Precoding for Outage Probability Minimization on Block Fading Channels

• Published in: IEEE transactions on information theory Vol. 59; no. 12; pp. 8250 - 8266
• Main Authors: Duyck, Dieter, Boutros, Joseph Jean, Moeneclaey, Marc
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Block fading channels; Codes; Coding, codes; Communication systems; Encoding; Exact sciences and technology; Fading; Information theory; Information, signal and communications theory; multidimensional mapping; Optimization; outage probability; precoding; Probability distribution; Signal and communications theory; Signal to noise ratio; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Vectors; Alphabet; Fading channels; Performance evaluation; Fading; Lower bound; Outage; Block fading channels; Diversity; Error rate; Gaussian distribution; Mapping; precoding; multidimensional mapping; Geometrical model; Upper bound; outage probability; Coding; Telecommunication system; Error correcting code; Pretreatment
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2281418

The outage probability limit is a fundamental and achievable lower bound on the word error rate of coded communication systems affected by fading. This limit is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, full diversity on a block fading channel can be achieved without error-correcting code. However, the effect of precoding on the coding gain is not well known, mainly due to the complicated expression of the outage probability. Using a geometric approach, this paper establishes simple upper bounds on the outage probability, the minimization of which yields to precoding matrices that achieve very good performance. For discrete alphabets, it is shown that the combination of constellation expansion and precoding is sufficient to closely approach the minimum possible outage achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing the coding gain.