coding block length in action

This article talks about the switch to 4096-byte sectors from the current 512-byte sectors for PC hard disks. This section is interesting:

4096 byte sectors don’t solve the analog problem—signals are getting weaker, and noise is getting stronger, and only reduced densities or some breakthrough in recording technology are going to change that—but it helps substantially with the error-correcting problem. Due to the way error correcting codes work, larger sectors require relatively less error correcting data to protect against the same size errors. A 4096 byte sector is equivalent to eight 512 byte sectors. With 40 bytes per sector for finding sector starts and 40 bytes for error correcting, protecting against 50 error bits, 4096 bytes requires (8 x 512 + 8 x 40 + 8 x 40) = 4736 bytes; 4096 of data, 640 of overhead. The total protection is against 400 error bits (50 bits per sector, eight sectors), though they have to be spread evenly among all the sectors.

With 4096 byte sectors, only one spacer start is needed, and to achieve a good level of protection, only 100 bytes of error checking data are required, for a total of (1 x 4096 + 1 x 40 + 1 x 100) = 4236 bytes; 4096 of data, 140 of overhead. 100 bytes per sector can correct up to 1000 consecutive error bits; for the forseeable future, this should be “good enough” to achieve the specified error rates. With an overhead of just 140 bytes per sector, about 96% of the disk’s capacity to be used.

With longer block lengths, the error correction capability generally goes up for the same coding overhead, however, it seems rather more complicated than this. First of all, I don’t think each manufacturer uses the same code or coding structure. (They used to just use Reed-Solomon code, though later they tried concatenating it with LDPC code, and now I hear some are switching to pure LDPC with iterative decoding.) But even if we assume they use some non-exotic block code, and use interleaving for bursts, the math still seems very strange: 40 error correction bytes can only correct 50 consecutive bits currently? I think not.

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