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In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications.
However, with the block sizes used in industry, the performance of the successive cancellation is poor compared to well-defined and implemented coding schemes such as low-density parity-check code (LDPC) and turbo code. Polar performance can be improved with successive cancellation list decoding, but its usability in real applications is still ...
As with ideal observer decoding, a convention must be agreed to for non-unique decoding. The maximum likelihood decoding problem can also be modeled as an integer programming problem. [1] The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized ...
One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the Voyager program. Voyager introduced Reed–Solomon coding concatenated with convolutional codes, a practice that has since become very widespread in deep space and satellite (e.g., direct digital broadcasting) communications.
Cyclic codes can be linked to ideals in certain rings. Let = [] / be a polynomial ring over the finite field = ().Identify the elements of the cyclic code with polynomials in such that (, …,) maps to the polynomial + + +: thus multiplication by corresponds to a cyclic shift.
Upon reception, the coding may be used to remove any errors introduced during transmission. The decoding is performed by repeated decoding and [de]interleaving of the received symbols. SCCCs typically include an inner code , an outer code , and a linking interleaver.
In coding theory, a standard array (or Slepian array) is a by array that lists all elements of a particular vector space. Standard arrays are used to decode linear codes ; i.e. to find the corresponding codeword for any received vector.
In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence of encoding symbols can be generated from a given set of source symbols such that the original source symbols can ideally be recovered from any subset of the encoding symbols of size equal to or only slightly larger than the number of ...