Browsing by Subject "codes"
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Item Capacity estimation and code design principles for continuous phase modulation (CPM)(Texas A&M University, 2004-09-30) Ganesan, AravindContinuous Phase Modulation is a popular digital modulation scheme for systems which have tight spectral efficiency and Peak-to-Average ratio (PAR) constraints. In this thesis we propose a method of estimating the capacity for a Continuous Phase Modulation (CPM) system and also describe techniques for design of codes for this system. We note that the CPM modulator can be decomposed into a trellis code followed by a memoryless modulator. This decomposition enables us to perform iterative demodulation of the signal and improve the performance of the system. Thus we have the option of either performing iterative demodulation, where the channel decoder and the demodulator are invoked in an iterative fashion, or a non-iterative demodulation, where the demodulation is performed only once followed by the decoding of the message. We highlight the recent results in the estimation of capacity for channels with memory and apply it to a CPM system. We estimate two different types of capacity of the CPM system over an Additive White Gaussian Noise (AWGN). The first capacity assumes that optimum demodulation and decoding is done, and the second one assumes that the demodulation is done only once. Having obtained the capacity of the system we try to approach this capacity by designing outer codes matched to the CPM system. We utilized LDPC codes, since they can be designed to perform very close to capacity limit of the system. The design complexity for LDPC codes can be reduced by assuming that the input to the decoder is Gaussian distributed. We explore three different ways of approximating the CPM demodulator output to a Gaussian distribution and use it to design LDPC codes for a Bit Interleaved Coded Modulation (BICM) system. Finally we describe the design of Multi Level Codes (MLC) for CPM systems using the capacity matching rule.Item Upper bounds on minimum distance of nonbinary quantum stabilizer codes(Texas A&M University, 2005-11-01) Kumar, SantoshThe most popular class of quantum error correcting codes is stabilizer codes. Binary quantum stabilizer codes have been well studied, and Calderbank, Rains, Shor and Sloane (July 1998) have constructed a table of upper bounds on the minimum distance of these codes using linear programming methods. However, not much is known in the case of nonbinary stabilizer codes. In this thesis, we establish a bridge between selforthogonal classical codes over the finite field containing q2 elements and quantum codes, extending and unifying previous work by Matsumoto and Uyematsu (2000), Ashikhmin and Knill (November 2001), Kim and Walker (2004). We construct a table of upper bounds on the minimum distance of the stabilizer codes using linear programming methods that are tighter than currently known bounds. Finally, we derive code construction techniques that will help us find new codes from existing ones. All these results help us to gain a better understanding of the theory of nonbinary stabilizer codes.