Joint Source Channel Coding Using Arithmetic Codes

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Morgan & Claypool Publishers, Sep 15, 2009 - Computers - 69 pages
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
 

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Contents

Introduction
1
12 Joint source and channel coding schemes
3
13 Joint source and channel coding with Arithmetic codes
5
Arithmetic Codes
9
22 Integer implementation of encoding and decoding with renormalization
11
221 Encoding with integer arithmetic
12
222 Decoding with integer arithmetic
14
223 Overflow and underflow problems
15
321 Encoding
30
33 Simulations with an Hd source
32
34 Simulation with Markov sources
35
341 Comparing scenario a and b
37
342 Comparing scenario b and c
38
Distance Property and Code Construction
41
412 Using the bound to get estimate of error probability
43
42 Verification
44

23 Optimality of arithmetic coding
17
231 Arithmetic codes are prefix codes
18
232 Efficiency
19
Arithmetic Codes with Forbidden Symbols
21
312 Error detection capability
24
313 Error correction with arithmetic codes
25
32 Viewing arithmetic codes as fixed trellis codes
27
43 Complexity factors and freedom in the code design
45
432 Freedom in the code design
49
441 Memory one arithmetic codes with forbidden symbols
51
442 Memory two arithmetic codes with forbidden symbols
52
Conclusion
57
Bibliography
61
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