The decoded 28-byte blocks, with erasure indications, are then spread by the deinterleaver to different blocks of the ( 28, 24 ) outer code.
12.
Decoding succeeds if this operation recovers a sufficient number of symbols, such that the outer code can recover the remaining symbols using the decoding algorithm appropriate for that code.
13.
Since the outer code C _ \ text { out } can correct at most \ gamma N errors, this is the decoding error probability of C ^ { * }.
14.
The natural code rate of the configuration shown is 1 / 4, however, the inner and / or outer codes may be punctured to achieve higher code rates as needed.
15.
In such a case some implementations might ask for the message to be resent, or the ambiguous bit may be marked as an erasure and a following outer code may correct it.
16.
Let R be the rate of the outer code C _ { out } and \ delta be the relative distance, then the rate of the concatenated codes satisfies the following bound.
17.
Decoding a message of length " k " with a belief propagation decoding algorithm requires " O ( k ) " time for the appropriate choice of inner / outer codes.
18.
In a combined approach, the relationships between symbols defined by both the inner and outer codes are considered as a single combined set of simultaneous equations which can be solved by the usual means, typically by Gaussian elimination.
19.
For example, within the DVB-S2 standard, a highly efficient LDPC code is combined with an algebraic outer code in order to remove any resilient errors left over from the inner LDPC code due to its inherent error floor.
20.
Look back to the definition of the outer code and linear inner codes, this definition of the Justesen code makes sense because the codeword of the outer code is a vector with N elements, and we have N linear inner codes to apply for those N elements.
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