Pre-computed sets of checksum packets of constant degree with various
size factors
EG
2006-04-10
For a set of K
source packets with a method described in 060406-setof-checksums
[ ch
| us
] and in 060407-setof-checksums [ ch
| us
] one can generate 
checksum packets of
constant degree, where 
. In our examples 
, degree is equal to 7 and the factor m is from 2 to 6. For each size factor m we correspondingly generated 500 distinct sets of checksum
packets (2’500 pre-computed sets). The corresponding 500 sets are sorted
according the average number of the excess packets needed for the successful
decoding of all source packets while receiving in a random order the checksum
packets of a given set. The average numbers of needed excess packets are
plotted for all pre-computed sets:
[ xls | m2.xls | m3.xls | m4.xls | m5.xls | m6.xls | cpp ]
This chart shows that the performance of the random linear fountain code can be achieved also with pre-computed of various sizes.
For the best set of checksum packets with the size factor of 6, the probability of recovery as a function of the received packets is plotted on the chart below:
A similar chart is given for the best pre-computed set of the size factor of 5:
Logically, as shown in the chart below, the probability of recovery is higher when transmitting the copies from the pre-computed set of the size factor 6 than of the size factor 5:
[xls]
Related links:
- The C++ program generating pre-computed sets (of checksum packets) of various size factors [ cpp | txt | csv ]
- The used classes and functions [ recv.cpp | recv.h | graph.cpp | graph.h | linear.cpp | linear.h | lt.cpp | lt.h ]
- Download all program files [zip]
- MS Word version of this page [doc]
- The average number of excess packets needed for successful decoding in a pre-computed set of checksum packets of constant degree [ ch | us ]
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