311 research outputs found
Rate adaptive binary erasure quantization with dual fountain codes
In this contribution, duals of fountain codes are introduced and their use for lossy source compression is investigated. It is shown both theoretically and experimentally that the source coding dual of the binary erasure channel coding problem, binary erasure quantization, is solved at a nearly optimal rate with application of duals of LT and raptor codes by a belief propagation-like algorithm which amounts to a graph pruning procedure. Furthermore, this quantizing scheme is rate adaptive, i.e., its rate can be modified on-the-fly in order to adapt to the source distribution, very much like LT and raptor codes are able to adapt their rate to the erasure probability of a channel
Cyclone Codes
We introduce Cyclone codes which are rateless erasure resilient codes. They
combine Pair codes with Luby Transform (LT) codes by computing a code symbol
from a random set of data symbols using bitwise XOR and cyclic shift
operations. The number of data symbols is chosen according to the Robust
Soliton distribution. XOR and cyclic shift operations establish a unitary
commutative ring if data symbols have a length of bits, for some prime
number . We consider the graph given by code symbols combining two data
symbols. If such random pairs are given for data symbols, then a
giant component appears, which can be resolved in linear time. We can extend
Cyclone codes to data symbols of arbitrary even length, provided the Goldbach
conjecture holds.
Applying results for this giant component, it follows that Cyclone codes have
the same encoding and decoding time complexity as LT codes, while the overhead
is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes
significantly decreases the overhead of extra coding symbols
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