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

@@ -85,6 +85,7 @@ use std::process::exit;
 use ark_ff::PrimeField;
 
 use clap::{Parser, ValueEnum};
+use indicatif::ProgressBar;
 use komodo::{
     error::KomodoError,
     fec::{self, Shard},
@@ -136,9 +137,9 @@ fn end_to_end<F: PrimeField>(
     let original_shards = setup(bytes, k, n)?;
     let mut shards = original_shards.clone();
 
-    for t in 0..max_t {
+    let pb = ProgressBar::new(max_t as u64);
+    for _ in 0..max_t {
         let inbreeding = measure_inbreeding(&shards, k, nb_measurements, rng);
-        eprint!("t: {} / {}\r", t + 1, max_t);
         println!("{}", inbreeding);
 
         // decode the data
@@ -148,8 +149,11 @@ fn end_to_end<F: PrimeField>(
         let encoding_mat = Matrix::vandermonde_unchecked(&[F::rand(rng)], k);
         let new_shard = fec::encode(&data, &encoding_mat)?.first().unwrap().clone();
         shards.push(new_shard);
+
+        pb.inc(1);
+
     }
-    eprintln!();
+    pb.finish_with_message("done");
 
     Ok(())
 }
@@ -165,9 +169,9 @@ fn recoding<F: PrimeField>(
 ) -> Result<(), KomodoError> {
     let mut shards = setup(bytes, k, n)?;
 
-    for t in 0..max_t {
+    let pb = ProgressBar::new(max_t as u64);
+    for _ in 0..max_t {
         let inbreeding = measure_inbreeding(&shards, k, nb_measurements, rng);
-        eprint!("t: {} / {}\r", t + 1, max_t);
         println!("{}", inbreeding);
 
         // recode a new random shard
@@ -175,8 +179,10 @@ fn recoding<F: PrimeField>(
         let s: Vec<_> = shards.iter().take(nb_shards_to_recode).cloned().collect();
         let new_shard = fec::recode_with_coeffs(&s, &coeffs).unwrap();
         shards.push(new_shard);
+
+        pb.inc(1);
     }
-    eprintln!();
+    pb.finish_with_message("done");
 
     Ok(())
 }