me a correction, but your name is not acknowledged below, please send me a gentle reminder.

Page xiii: “4.B Various Bandwidth Definitions” (Etienne)
Page 3, first line of the second paragraphs (line 12): “maNy” spelled “may” (Cambazard)
Page 11, in the second last sentence before the chapter 2.2.1: “Notice that he” which should be “Notice that the”. (Buet, Cambazard)
Page 11, sentence preceding formula (2.2): “The expected valued”. (Etienne)
Page 12, first line: “is irrelevant since f_Y(y) is a … ”, the Y in f_Y(y) is missing (Girard)
Page 12,middle: “However, from an algorithmic point of view the test it is not …” (Laupre)
Page 13, second paragraph from bottom, middle: “we Know How to” (Ahluwalia)
Page 18, top paragraph: this is a repetition of the last paragraph on page 17 (Girard, Sabatier)
Page 24: “from the context which is the hypothesis and which IS THE observable” (Ruslan)
Page 25 and 30 (3 times): there are references to “Problem ??” (Cambarzard,Sabatier, Chamov)
Page 25 theorem: perhaps say what h(y) is (Sabatier)
Page 27, middle: “What can be gained … than over R_i^c” (instead of R_j^c). (???)
Page 31, middle: “where in (a) …”, the words “first” and “second” should be exchanged (Youssef)
Page 33: Figure 2.13 is mentioned but only appears on page 82 (Cambazard,Ahluwalia)
Page 34, Theorem 21, start:“If” should have capital “I” (De Tiberge)
Page 34, Theorem 21, (d): “;” is missing at the end (De Tiberge)
Page 35, Definition 26: “, then A H is said to be positive semidefinite” (Chamov)
Page 35, Definition 23: “H \in \mathbb C^{n x n}” and not “C^{n x x}” (Ruslan)
Page 41: Figure 2.14 only appears on page 82 (Samit)
Page 42, Definition 31: “Y_1, …, Y_m” (Sabatier)
Page 43, second line from top: “we we can write”, scratch one “we” (Ruslan)
Page 43, last line: “Problem ??” (Ruslan)
Page 43, end of second paragraph: rewrite “has iid ~N(0, I_n) components” [the whole vector is what is written but the components are ~N(0, 1)] (De Tiberge)
Page 45: “Vector Space??” (Ruslan)
Page 50: \psi and \phi are mixed on this page (Sabatier)
Page 51, lower third: “By PythagoraS” (Ruslan)
Page 57, 4th line from the bottom: “probabilities” (Ahluwalia)
Page 59, problem 13 – solution is printed there instead of problem itself (Ahluwalia)
Page 68, first line: “When does the observer make sense?” (Ahluwalia)
Page 83: the entire Chapter 3 is in italic (Cambazard)
Page 83, middle: “for free from what WE have learned in the previous chapter” (Girard)
Page 84, third paragraph: “inner-producET space” (Girard, Etienne)
Page 87, (3.4): integration goes from minus infinity to infinity; the minus sign does not appear; same problem on Page 88 top; (Girard, Ahluwalia)
Page 88: the phi_j and U_j are defined for j in [1, ñ] at the top; but they are used in a sum with index ranging in [n+1, n+ñ] (Sabatier)
Page 91, Fig. 3.5: “… AWGN channel into and encoder …” (Etienne)
Page 93, last paragraph: “Even tHough the mathematical expressionS …” (Ruslan)
Page 93, 6th line from the bottom: “… in Figure 3.7 equals to THE dimensionality …” (Ruslan)
Page 93, bottom of page: “Second, test (T@) requires …” (Sabatier)
Page 97, Section 3.5, second paragraph: “onto each of the basis vectorS” (Chamov)
Page 100, first line: “we” is repeated (Etienne)
Page 101, last paragraph: “inner-produce” instead of “inner-product” (Chamov)
Page 101, last line of 2nd paragraph: “via matched filter” (Etienne)
Page 102 and 103: the plots of the sinc functions are missing (Girard)
Page 103, example 55: “… height 2ab … at 1/2a … sinc_{1/2a, 2ab}(f) = 2ab sinc(2af)” (Etienne, Sabatier)
Page 104, problem 1, question (a): remove the extra dot after the definition of the basis just before the “for” (Cambazard)
Page 104, problem 1, question (d): “result” instead of “rseult” (Etienne)
Page 119, last word: typicalLY (Etienne, Chamov)
Page 119, beginning of the second paragraph: “The reason for this lies in the fact …” (Laupre)
Page 124, line 2: replace “power” by “energy” (Ruslan)
Page 125, bottom: “rseult” instead of “result” (Etienne)
Page 125, third line from bottom: “As shown in problem ???” (Cambazard, El Baba, Chamov)
Page 125, last line: the definition of \epsilon_{b} is only given on page 127 (Ruslan)
Page 135, 2nd paragraph, 5th line: double “and” (Etienne)
Page 135, Equivalent Noise Bandwidth: double “impulse” (Chamov)
Page 135, Equivalent Noise Bandwidth, last sentence: reword the sentence (Chamov)
Page 140, first line: “Integragte” (Ahluwalia, Cambazard)
Page 140, problem 5 (d): “How does it behave as a function of …” (Etienne)
Page 147, middle: “ … transform of the autocorrelation R_X …” [not R_zeta] (Sabatier)
Page 149, middle: “w.s.s. stationary” (Sabatier)
Page 149, Example 67: example is still missing (Sabatier)
Page 152, last paragraph, 3rd line: “the n-tuples, i=0, …, n-1” (Etienne)
Page 157, end of page, last formula: “n=-\infty” (Laupre)
Page 157, last formula on this page: replace the variable t with f in the formula (Ouhmad)
Page 158, last line of first paragraph: “filter” (Etienne)
Page 159, Figure 5.6: In the third plot from the top the label should be s’_{F} without the tilde (Buet) Page 164, problem 5, question ©: replace question mark with dot (Cambazard)
Page 164, problem 5, question (b): repetition of “THE” (Etienne)
Page 167, first line: “continuous” (Cambazard)
Page 167, 5th line: “waveformr” (Etienne, Ruslan, Ahluwalia, Girard)
Page 167, 8th line: “continuous” (Cambazard)
Page 168, 2nd paragraph: “The n0 output streams of a convolutional …” (Etienne)
Page 168, bottom of page: “(which is not …, s_{m-1}(t)); [missing )]” (Cambazard)
Page 170, Figure 6.2: “d_{nj-2}→ d_{j-2}” (Etienne, Ahluwalia)
Page 172, first line: “sequence be y = …” (Etienne)
Page 172, first and third paragraph: “vy → y [in bold letters]” (Etienne)
Page 172, third paragraph, near the end of example 70: “The subpath with the highest branch metric …” (Etienne)
Page 172, middle: “we would not need thirD trellis …” (Alban) Page 172, last line: extensionS (Alban)
Page 174, end : “where Edges are labeled” (Alban)
Page 176, third paragraph: “The input distance is the number of positions …” (Cambazard)
Page 178, bottom: f(dd^) = f(d)f(d^) [the second “f” is missing] (Sabatier)
Page 179, expression (6.4) : “P_b=E*1/(k k0) …” (Etienne, Youssef)
Page 182, top of page: “Notice that in (6.6) the characteristics of the channel …” (Etienne)
Page 182, top of page: “Problem ???” (Etienne)
Page 184. 3rd line from bottom: “the Viterbi algorithms computes” (Laupre) Page 199, second paragraph, second line: “contain what we need and at the same time …” (Etienne, Cambazard)
Page 209, Appendix 7.C, 2nd paragraph, 2nd line: “This is so since the input/output relationship of an LTI system ” (Etienne)
Page 214, Problem 16, 17, and 18 should be Problem 1, 2, and 3 (Ahluwalia)
Page 219, second paragraph: “is very convenient, since the Nyquist criterion allows us to test …” (Cambazard)
Page 221, 9th line from the bottom: based band-equivalent (Ahluwalia)
Last page: add an index (Sabatier)
Page 222, top figure: add legend and description to this figure (Laupre)

Special Announcements

The midterm takes place, next Wednesday, April 4th from 3:15pm till 5:15pm in CO3. You are allowed one A4-sized piece of paper as crypt sheet. No course book, exercises, or electronic devices. Good luck!

The final takes place on June 25, 8:15am – 11:15am in INJ 218. Essentially the same rules as for the midterm, except that you are allowed two A4-sized pieces of paper as crypt sheet. No course book, exercises, or electronic devices. Good luck!


The following project is due on May 30th. You will work in groups of at least two and at most four. All members of the group will get the same grade for the project. It is up to you to distribute the work load. Description: You are given two laptops. Using ONLY the loudspeakers and the microphone of these laptops you are asked to design a communication system which can transmit a file consisting of 100 ASCII characters as quickly as possible. The two laptops are located 5 meters apart from each other. You will receive the full 20% if by the deadline you present us with a working system which operates reliably. The group which has the fastest system receives a 5% bonus.

Here are final rules for your project. You will be given a text of length 100 on a USB key. It is in plain English with no special characters. The two laptops will be placed 5 meters apart. Of course WiFi, Bluetooth, etc should be switched off. :-) To start you can press on both computers a key. After that, all processing should be done automatically. On the screen of the receiver print out the text. Take a VGA connector with you so that we can connect your laptop to the beamer. On the day of the project presentation, send us a zip file containing (we have not received the required material from some of the groups; if we do not received it by Friday June 1st, by midnight, we cannot evaluate your project and so cannot give you credit)

  • (i) All programs you use with instructions on how to install them and what hardware is required to run them.
  • (ii) A write up between 2 and 4 pages which describes the system, explains your choices of parameters; include in there also a paragraph which comments on what parts of the system could be improved.


  • 1. You will receive maximum points if (i) your system is ”reliable” and (ii) it transmits at a ”reasonable” speed; ”reliable” means that at most 2 of the 100 characters are wrong; ”reasonable speed” means no slower than 5 bits per second.
  • 2. The fastest system gets bonus points. Further, we will give bonus points for the most sophisticated system (the system which has the most features) and perhaps some other categories.

Detailed Schedule


Date Topic Assignment Due Date/Solutions Posted Remarks    
22 Feb   hw01 hw01_sol      
24 Feb   hw02 hw02_sol      
24 Feb   hw03 hw03_sol      
02 Mar            
07 Mar   hw04 hw04_sol      
09 Mar            
14 Mar   hw05 hw05_sol      
16 Mar            
21 Mar   hw06 hw06_sol      
23 Mar            
28 Mar   hw07 hw07_sol      
30 Mar            
04 Apr MIDTERM in CO3   Midterm Solution      
06 Apr Good Friday no course =)        
11 Apr Easter Break no course        
13 Apr Easter Break no course        
18 Apr   hw08 hw08_sol      
20 Apr            
25 Apr   hw09 hw09_sol      
27 Apr            
02 May   hw10 hw10_sol      
04 May            
09 May   hw11 hw11_sol      
11 May            
16 May   hw12 hw12_sol      
18 May            
23 May   hw13 hw13_sol      
25 May            
30 May Project due date: presentation of projects and competition        
01 Jun            

Course Notes

The course is based on the lecture notes by Prof. Bixio Rimoldi. You will receive a copy of the notes on the first day of class. If you find typos, mistakes, or have suggestions please let us know. You can collect some additional bonus points this way!