add an example to study the _recoding inbreeding_ phenomenon

this MR adds examples/inbreeding.rs which allows to do two things

• naive recoding: in order to generate a new random shard, we first k-decode the whole data and then 1-encode a single shard
• true recoding: to achieve the same goal, we directly k-recode shards into a new one

the scenario

regardless of the recoding strategy, the scenario is the same

1. data is split into k shards and n original shards are generated
2. for a given number of steps s, k shards are drawn randomly with replacement and we count the number of successful decoding, given a measure of the diversity, \delta = \frac{\#success}{\#attempts}
3. create a new recoded shard and add it to the n previous ones, i.e. n increases by one
4. repeat steps 2. and 3. as long as you want

results

examples/inbreeding.rs

@@ -154,7 +154,6 @@ fn end_to_end<F: PrimeField>(
         shards.push(new_shard);
 
         pb.inc(1);
-
     }
     pb.finish_with_message("done");