Dynamic Shannon Coding

We present a new algorithm for dynamic prefix-free coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient length-restricted coding, alphabetic coding and coding with unequal letter costs.Comment: 6 pages; conference version presented at ESA 2004; journal version submitted to IEEE Transactions on Information Theor

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon theory literature. We also demonstrate that the "quantum dynamic capacity formula" characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula simplifies the computation of the trade-off surface, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections; v3 has correction regarding the optimizatio

A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal

Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizing both of the above examples. The dual protocols responsible for this decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf'' protocol (FQSW), a generalization of the recently discovered ``quantum state merging'', is related to FF by source-channel duality, and to FQRS by time reversal duality, thus forming a triangle of dualities. The source-channel duality is identified as the origin of the previously poorly understood ``mother-father'' duality. Due to a symmetry breaking, the dualities extend only partially to classical information theory.Comment: 5 pages, 5 figure

STUDI BANDING ALGORITMA KOMPRESI HUFFMAN CODING DAN ADAPTIVE HUFFMAN CODING

ABSTRAK Algoritma kompresi menurut David Solomon (2007:2) adalah proses mengkonversikan sebuah input data stream (streamsumber, atau data mentah asli) menjadi data stream lainnya (bitstream hasil, atau stream yang telah terkompresi) yang berukuran lebih kecil. Berbagai tipe algoritma kompresi, antara lain: Huffman, LIFO, LZHUF, LZ77 dan variannya ( LZ78, LZW, GZIP), Dynamic Markov Compression (DMC), Block-SortingLossLess, Run-Length, Shannon-Fano, Arithmetic, PPM (Prediction by PartialMatching), Burrows-Wheeler, Block Sorting, dan Half Byte. Huffman Coding dan Adaptive Huffman Coding adalah salah satu tipe algoritma kompresi yang menjadi pokok bahasan dalam tugas akhir ini. Huffman Coding adalah sebuah tipe kode optimal yang biasanya digunakan untuk lossless data compression. Huffman coding ditemukan oleh David A. Huffman pada saat ia masih seorang mahasiswa di MIT, ia menerbitkan karyanya ditahun 1952 yang berjudul “A Method for the Contruction of Minimum Redudancy Codes”. Adaptive Huffman Coding adalah teknik pengkodean adaptif berdasarkan pengkodean Huffman. Adaptif mempunyai implementasi antara lain algoritma FGK dan algoritma Vitter. Hasil dari studi banding mengenai tugas akhir ini adalah mengenai apa saja yang menjadi keunggulan Huffman coding dan Adaptive Huffman coding. Kata kunci : algoritma kompresi, tipe algoritma kompresi, Huffman Coding, Adaptive Huffman Codin

Robust And Optimal Opportunistic Scheduling For Downlink 2-Flow Network Coding With Varying Channel Quality and Rate Adaptation

This paper considers the downlink traffic from a base station to two different clients. When assuming infinite backlog, it is known that inter-session network coding (INC) can significantly increase the throughput of each flow. However, the corresponding scheduling solution (when assuming dynamic arrivals instead and requiring bounded delay) is still nascent. For the 2-flow downlink scenario, we propose the first opportunistic INC + scheduling solution that is provably optimal for time-varying channels, i.e., the corresponding stability region matches the optimal Shannon capacity. Specifically, we first introduce a new binary INC operation, which is distinctly different from the traditional wisdom of XORing two overheard packets. We then develop a queue-length-based scheduling scheme, which, with the help of the new INC operation, can robustly and optimally adapt to time-varying channel quality. We then show that the proposed algorithm can be easily extended for rate adaptation and it again robustly achieves the optimal throughput. A byproduct of our results is a scheduling scheme for stochastic processing networks (SPNs) with random departure, which relaxes the assumption of deterministic departure in the existing results. The new SPN scheduler could thus further broaden the applications of SPN scheduling to other real-world scenarios