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.

The Perception of Natural, Cell Phone, and Computer-Synthesized Speech During The Performance Of Simultaneous Visual-Motor Tasks

This study investigated the influence of top-down and bottom-up information on speech perception in complex listening environments. Specifically, the effects of listening to different types of processed speech were examined on intelligibility and on simultaneous visual-motor performance. The goal was to extend the generalizability of results in speech perception to environments outside of the laboratory. The effect of bottom-up information was evaluated with natural, cell phone and synthetic speech. The effect of simultaneous tasks was evaluated with concurrent visual-motor and memory tasks. Earlier works on the perception of speech during simultaneous visual-motor tasks have shown inconsistent results (Choi, 2004; Strayer & Johnston, 2001). In the present experiments, two dual-task paradigms were constructed in order to mimic non-laboratory listening environments. In the first two experiments, an auditory word repetition task was the primary task and a visual-motor task was the secondary task. Participants were presented with different kinds of speech in a background of multi-speaker babble and were asked to repeat the last word of every sentence while doing the simultaneous tracking task. Word accuracy and visual-motor task performance were measured. Taken together, the results of Experiments 1 and 2 showed that the intelligibility of natural speech was better than synthetic speech and that synthetic speech was better perceived than cell phone speech. The visual-motor methodology was found to demonstrate independent and supplemental information and provided a better understanding of the entire speech perception process. Experiment 3 was conducted to determine whether the automaticity of the tasks (Schneider & Shiffrin, 1977) helped to explain the results of the first two experiments. It was found that cell phone speech allowed better simultaneous pursuit rotor performance only at low intelligibility levels when participants ignored the listening task. Also, simultaneous task performance improved dramatically for natural speech when intelligibility was good. Overall, it could be concluded that knowledge of intelligibility alone is insufficient to characterize processing of different speech sources. Additional measures such as attentional demands and performance of simultaneous tasks were also important in characterizing the perception of different kinds of speech in complex listening environments.