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le (6m37s)

3.6. Stern/Dumer Algorithm

In this session, we will present the Stern algorithm for decoding. In fact, the idea is to combine two algorithms that we have seen before, the Lee and Brickell algorithm and the Birthday Decoding.  So, instead of a full Gaussian elimination, we will simply have a partial Gaussian elimination as presented here. And if we look at the lower part, what is called step 1, in red here in this slide, it is, in fact, a smaller CSD problem with a smaller matrix H', with a smaller target syndrome s' and with ...
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le (6m38s)

1.7. Reed-Solomon Codes

Reed-Solomon codes were introduced by Reed and Solomon in the 1960s. These codes are still used in storage device, from compact-disc player to deep-space application. And they are widely used mainly because of two features: first of all, because they are MDS code, that is, they attain the maximum error detection and correction capacity. The second thing is that they have efficient decoding algorithms. Reed-Solomon codes are particularly useful for burst error correction, that is, they are effective for channels that have memory.So, suppose that we consider n and k ...
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le (6m39s)

4.7. Alignment costs

We have seen how we can compute the cost of the path ending on the last node of our grid if we know the cost of the sub-path ending on the three adjacent nodes. It is time now to see more deeply why these costs are used to compute the cost in the last node. So again, we saw how we can compute the cost here of the path ending on that node if we know the cost of the sub-path ending on these three red nodes. Indeed, if we come from that node, the cost on that node will be the cost of that node plus the ...
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