Convolutional code[1]


Classical codes that are formed using generator polynomials over the finite field with two elements. The encoder slides across contiguous subsets of the input bit-string (like a convolutional neural network) evaluating the polynomials on that window to obtain a number of parity bits. These parity bits are the encoded information. There are many ways to formulate these codes


Depends on the polynomials used. Using puncturing removal [2] the rate for the code can be increased from \(\frac{1}{t}\) to \(\frac{s}{t}\), where \(t\) is the number of output bits, and \(s\) depends on the puncturing done. This is done by deleting some pieces of the encoder output such that the most-likely decoders remain effective


Evaluation on the generator polynomials. Can be implemented with a small number of XOR gates


Decoders based on the Viterbi algorithm (trellis decoding) were developed first, which result in the most-likely codeword for the encoded bits [3]. Following, other trellis decoders such as the BCJR decoding algorithm [4] were developed later.


A type of convolutional code used in Real-time Application networks [5].Mobile and radio communications (3G networks) use convolutional codes concatenated with Reed-Solomon codes to obtain suitable performance [6].A convolutional code with rate 1/2 was used for deep-space and satellite communication [7]



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Internal code ID: convolutional

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Zoo Code ID: convolutional

Cite as:
“Convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_convolutional, title={Convolutional code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Peter Elias. Coding for noisy channels. IRE Convention Records, 3(4):37–46, 1955.
L. Sari, “Effects of Puncturing Patterns on Punctured Convolutional Codes”, TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 10, (2012). DOI
A. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm”, IEEE Transactions on Information Theory 13, 260 (1967). DOI
L. Bahl et al., “Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)”, IEEE Transactions on Information Theory 20, 284 (1974). DOI
S. I. Mrutu, A. Sam, and N. H. Mvungi, “Forward Error Correction Convolutional Codes for RTAs' Networks: An Overview”, International Journal of Computer Network and Information Security 6, 19 (2014). DOI
T. Halonen, J. Romero, and J. Melero, editors , GSM, GPRS and EDGE Performance (Wiley, 2003). DOI
Butman, Deutsch, and Miller. Performance of concatenated codes for deep space missions. 1981.

Cite as:

“Convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.