Code and codec performance

This page gives some information on the expected performance in terms of erasure recovery. For the moment it is limited to LDPC-Staircase codes.

Testing conditions:

  • LDPC-Staircase codec;
  • k=1024 symbols, encoded as a single source block (NB: the symbol size does not matter for erasure recovery performance evaluation);
  • symbol transmission order is fully random (NB: results only depend on the average loss rate, no matter whether they happen in bursts or not);
  • evaluated using the openfec integrated performance evaluation tools;

Result summary

conditions
average overhead
overhead for a failure probability < 10-4
CR=2/3, N1=5
0.636%
with 2.1% overhead (22 extra symbols), Pr_fail=5.9*10-5
CR=2/3, N1=7
0.238%
with 1.5% overhead (15 extra symbols), Pr_fail=8.2*10-5
CR=1/2, N1=5
01.228%
with 3.1% overhead (28 extra symbols), Pr_fail=7.2*10-5
CR=1/2, N1=7
0.378%
with 1.7% overhead (17 extra symbols), Pr_fail=9.6*10-5

Results are excellent and approach that of an ideal code where the overhead is 0. The details are given in the curves below, and one can see that if an error floor is still visible when using N1=5, it is no longer visible (i.e., if any is below 10-5) with N1=7. Note that higher values of N1 can still be used if needed...

Erasure recovery performance as a function of the overhead

dec_error_proba_wrt_overhead_n1_5_and_7_k_1024_cr_2_3.png

This curve indicates the probability decoding fails as a function of the overhead (said differently the number of symbols received). Here code rate=2/3; N1=5 or 7.
(NB: don't be fooled by the horizontal scale, an extra 40 symbols only represents a 3.9% overhead when dealing with k=1024. This curve is therefore a close-up.)
(NB2: on the left of the vertical line, no decoding is possible since fewer than k symbols have been received)


dec_error_proba_wrt_overhead_n1_5_and_7_k_1024_cr_1_2.png

Same conditions as above for code rate=1/2.


Erasure recovery performance as a function of the channel loss rate

(nb: this is a different view of the same results, the number of symbols actually erased corresponding to a certain loss rate)

dec_error_proba_wrt_overhead_n1_5_and_7_k_1024_cr_2_3.png

This curve indicates the probability decoding fails as a function of the loss rate (said differently the number of symbols received/n). Here code rate=2/3; N1=5 or 7.
(NB: on the right of the vertical line, no decoding is possible since fewer than k symbols have been received)


dec_error_proba_wrt_overhead_n1_5_and_7_k_1024_cr_1_2.png

Same conditions as above for code rate=1/2.