1 research outputs found
Joint error correction enhancement of the fountain codes concept
Fountain codes like LT or Raptor codes, also known as rateless erasure codes,
allow to encode a message as some number of packets, such that any large enough
subset of these packets is sufficient to fully reconstruct the message. It
requires undamaged packets, while the packets which were not lost are usually
damaged in real scenarios. Hence, an additional error correction layer is often
required: adding some level of redundancy to each packet to be able to repair
eventual damages. This approach requires a priori knowledge of the final damage
level of every packet - insufficient redundancy leads to packet loss,
overprotection means suboptimal channel rate. However, the sender may have
inaccurate or even no a priori information about the final damage levels, for
example in applications like broadcasting, degradation of a storage medium or
damage of picture watermarking.
Joint Reconstruction Codes (JRC) setting is introduced and discussed in this
paper for the purpose of removing the need of a priori knowledge of damage
level and sub-optimality caused by overprotection and discarding underprotected
packets. It is obtained by combining both processes: reconstruction from
multiple packets and forward error correction. The decoder combines the
resultant informational content of all received packets accordingly to their
actual noise level, which can be estimated a posteriori individually for each
packet. Assuming binary symmetric channel (BSC) of bit-flip
probability, every potentially damaged bit carries
bits of information, where is the Shannon
entropy. The minimal requirement to fully reconstruct the message is that the
sum of rate over all bits is at least the size of the message.
We will discuss sequential decoding for the reconstruction purpose, which
statistical behavior can be estimated using Renyi entropy.Comment: 14 pages, 9 figure