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Distributed Source Coding
Distributed source coding (DSC) is an important problem in information theory and communication. DSC problems regard the compression of multiple correlated information sources that do not communicate with each other. By modeling the correlation between multiple sources at the decoder side together with channel codes, DSC is able to shift the computational complexity from encoder side to decoder side, therefore provide appropriate frameworks for applications with complexity-constrained sender, such as sensor networks and video/multimedia compression (see distributed video coding). One of the main properties of distributed source coding is that the computational burden in encoders is shifted to the joint decoder. History In 1973, David Slepian and Jack Keil Wolf proposed the information theoretical lossless compression bound on distributed compression of two correlated i.i.d. sources X and Y. After that, this bound was extended to cases with more than two sources by Thomas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, Neuroscience, neurobiology, physics, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a Fair coin, fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a dice, die (which has six equally likely outcomes). Some other important measu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-density Parity-check Code
Low-density parity-check (LDPC) codes are a class of error correction codes which (together with the closely-related turbo codes) have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely used in applications ranging from wireless communications to flash-memory storage. Together with turbo codes, they sparked a revolution in coding theory, achieving order-of-magnitude improvements in performance compared to traditional error correction codes. Central to the performance of LDPC codes is their adaptability to the iterative belief propagation decoding algorithm. Under this algorithm, they can be designed to approach theoretical limits (Channel capacity, capacities) of many channels at low computation costs. Theoretically, analysis of LDPC codes focuses on sequences of codes of fixed code rate and increasing block length. These sequences are typically tailored to a set of channels. For appropriately designed sequences, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Code
In coding theory, a linear code is an error-correcting code for which any linear combination of Code word (communication), codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding). Linear codes are used in forward error correction and are applied in methods for transmitting symbols (e.g., bits) on a communications channel so that, if errors occur in the communication, some errors can be corrected or detected by the recipient of a message block. The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. A linear code of length ''n'' transmits blocks containing ''n'' symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity Check Matrix
In coding theory, a parity-check matrix of a linear block code ''C'' is a matrix which describes the linear relations that the components of a codeword must satisfy. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms. Definition Formally, a parity check matrix ''H'' of a linear code ''C'' is a generator matrix of the dual code, ''C''⊥. This means that a codeword c is in ''C ''if and only if the matrix-vector product (some authors would write this in an equivalent form, c''H''⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. That is, they show how linear combinations of certain digits (components) of each codeword equal zero. For example, the parity check matrix :H = \left \begin 0&0&1&1\\ 1&1&0&0 \end \right, compactly represents the parity check equations, :\begin c_3 + c_4 &= 0 \\ c_1 + c_2 &= 0 \end, that must be satisfied for the vector (c_1, c_2, c_3, c_4) to be a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generator Matrix
In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix. Terminology If G is a matrix, it generates the codewords of a linear code ''C'' by : w=sG where w is a codeword of the linear code ''C'', and s is any input vector. Both w and s are assumed to be row vectors. A generator matrix for a linear , k, dq-code has format k \times n, where ''n'' is the length of a codeword, ''k'' is the number of information bits (the dimension of ''C'' as a vector subspace), ''d'' is the minimum distance of the code, and ''q'' is size of the finite field, that is, the number of symbols in the alphabet (thus, ''q'' = 2 indicates a binary code, etc.). The number of redundant bits is denoted by r = n - k. The ''standard'' form for a generator matrix is, : G = \begin I_k , P \end, where I_k is the k \times k identity m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Code
In coding theory, a linear code is an error-correcting code for which any linear combination of Code word (communication), codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding). Linear codes are used in forward error correction and are applied in methods for transmitting symbols (e.g., bits) on a communications channel so that, if errors occur in the communication, some errors can be corrected or detected by the recipient of a message block. The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. A linear code of length ''n'' transmits blocks containing ''n'' symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Code
In computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect codes, that is, they achieve the highest possible rate for codes with their block length and minimum distance of three. Richard W. Hamming invented Hamming codes in 1950 as a way of automatically correcting errors introduced by punched card readers. In his original paper, Hamming elaborated his general idea, but specifically focused on the Hamming(7,4) code which adds three parity bits to four bits of data. In mathematical terms, Hamming codes are a class of binary linear code. For each integer there is a code-word with block length and message length . Hence the rate of Hamming codes is , which is the highest p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
