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A natural concept for a decoding algorithm for concatenated codes is to first decode the inner code and then the outer code. For the algorithm to be practical it must be polynomial-time in the final block length. Consider that there is a polynomial-time unique decoding algorithm for the outer code.
As with ideal observer decoding, a convention must be agreed to for non-unique decoding. The maximum likelihood decoding problem can also be modeled as an integer programming problem. [1] The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized ...
One significant application of Reed–Solomon coding was to encode the digital pictures sent back by the Voyager program. Voyager introduced Reed–Solomon coding concatenated with convolutional codes, a practice that has since become very widespread in deep space and satellite (e.g., direct digital broadcasting) communications.
Decoding via a standard array is a form of nearest neighbour decoding. In practice, decoding via a standard array requires large amounts of storage - a code with 32 codewords requires a standard array with entries. Other forms of decoding, such as syndrome decoding, are more efficient.
This process is iterated until a valid codeword is achieved or decoding is exhausted. This type of decoding is often referred to as sum-product decoding. The decoding of the SPC codes is often referred to as the "check node" processing, and the cross-checking of the variables is often referred to as the "variable-node" processing.
Viterbi decoding allows asymptotically optimal decoding efficiency with increasing constraint length of the convolutional code, but at the expense of exponentially increasing complexity. A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is ...
However, with the block sizes used in industry, the performance of the successive cancellation is poor compared to well-defined and implemented coding schemes such as low-density parity-check code (LDPC) and turbo code. Polar performance can be improved with successive cancellation list decoding, but its usability in real applications is still ...
In practice, this meant that two codebooks were now required, one to find codegroups for encoding, the other to look up codegroups to find plaintext for decoding. Such "two-part" codes required more effort to develop, and twice as much effort to distribute (and discard safely when replaced), but they were harder to break.