## Joint Source Channel Coding Using Arithmetic CodesBased 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

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 |

### Other editions - View all

Joint Source Channel Coding Using Arithmetic Codes Bi Dongsheng,Khalid Sayood,Michael Hoffman Limited preview - 2009 |

### Common terms and phrases

Am,l arithmetic codes arithmetic encoder AWGN AWGN channel binary code rate codes with forbidden coding interval coding schemes complexity concatenated conditional probabilities convolutional codes correct path cumulative probabilities decoding trellis distance properties distance spectrum E3 mapping Eb/No efﬁciency encoding and decoding error correction error detection error path error probability Fano algorithm ﬁnd ﬁnite state machine forbidden symbols gap gap gap Hamming distance Huffman codes inﬁnite input sequence integer arithmetic iterative decoding joint source channel list Viterbi decoding machine interpretation mapping functions number of reduced output length P(ai packet error rate partial distance spectra path length performance precision arithmetic redundancy register length rescaling reserved probability space Sayood scenario shown in Figure simulation results source and channel source channel coding source coder source probabilities source sequence source symbol Top_value Total_Count trellis codes turbo codes unit interval update the interval upper limit variable length codes Viterbi algorithm Viterbi decoding algorithm