Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Towards Practical Minimum-Entropy Universal Decoding
DCC '05 Proceedings of the Data Compression Conference
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Secret Key Agreement from Correlated Source Outputs Using Low Density Parity Check Matrices
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Construction of Universal Codes Using LDPC Matrices and Their Error Exponents
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Hash property and coding theorems for sparse matrices and maximum-likelihood coding
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
On the application of LDPC codes to arbitrary discrete-memoryless channels
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
Low-density parity-check matrices for coding of correlated sources
IEEE Transactions on Information Theory
Source Coding Using Families of Universal Hash Functions
IEEE Transactions on Information Theory
Hash property and coding theorems for sparse matrices and maximum-likelihood coding
IEEE Transactions on Information Theory
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The aim of this paper is to prove the fixed-rate universal coding theorems by using the notion of the hash property. These theorems are the fixed-rate lossless universal source coding theorem and the fixed-rate universal channel coding theorem. Since an ensemble of sparse matrices (with logarithmic column degree) satisfies the hash property requirement, it is proved that we can construct universal codes by using sparse matrices.