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In coding theory, the Forney algorithm ... It is used as one of the steps in decoding BCH codes and Reed–Solomon codes ... EE387 Notes #7, Handout #28 (PDF), ...
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.
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 ...
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] Linear block codes; Convolutional codes
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 ...
Proof [3]; The capacity is defined as the maximum mutual information between input and output for all possible input distributions (): = {(;)} The mutual information can be reformulated as
This process is iterated until a valid codeword is achieved or decoding is exhausted. This type of decoding is often referred to as sum-product decoding. The decoding of the SPC codes is often referred to as the "check node" processing, and the cross-checking of the variables is often referred to as the "variable-node" processing.
Viterbi decoding allows asymptotically optimal decoding efficiency with increasing constraint length of the convolutional code, but at the expense of exponentially increasing complexity. A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is ...