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The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way. Such limitations often take the form of bounds that relate different parameters of the block code to each other, such as its rate and its ability ...
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 ...
MIT Lecture Notes on Essential Coding Theory – Dr. Madhu Sudan; University at Buffalo Lecture Notes on Coding Theory – Dr. Atri Rudra; Algebraic Codes on Lines, Planes and Curves, An Engineering Approach – Richard E. Blahut; Welch Berlekamp Decoding of Reed–Solomon Codes – L. R. Welch
In information theory and coding theory, linear programming decoding (LP decoding) is a decoding method which uses concepts from linear programming (LP) theory to solve decoding problems. This approach was first used by Jon Feldman et al. [ 1 ] They showed how the LP can be used to decode block codes.
The free distance [7] (d) is the minimal Hamming distance between different encoded sequences. The correcting capability ( t ) of a convolutional code is the number of errors that can be corrected by the code.
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. [ citation needed ] Algebraic coding theory is basically divided into two major types of codes: [ citation needed ]
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 ...