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In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...
VideoLAN dav1d – An AV1 decoder for decoding videos with AV1 codec; Xiph.Org rav1e – An AV1 encoder written in Rust; Google libgav1 – An AV1 decoder by Google; xvc – An open source video codec, aiming to compete with h.265 and AV1. The reference implementation is released under the LGPL 2.1 and currently available in version 2.0 (as of ...
The codes that they are given are called folded Reed-Solomon codes which are nothing but plain Reed-Solomon codes but viewed as a code over a larger alphabet by careful bundling of codeword symbols. Because of their ubiquity and the nice algebraic properties they possess, list-decoding algorithms for Reed–Solomon codes were a main focus of ...
Syndrome decoding is a highly efficient method of decoding a linear code over a noisy channel, i.e. one on which errors are made. In essence, syndrome decoding is minimum distance decoding using a reduced lookup table. This is allowed by the linearity of the code. [3]
Using these highly efficient codes and with the computing power in today's digital signal processors, it is now possible to reach very close to the Shannon limit. In fact, it was shown that LDPC codes can reach within 0.0045 dB of the Shannon limit (for binary additive white Gaussian noise (AWGN) channels, with very long block lengths). [1]
The RM(0, m) code is the repetition code of length N =2 m and weight N = 2 m−0 = 2 m−r. By 1 (,) = and has weight 1 = 2 0 = 2 m−r. The article bar product (coding theory) gives a proof that the weight of the bar product of two codes C 1, C 2 is given by
A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm ).
A code is a prefix code if no target bit string in the mapping is a prefix of the target bit string of a different source symbol in the same mapping. This means that symbols can be decoded instantaneously after their entire codeword is received. Other commonly used names for this concept are prefix-free code, instantaneous code, or context-free ...