Convolutional code[1] 


Infinite-block code that is 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.


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].BCJR decoder, also a trellis-based decoder [4].


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]


  • Block code — Convolutional codes for infinite block size are block codes consisting of infinite blocks.




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Zoo Code ID: convolutional

Cite as:
“Convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021.
@incollection{eczoo_convolutional, title={Convolutional code}, booktitle={The Error Correction Zoo}, year={2021}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Convolutional code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021.