Some of the super optimal coding schemes don't work on really small blocks.
On 03/06/2013 11:50 AM, ZPO wrote:
Are there any LDPC implementations out there that aren't patent
encumbered?
73-KY9K/Brian
On Mar 6, 2013 10:05 AM, "Rick Muething" <[email protected]
<mailto:[email protected]>> wrote:
Daniel,
RS and similar block codes are fairly efficient and have some nice
properties especially when mixed (layered) with other types of
FEC. E.g. Viterbi (convolutional) type decoders work well with
random errors. But these type codes perform poorly in burst error
situations. Sometimes if the timing permits bursts can be reduced
by interleaving but there are limits especially when you don’t
want to delay the signal much in time as in the case of digital
voice. In such cases adding a block code “outside” the
convolutional codes can be effectively in many systems.
Reed Solomon adds two “parity” characters for each carrier
correction desired. ( a character can be any number of bits from 2
on up although often is done with 8 bit characters) E.g. if I
were sending 8 bit characters and I wanted to correct up to 8
character errors I would have to add 16 8 bit “parity” characters
to my data and these could correct up to 8 character errors in the
entire block of data (data + Parity). The amount of Parity you
need is a function of the channel and the error rates. So the
“efficiency” of a RS type code is a function of how many errors
you wish to be able to correct. For example if I were sending a
block of 100 data characters and wished to correct up to 8
erroneous characters I would need to add 16 total parity
characters so my overall efficiency would be 100/116 or about 86%
which is reasonable. As the number of corrected characters
desired increases the efficiency of course goes down but the
robustness increases. Correcting up to 32 characters would
require 64 characters of Parity so the efficiency would be 100/164
or about 61%. The beauty of RS and other similar block codes is
they are tolerant of block errors. It corrects by character
whether there is one bit in error or 8 bits in error of the
character. So it compliments the convolutional code nicely by
correcting bursts that the convolutional code can’t correct.
This is why layering two types of FEC is effective and why for
example NASA often uses layered block coding on top of
convolutional coding in very weak signal transmission.
In the end the amount and selection of FEC is a function of the
channel and the type and number and type of errors expected. But
in general adding the correct type and level of FEC can usually
provide a net improvement over uncoded systems in terms of net
BER. This is usually expressed as equivalent dB improvement. (the
amount of improvement you would get by increasing the S/N by the
same number of dB.
In digital Voice we have another issue in that unlike in binary
message transmission some level of uncorrected errors may be
acceptable (resulting in some speech artifact which may not
severely impact intelligibility).
I have experimented with this a lot in the development of WINMOR
and often optimization is the result of iterating different
promising FEC coding and evaluating them over specific (some times
standardized CCIR) channels using a HF channel simulator.
Prediction with theory alone is possible on White Gaussian Noise
channels but we seldom see these channels in HF propagation.
73,
Rick Muething, KN6KB
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