Skip to main content

convolutional code

convolutional code A linear error-correcting code, characterized by a k × n generator matrix, G = (gij[x]),

whose elements gij[x] are polynomials whose highest degree, m, is called the memory of the code. The quantity c = m + 1

is called the constraint length of the code.

The convolutional encoder operates as follows. The input stream, regarded as the coefficients of a polynomial of arbitrary degree, is cyclically distributed (i.e. demultiplexed) among the inputs of k shift registers, all of length c: the contents of the ith shift register is serially multiplied by each of the n polynomials gij[x] (using n serial multipliers in parallel). Then n output streams are formed by summing the outputs of the jth multiplier on each register. These streams are cyclically multiplexed to form the output of the encoder. All this can be carried out to base q, for q prime; such codes are usually implemented in binary form (q = 2). In practice, the parameter k is normally equal to 1.

The main decoding algorithms for convolutional codes are Viterbi's algorithm and various sequential algorithms, of which the most important are Fano's algorithm and the stack algorithm. Viterbi's is a maximum-likelihood algorithm.

Linear block codes can be regarded as a special case of convolutional codes with m = 0 and c = 1. Convolutional codes are often specified by the parameters (n, k) or (n, k, c), although the simple phrase (n, k) code usually specifies a block code rather than a convolutional code.

Convolutional codes are of increasing importance as they become better understood theoretically, as better decoding algorithms are found, and as it becomes increasingly economical to provide programmable decoders, the decoding algorithms being best programmed in software owing to their complexity.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"convolutional code." A Dictionary of Computing. . Encyclopedia.com. 13 Nov. 2018 <https://www.encyclopedia.com>.

"convolutional code." A Dictionary of Computing. . Encyclopedia.com. (November 13, 2018). https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/convolutional-code

"convolutional code." A Dictionary of Computing. . Retrieved November 13, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/convolutional-code

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.