Based on the encoding process arithmetic codes can be viewed as tree codes and current
proposals for decoding arithmetic codes with forbidden symbols belong to sequential decoding
algorithms and their variants. In this monograph we propose a new way of looking at arithmetic
codes with forbidden symbols. If a limit is imposed on the maximum value of a key parameter in
the encoder this modified arithmetic encoder can also be modeled as a finite state machine and
the code generated can be treated as a variable-length trellis code. The number of states used
can be reduced and techniques used for decoding convolutional codes such as the list Viterbi
decoding algorithm can be applied directly 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 a similar
performance as turbo codes when we apply this approach to rate 2 3 arithmetic codes.Table of
Contents: Introduction Arithmetic Codes Arithmetic Codes with Forbidden Symbols Distance
Property and Code Construction Conclusion
