Cryptography Reference
In-Depth Information
Figure 8.3 - Calculation of the weight of row coming from the first step of the Reddy-
Robinson algorithm.
The two other columns with errors are also decoded. However for the most
right-hand column, the second decoding fails (since there is one error in the
non-erased symbols) and the word decoded for this column is therefore that of
the third decoding. Finally, all the errors are corrected.
In this algorithm the role of the rows and of the columns is not symmetric.
Thus, if the whole decoding fails in the initial order, it is possible to try again
by inverting the role of the rows and the columns.
The Reddy-Robinson decoding algorithm is not iterative in its initial version.
We can make it iterative, for example, by starting another decoding with the
final word of step 2, if one of the decodings of step 2 succeeded. There are also
more sophisticated iterative versions [8.16].
8.4
Soft input decoding of product codes
8.4.1 The Chase algorithm with weighted input
The Chase algorithm, in the case of a block code, enables the values received
on the transmission channel to be used to decode in the maximum likelihood
sense or, at least approximate its performance. In its basic version, it produces
hard decoding. Following the idea of convolutional turbo code decoding [8.2],
Pyndiah's improved version [8.14] of the algorithm allows a soft value of the
decoded bit to be obtained at the output. With the help of iterative decoding,
it is then possible for the row and column decoders of a product code to exchange
