**Week ** |
**Topic ** |

**1** |
Introduction to data compression: Types, performance measures, adaptive vs. universal compression.
Lossless source coding theory: Source coding theorem.Independent and identically distributed, Markov, linear system models, probability models. Conditional entropy, advantage of conditional coding. |

**2** |
Lossless source codes: Uniquely decodable and prefix codes. Kraft-McMillan inequality. Huffman coding (algorithm, optimality, code length, block Huffman coding). |

**3** |
Adaptive Huffman coding. Golomb, Rice, Tunstall codes. Arithmetic coding (tag generation). |

**4** |
Arithmetic coding ( tag deciphering, scaling). Bounds on Huffman&Arithmetic coding. Dictionary based techniques (LZ77,LZ78, LZW). |

**5** |
Lossy source coding theory: Distortion criteria, mutual information, differential entropy . Test channel. Rate-Distortion and Distortion-Rate functions. Distortion-Rate theorem and converse. Rate-Distortion functions for binary, memoryless, Gaussian memoryless sources. Shannon lower bound. |

**6** |
Scalar quantization (SQ): Decision thresholds, quantizers levels, mapping. Distortion and rate computation. Uniform quantization. Mean Square Error and Peak Signal to Noise Ratio. Optimal uniform quantization for a nonuniform distributed source. Step size adaptive quantization. |

**7** |
Lloyd-Max optimum quantizer. Companding and Bennett integral. |

**8** |
Entropy coded quantization (Uniform entropy coded advantage, Gish&Pierce and Goblick&Holsinger results).
Entropy constrained quantization. |

**9** |
Vector coding and vector quantization (VQ): Optimal performance bounds. Block rate-distortion function. Advantage of VQ over SQ |

**10** |
Linde-Buzo-Gray(LBG) Algorithm (Local optimality, LBG algorithm based on source statistics, LBG algorithm based on training set, initialization by splitting).
Tree structured vector quantization (Balanced, unbalanced trees). |

**11** |
Differential coding: Energy reduction by difference coding of correlated samples. Differential pulse code modulation (DPCM) Tracking issue , encoder and decoder loops. Optimal linear prediction and Wiener-Hopf equation. Adaptive quantization in DPCM. Adaptive prediction in DPCM (autocorrelation estimation for forward adaptive prediction, Least Mean Square algorithm for backward adaptive prediction). DPCM coding error and gain for wide sense stationary source. Delta modulation and Adaptive delta modulation. |

**12** |
Transform coding: Orthonormal transforms. Karhunen Loeve transform (KLT).Rate-distortion formula for block coding. Rate allocation to transform coefficients (via Kuhn Tucker theorem). Transform coding gain derivation. Discrete Cosine Transform (DCT) and Discrete Sine Transform. Asymptotic equivalence of DCT to KLT. Subband and wavelet transform coding. |

**13** |
Project presentations. |