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Abstract
In this dissertation, we propose a new way of looking at arithmetic codes with forbidden symbols. With a finite state machine interpretation of arithmetic codes, we can derive a variable input symbol length and variable output bit length trellis to decode the arithmetic codes. Compared to previous results, a significant performance gain (2dB) can be achieved by applying the list Viterbi algorithm on the trellis. The finite state machine interpretation can be easily migrated to Markov source case. We can encode Markov sources without considering the conditional probabilities, while using the list Viterbi decoding algorithm which utilizes the conditional probabilities. We can also use context-based arithmetic coding to exploit the conditional probabilities of the Markov source and apply a finite state machine interpretation to this problem.
The finite state machine interpretation also allows us to more systematically understand arithmetic codes with forbidden symbols. It allows us to find the partial distance spectrum of arithmetic codes with forbidden symbols. We also propose arithmetic codes with memories which use high memory but low implementation precision arithmetic codes. The low implementation precision results in a state machine with less complexity. The introduced input memories allow us to switch the probability functions used for arithmetic coding. Combining these two methods give us a huge parameter space of the arithmetic codes with forbidden symbols. Hence we can choose codes with better distance properties while maintaining the encoding efficiency and decoding complexity. A construction and search method is proposed and simulation results show that we can achieve about 0.8dB performance gain when we apply this approach to rate 2/3 arithmetic codes.
