ELEC 476 Class Notes, Fall 2001

August 29:

Survey of background

Some links about Claude Shannon, the father of information theory

• Short biographies: #1 and #2
• Read Shannon's classic 1948 paper, or click here for a PDF file
• Death in February, 2001

Chapter 1 of text

September 24: Matlab programs bsccap.m (capacity of BSC) and bsc.m (BER simulation of repetition code)

September 26:

• Matlab program bsckoz.m (Kozick's BER simulation of repetition code)
• Plots comparing simulated and analytical BER

October 3: BSC capacity plot produced with bsccap.m

October 12: Matched Filter Demonstrations

MATLAB program matchfilt.m

• Note that rectangular filtering of the rectangular pulse performs the best out of the three methods.
• Run the program until you see a case where the matched filtering of the triangular pulse is better than rectangular filtering. That is, the matched filter output is positive while the rectangular filter output is negative.
• Try changing the noise amplitude with the variable wstddev.
• The program mc_matchfilt.m simulates the detection performance of the various filters over 10,000 runs.
• Why do rectangular pulses perform better (fewer bit errors) than triangular pulses, even when both pulses have the same energy and when the proper matched filter is used?
  (Hint: How do the pulses differ in the frequency domain?)

October 31: BER for BPSK in AWGN

• Program for you to modify, BER_Eb_N0.m
• Marcum's Q function: Qf.m
• BER versus Eb/N0 should look like this plot
• Program with solution, BER_Eb_N0sol.m

November 2: Teams for projects and reports

November 14:

• Graphical Viterbi Decoder Applet
• Demo Movie of the Viterbi Algorithm
• Biography of A.J. Viterbi

November 19:

• The following paper is posted on Blackboard under ELEC 476, in the "Course Documents" folder:

  R.G. Gallager, "Claude E. Shannon: A Retrospective on his Life, Work, and Impact", IEEE Transactions on Information Theory, vol. 7, no. 47, pp. 2681-2695, November 2001.

• You will need the following three Matlab functions to implement the Viterbi algorithm: initvit1.m, viterbi1.m, and vitflush.m. These functions are also available in my public space on NT. These functions are taken from the book T.K. Moon and W.C. Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice-Hall, 2000.

• Schedule for student reports

• Multi-Carrier CDMA Demonstration

November 26 and 28:

• Matlab program hardvit.m and dH.m, status as of the end of class on November 26.
• BER plots for various codes over BSC, computed with codebounds.m
• Simulated BER of convolutional code
• Matlab programs for BER simulation: rjkvit2.m and dH.m

December 5:

• BER versus Eb/N0, including rate 1/2 convolutional code:
  • Plot
  • Matlab program BER_Eb_N0_hc.m
• Matlab programs for hard-decision Viterbi algorithm over BSC:
  rjkvit2.m and dH.m
• Matlab programs for soft-decision Viterbi algorithm over AWGN channel:
  softvit2.m and sqerr.m
• Results:

  Hard decision: BER = 2 x 10^-6 for E_b/N₀ = 6 dB (p = 0.0024 for BSC)
  Hard decision: BER = 10^-4 for E_b/N₀ = 4 dB (p = 0.0125 for BSC)
  Soft decision: 0 errors in 10⁷ bits for E_b/N₀ = 4 dB
  Soft decision: BER = 6.3 x 10^-6 for E_b/N₀ = 3 dB
  Soft decision: BER = 8.7 x 10^-5 for E_b/N₀ = 2 dB