Codec.Fountain

Fountain codes are forward error correction codes for erasure channels. They are able to recover lost packets without needing a backchannel. As a rateless code, transmitters generate packets at random, on the fly. Receivers then listen to as many packets as needed to reconstruct the message.

Datatypes

data Droplet a

A message droplet is a set of message indices and the combined symbol.

Constructors

Droplet IntSet a

Instances

Eq a => Eq (Droplet a)

Show a => Show (Droplet a)

data Decoder a

A decoder holds the state of the decoding process.

type Precoding = [IntSet]

A precoding matrix that appends extra symbols to a message.

Functions

precoding :: Int -> Int -> Int -> (Int, Int) -> Precoding

Generates a random precoding matrix.

 precoding seed messageLength extraSymbols boundaries

droplets :: (Num a, Bits a) => Int -> Int -> Precoding -> [a] -> [Droplet a]

An infinite list of droplets, given a seed, the max degree, precoding, and a message.

decoder :: (Num a, Bits a) => Int -> Precoding -> Decoder a

Creates a new decoder given a message length and the precoding.

decode :: (Num a, Bits a) => Decoder a -> Droplet a -> (Decoder a, Maybe [a])

Given a Decoder and a new Droplet, returns either an updated Decoder or the decoded message.

Test

test :: Int -> Int -> Precoding -> Int -> (Int, Bool, [Decoder Word8])

Runs a test of a [Word8] message given the message length, max droplet degree, and a seed. Returns the number of droplets that were needed to decode the message and if the message was sucessfully decoded.

test' :: Int -> Int -> Int -> (Int, Int) -> Int -> (Int, Bool, [Decoder Word8])

Runs a test with a randomly generated precoding.

 test' messageLength dropletMaxDegree extraSymbols (precodingMinDegree, precodingMaxDegree) seed

decoderProgress :: Decoder a -> String

A visual of Decoder progress.