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Download as PDF; Printable version; In other projects ... move to sidebar hide. In coding theory , the Forney algorithm (or ... It is used as one of the steps in ...
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 ...
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
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 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 sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision ...
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.