# 编码理论(袁平之）

Information Theory, Coding and Cryptography

1. 信息论引言。Introduction to Information Theory.
2. 不确定性和信息。Uncertainty and Information.
3. 平均互信息和墒。 Average Mutual Information and entropy.
4. 连续变量的信息测度。Information measures for continuous variables.
5. 信源编码定理。 Source coding theorem.
6. Huffman 编码。 Huffman coding.
7. Lempel-Ziv 算法。 The Lempel-Ziv algorithm
8. 率失真函数。Rate distortion function.
9. 保真压缩的Jpeg标准The Jpeg standard for lossless compression.
10. 失真压缩的Jpeg标准The Jpeg standard for lossy compression.

1. 信道模型。Channel models.
2. 信道容量。Channel capacity.
3. 信道编码。Channel coding.
4. 信息量定理。Information capacity theorem.
5. Shannon极限。The Shannon limit.
6. 码的随机选择。Random selection of codes.

1. 引言。Introduction.
2. 基本定义。Basic definitions.
3. 线性码的矩阵描述。Matrix description of linear block codes.
4. 等价码。Equivalent codes
5. 校验矩阵。Parity check matrix.
6. 线性码的译码。Decoding of a linear block code.
7. 综合译码。Syndrome decoding.
8. 纠错码的概率。Probability of error correction.
9. 完全码。Perfect codes.
10. Hamming 码. Hamming codes.
11. 优化线形码。Optimal linear codes.
12. MDS码。Maximum distance separable codes.

1. 循环码导引。Introduction to cyclic codes.
2. 多项式。Polynomials.
3. 多项式的除法。The division algorithm for polynomials
4. 生成循环码的一个方法。A method for generating cyclic codes.
5. 循环码的矩阵描述。Matrix description of cyclic codes.
6. 火码. Fire codes.
7. Golay 码。Golay codes.
8. CRC码。 Cyclic redundancy codes.
9. 码的实现。Implementation of cyclic codes.

1. 引言。Introduction.
2. 本原元。Primitive elements.
3. 极小多项式。Minimal polynomial.
4. 生成多项式。Generator polynomials in terms of minimal polynomials.
5. BCH的几个例子。Some examples of BCH codes.
6. BCH译码。Decoding of BCH codes.
7. Reed-Solomon码。Reed-Solomon codes.
8. Reed-Solomon码编译的实现。Implementation of Reed-Solomon encoders and decoders.

1. 引言。Introduction.
2. 树码和Trellis码。Tree codes and Trellis codes.
3. 卷积码的多项式描述。Polynomial description of convolutional codes.
4. 卷积码的距离概念。Distance notions for convolutional codes.
5. 生成函数。The generating functions.
6. 卷积码的矩阵描述。Matrix description of convolutional codes.
7. 卷积码的译码法。Decoding of convolutional codes.
8. 卷积码的距离的界。Distance bounds for convolutional codes.
9. 已知好的卷积码。Known good convolutional codes.
10. Turbo码及译码。Turbo codes and its decoding.

1. 密码学引论。Introduction to Cryptography.
2. 加密技术概论。An overview of encryption techniques.
3. 加密算法中使用的运算。Operations used by encryption algorithms.
4. 对称密码学。Symmetric Cryptography.
5. DES. Data Encryption Standard.
6. IDES. International Data Encryption Algorithm.
7. RC密码。RC Ciphers.
8. 公开密码算法。Public Key algorithm.
9. RSA算法。The RSA algorithm.
10. PGP. Pretty good privacy.
11. 单向陷门函数。One-way hashing.
12. 密码分析。Cryptanalysis.