UNIVERSITY OF CALIFORNIA, SAN DIEGO
Electrical & Computer Engineering Department
ECE 259B  Winter Quarter 2011
Probabilistic Coding
Problem Set #1
Due Thursday, January 13, 2011
1. Recall Shannon’s capacity formula for the bandlimited, powerlimited Gaussian channel:
C
=
W
log
2
(1 +
SNR
)
where the signaltonoise ratio (SNR) is given by
SNR
=
P
ave
/N
0
W.
(a) Draw a detailed plot of
C
versus
W
, assuming fixed average signal power
P
ave
and two
sided noise spectral density
N
0
2
. What is the limiting value of capacity as the bandwidth
approaches infinity? Interpret your result.
(b) In class we rewrote the capacity formula in terms of the average SNR per bit
E
b
/N
0
and
then solved for
E
b
/N
0
in terms of the spectral efficiency
C/W
. Give the details of the
calculation of
E
b
/N
0
corresponding to the limiting case of zero spectral efficiency, and
provide your interpretation of the result.
2. This problem will familiarize you with properties of generator matrices and physical encoder
realizations for convolutional codes. Consider the following polynomial generator matrices for
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Song
 Coding theory, Convolutional code, convolutional, distance df ree, timevarying trellis diagram, free distance df

Click to edit the document details