- Announcements
- Suggested topics for the individual presentations have been posted.
- Please read the Syllabus.
- Office hours will be: 3 PM -- 4 PM on Mondays and 4 PM -- 5 PM on Wednesdays, or by appointment. If you want an appointment, please check my schedule and send me an email with a proposed appointment time that does not conflict with my busy times.

- Lecture Notes
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 14, February 8
- Lecture 33, April 7
- Assignments
- Homework Project 1 is due by Friday, March 7. Note that you do not have to use PARI for homeworks 4 and 5.

- Handouts, etc.
- Syllabus
- Intro to conditional probability and application to communication systems
- PARI/GP is available for most platforms from the
Main PARI/GP web site.
Please download an appropriate version if you are not on the DSP
subgroup. On the DSP subgroup, the Solaris version of PARI/GP can be
executed from
**/home/users/jshea/bin/gp** - Very Brief intro to Galois Fields in MATLAB

- Literature

Here is some relevant literature on error-control coding. Some represent important topics that are covered (at least in part) in class. Others represent recent contributions.- A good survey on error-control coding is given in
"Applications of
Error Control Coding," by D. J. Costello, Jr., et al., in
*Information Theory: 50 Years of Discovery*, edited by S. Verdu and S. McLaughlin. - The BCJR decoding algorithm that we will discuss in class is from
L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv,
"Optimal decoding of linear codes for
minimizing symbol error rates,"
*IEEE Trans. Inform. Theory*, vol. IT-20, pp. 284-287, Mar. 1974. - An alternative (subopimtal but somewhat lower complexity)
approach to soft-decision decoding of convolutional codes is given by
the soft-output Viterbi algorithm: J. Hagenauer and
P. Hoeher, "A Viterbi algorithm with soft
outputs and its applications," in
*Proc. 1989 IEEE Global Communications Conf.*(Dalla,s, TX, Nov., 1989), pp. 47.1.1-47.1.7. - Another suboptimal approach to soft-decision decoding is to use
the max-log-MAP approximation in the BCJR decoding algorithm:
P. Robertson, E. Villebrun, and
P. Hoeher, "A
comparison of optimal and sub-optimal MAP decoding algorithms
operating in the log domain", in
*Proc. 1996 IEEE Int. Conf. on Communications*(Seattle, WA), June 1995, vol. 2, pp. 1009-1013. - In fact, it has been shown that the SOVA and max-log-MAP/BCJR are
equivalent:
M. P. C. Fossorier, F. Burkert, S. Lin, and J. Hagenauer,
"On the equivalence
between SOVA and max-log-MAP decodings,"
*IEEE Communications Letters*, vol. 2, pp. 137-139, May 1998. - This paper gives a good overview of soft-decision decoding of
block and convolutional codes: J. Hagenauer, E. Offer, and L. Papke,
"Iterative decoding of binary
block and convolutional codes,"
*IEEE Trans. Inform. Theory*, vol.~42, pp.~429--445, Mar. 1996. - Two of the best introductions to turbo codes are by William Ryan
in an unpublished manuscript entitled A
Turbo Code Tutorial and in a chapter of the Wiley
*Encyclopedia of Telecommunications*entitled Concatenated Convolutional Codes and Iterative Decoding. - Sklar also published an introduction to turbo concepts in
B. Sklar, "A primer on turbo code
concepts",
*IEEE Communications Magazine*, vol. 35, pp. 94-102, Dec. 1997. - Parallel concatenated turbo codes were developed by Berrou, Glavieux, and Thitimajshima in
"Near Shannon limit
error-correcting coding and decoding: turbo codes (1)",
in
*Proc. 1993 IEEE Int. Conf. on Communications*, vol. 2, pp. 23-26, May 1993. - Some of the first works to well explain the performance of turbo codes
are S. Benedetto and G. Montorsi,
"Unveiling turbo codes: Some results on parallel concatenated coding schemes,"
*IEEE Trans. Inform. Theory*, vol. 42, pp. 409-428, Mar. 1996
and L. C. Perez, J. Seghers, and D. J. Costello, Jr.,
"A distance spectrum
interpretation of turbo codes," - An alternative type of turbo code based on serial concatenation is
proposed in S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara,
"Serial concatenation of
interleaved codes: Performance analysis, design, and iterative decoding,"
*IEEE Trans. Inform. Theory*, vol. 44, pp. 909-926, May 1998. - Finding weight spectrum needed to estimate the error floors for turbo
codes can be simplified using the approach in O. Takeshita, M. P. C.
Fossorier, and D. J. Costello, Jr.,
"A new technique for computing
the weight spectrum of turbo-codes,"
*IEEE Communications Letters*, vol. 3, pp. 251-253, Aug. 1999. - Here is the paper I used as reference when creating the notes for
the transition matrix approach to finding the weight spectrum of
convolutional codes: J. K. Wolf and
A. J. Viterbi, "On the
weight distribution of linear block codes formed from convolutional
codes,"
*IEEE Trans. Commun.*, vol. 44, pp. 1049-1051, Sept. 1996. - J. Hagenauer, "Rate-compatible punctured
convolutional codes and their applications,"
*IEEE Trans. Commun.*, vol. 36, pp. 389-400, Apr. 1988. - When block codes do not have a nice structure that permits the
application of low-complexity replication decoding or other
graph-based soft-decision decoding, Chase decoding represents an
alternative: D. Chase, "A class of
algorithms for decoding block codes with channel measurement
information",
*IEEE Trans. Inform. Theory*, vol. IT-18, pp. 170--182, Jan. 1972. - Here is an Introduction to Hidden Markov Models that may be helpful. In particular, it talks about the Baum-Welch algorithm, which is a generalized form of the BCJR algorithm.

*IEEE Trans. Inform. Theory*, vol. 42, pp. 1698--1709, Nov. 1996. - A good survey on error-control coding is given in
"Applications of
Error Control Coding," by D. J. Costello, Jr., et al., in
- Other Useful Links