EE814: Communications Theory II
(Error Control Coding)
Ha H. Nguyen, 3B05 Engineering Building
Wednesdays and Fridays, 9:30am-10:50am, Room AGRI 2D79
In 1948, Shannon demonstrated in his landmark paper ("A mathematical theory of communication", Bell Syst. Tech. J., vol. 27, pp. 379-423) that, by proper encoding of the information, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transmission as long as the information rate is less than the capacity of the channel. Shannon's work, however, does not indicate how to perform the encoding and decoding to achieve the above result. Since then much effort has been expended on the problem of devising efficient encoding and decoding methods for error control in a noisy environment. Recent developments have contributed toward achieving the reliability required by today's high-speed digital communication systems. The use of coding for error control has, in fact, become an integral part in the design of modern communication systems.
The major engineering problem to be addressed in this course is to design and implement the channel encoder/decoder pair such that (i) information can be transmitted over a noisy channel as fast as possible; (ii) the information can be reliably reproduced at the output of the channel decoder; and (iii) the cost of implementing the encoder and decoder falls within acceptable limits. The course will be organized roughly as follows.
Linear Block Codes:
Introduction to linear block codes, syndrome and error detection, the minimum distance of a block code, error-detecting and error-correcting capabilities of a block code, standard array and syndrome decoding, important linear block codes, reliability-based decoding algorithms for linear block codes.
Encoding of convolutional codes, structural properties of convolutional codes, distance properties of convolutional codes,
the Viterbi algorithm, performance bounds for convolutional codes, the soft-output Viterbi algorithm (SOVA), the BJCR algorithm, suboptimal decoding of convolutional codes, trellis-based soft-decision decoding algorithms for convolutional codes.
Introduction to turbo coding, distance properties, performance analysis, iterative decoding of turbo codes.
Trellis-Coded Modulation (TCM):
Introduction to TCM, TCM code construction, TCM performance analysis, multidimensional TCM, turbo TCM (TTCM).
Low-Density Parity-Check (LDPC) Codes:
Introduction to LDPC codes, decoding of LDPC codes, random LDPC codes, irregular LDPC codes, concatenations with LDPC and turbo codes.
Distance concepts, multilevel coded modulation, multistage decoding of multilevel coded modulation, bit-interleaved coded modulation (BICM), BICM with iterative decoding (BICM-ID).
S. Lin and D. J. Costello, Jr., Error Control Coding: Fundamentals and Applications, 2nd Edition, Prentice-Hall, 2004.
R. E. Blahut, Theory and Practice of Error Control Codes, Addison-Wesley, 1983.
S. B. Wicker, Error Control Systems for Digital Communication and Storage, Prentice-Hall, 1995.
E. Biglieri, D. Divsalar, P. J. McLane and M. K. Simon, Introduction to Trellis-Coded Modulation with Applications, Macmillan, 1991.
C. Heegard and S. B. Wicker, Turbo Coding, Kluwer Academic Publishers, 1999.
C. B. Schlegel and L. C. Perez, Trellis and Turbo Coding, IEEE Press and Wiley-Interscience, 2004.
B. Sklar, Digital Communications: Fundamentals and Applications, Prentice-Hall, 2001.
J. G. Proakis, Digital Communications, McGraw-Hill, 2001.
Final grades will be determined on the basis of assignments (50%) and a final examination (50%).
Note regarding the assignments: Though I do not object to students discussing the concepts, I do expect that the work handed in is essentially the effort of the student. You are of course always welcome to discuss a problem(s) with me.
Basic knowledge of probability theory and random processes.
Basic knowledge of digital modulation techniques. If you are not familiar with this subject, please review Chapters 5-8 in EE456 textbook, "A First Course in Digital Communications".
Other Useful Materials
C. E. Shannon, "A mathematical theory of communication", Bell Syst. Tech. J., vol. 27, pp. 379-423, 1948.
I. M. Jacobs, “Practical applications of coding,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 305–310, May 1974.
D. J. Costello, Jr., J. Hagenauer, H. Imai and S. B. Wicker, "Applications of Error-Control Coding", IEEE Trans. Inform. Theory, vol. 44, pp. 2531-2560, Oct. 1998.
G. Ungerboeck, "Channel coding with multilevel/phase signals", IEEE Trans. Inform. Theory, vol. IT-28, pp.55-67, Jan. 1982.
G. Ungerboeck, "Trellis-coded modulation with redundant signal sets—Part I: Introduction," IEEE Commun. Mag., vol. 25, pp. 5–11, Feb. 1987.
G. Ungerboeck, "Trellis-coded modulation with redendant signal sets—Part II: State of the art," IEEE Commun. Mag., vol. 25, pp. 12–21, Feb. 1987.
C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo codes," in Proc. 1993 IEEE Int. Communications Conf. (Geneva, Switzerland, May 1993), pp. 1064–1070.