Convolutional code: Difference between revisions

Revision as of 07:56, 4 May 2025

Latest revision as of 07:56, 4 May 2025

Line 3:

In [[Telecommunications|telecommunication]], a '''convolutional code''' is a type of [[Error correction code|error-correcting code]] that generates parity symbols via the sliding application of a [[Algebraic normal form|boolean polynomial]] function to a data stream. 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 (graph)|trellis]] decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity.

The ability to perform economical maximum likelihood soft decision decoding is one of the major benefits of convolutional codes. This is in contrast to classic block codes, which are generally represented by a time-variant trellis and therefore are typically hard-decision decoded. Convolutional codes are often characterized by the base [[code rate]] and the depth (or memory) of the encoder <math>[n,k,K]</math>. The base code rate is typically given as <math>k/n/k</math>, where {{mvar|n}} is the raw input data rate and {{mvar|k}} is the data rate of output channel encoded stream. {{mvar|n}} is less than {{mvar|k}} because channel coding inserts redundancy in the input bits. The memory is often called the "constraint length" {{mvar|K}}, where the output is a function of the current input as well as the previous <math>K-1</math> inputs. The depth may also be given as the number of memory elements {{mvar|v}} in the polynomial or the maximum possible number of states of the encoder (typically: <math>2^v</math>).

Convolutional codes are often described as continuous. However, it may also be said that convolutional codes have arbitrary block length, rather than being continuous, since most real-world convolutional encoding is performed on blocks of data. Convolutionally encoded block codes typically employ termination. The arbitrary block length of convolutional codes can also be contrasted to classic [[block code]]s, which generally have fixed block lengths that are determined by algebraic properties.