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In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a 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 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 . The base code rate is typically given as , where n is the raw input data rate and k is the data rate of output channel encoded stream. n is less than k because channel coding inserts redundancy in the input bits. The memory is often called the "constraint length" K, where the output is a function of the current input as well as the previous inputs. The depth may also be given as the number of memory elements v in the polynomial or the maximum possible number of states of the encoder (typically: ).
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 codes, which generally have fixed block lengths that are determined by algebraic properties.
The code rate of a convolutional code is commonly modified via symbol puncturing. For example, a convolutional code with a 'mother' code rate may be punctured to a higher rate of, for example, simply by not transmitting a portion of code symbols. The performance of a punctured convolutional code generally scales well with the amount of parity transmitted. The ability to perform economical soft decision decoding on convolutional codes, as well as the block length and code rate flexibility of convolutional codes, makes them very popular for digital communications.
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Serial concatenated convolutionalcodes (SCCC) are a class of forward error correction (FEC) codes highly suitable for turbo (iterative) decoding. Data...
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the inner code is not a block code but a soft-decision convolutional Viterbi-decoded code with a short constraint length. For the outer code, a longer...
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convolutionalcode. In GPRS Coding Schemes CS-1 through CS-3, the convolutionalcode is of rate 1/2, i.e. each input bit is converted into two coded bits...
k / n {\displaystyle \leq R\cdot k/n} . For example: The code rate of a convolutionalcode will typically be 1⁄2, 2⁄3, 3⁄4, 5⁄6, 7⁄8, etc., corresponding...
In telecommunication, a Hagelbarger code is a convolutionalcode that enables error bursts to be corrected provided that there are relatively long error-free...
the output of the convolutionalcode is punctured to achieve the desired code rate. In Coding Scheme CS-4, no convolutionalcoding is applied. The following...
technique closely resembles a trellis lattice. The scheme is basically a convolutionalcode of rates (r, r+1). Ungerboeck's unique contribution is to apply the...
message: It uses forward error correction (FEC) provided by a rate 1/2 convolutionalcode, so while the navigation message is 25-bit/s, a 50-bit/s signal is...
error-detecting codes. Linear codes are usually implemented as systematic error-correcting codes (e.g., Reed-Solomon codes in CDs). Convolutionalcodes are implemented...
coder is a memoryless device. Under this definition codes such as turbo codes, terminated convolutionalcodes and other iteratively decodable codes (turbo-like...
and RAM. Error-correcting codes are usually distinguished between convolutionalcodes and block codes: Convolutionalcodes are processed on a bit-by-bit...
(HMM). The algorithm has found universal application in decoding the convolutionalcodes used in both CDMA and GSM digital cellular, dial-up modems, satellite...
decoding tree codes. Sequential decoding is mainly used as an approximate decoding algorithm for long constraint-length convolutionalcodes. This approach...
partitioned into block codes and convolutionalcodes, although turbo codes can be seen as a hybrid of these two types. Linear codes allow for more efficient...
algorithm" may also refer specifically to an algorithm for decoding a convolutionalcode. Online algorithm Streaming algorithm "A Dictionary of Computing at...
is a convolutional neural network structure proposed by LeCun et al. in 1998. In general, LeNet refers to LeNet-5 and is a simple convolutional neural...
Recursive Systematic Convolutionalcode, a type of convolutionalcode Reed–Solomon code, a non-binary cyclic error-correcting code Regular Slotted Container...