Applications of Linear Programming to Coding Theory

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem. In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such vectors are known as pseudocodewords. In this work, we completely classify the set of linear programming pseudocodewords for the family of cycle codes. For the case of the binary symmetric channel, another approximation of maximum-likelihood decoding was introduced by Omura in 1972. This decoder employs an iterative algorithm whose behavior closely mimics that of the simplex algorithm. We generalize Omura's decoder to operate on any binary-input memoryless channel, thus obtaining a soft-decision decoding algorithm. Further, we prove that the probability of the generalized algorithm returning the maximum-likelihood codeword approaches 1 as the number of iterations goes to infinity.

Nebraska Winery and Grape Growers Forum and Trade Show

Good afternoon, everyone, and welcome to this 11th annual Nebraska Winery and Grape Growers Forum and Trade Show. I'm John Owens, University of Nebraska Vice President and Harlan Vice Chancellor of the Institute of Agriculture and Natural Resources. I'm delighted to be with you on this second day of a very fine and informative conference.

Applications and Potentials for Biogenic Methane Recovery Operations in Nebraska Agriculture, Industry, and Economic Development

ABSTRACT: This thesis report illustrates the applications and potentials of biogenic methane recovery in Nebraska’s agricultural and industrial sectors and as a means for increasing sustainable economic development in the state’s rural communities. As the nation moves toward a new green economy, biogenic methane recovery as a waste management strategy and renewable energy resource presents significant opportunities for Nebraska to be a national and world leader in agricultural and industrial innovation, advanced research and development of renewable energy technology, and generation of new product markets. Nebraska’s agricultural economy provides a distinct advantage to the state for supporting methane recovery operations that provide long-term economic and environmental partnerships among producers, industry, and communities. These opportunities will serve to protect Nebraska’s agricultural producers from volatile energy input markets and as well as creating new markets for Nebraska agricultural products. They will also serve to provide quality education and employment opportunities for Nebraska students and businesses. There are challenges and issues that remain for the state in order to take advantage of its resource potential. There is a need to produce a comprehensive Nebraska biogenic methane potential study and digital mapping system to identify high-potential producers, co-products, and markets. There is also a need to develop a web-based format of consolidated information specific to Nebraska to aid in connecting producers, service providers, educators, and policy-makers.

Politics and Trade in the Former Soviet Union

Fifteen independent countries emerged from the collapse of the Soviet Union in 1989-91. Aside from the Russian Federation, the former Soviet Republics lie in four geographic regions: the Caucasus (Armenia, Azerbaijan, Georgia); Central Asia (Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan); the Baltics (Estonia, Latvia, Lithuania); and Eastern Europe (Belarus, Moldova, Ukraine).