Cyclone Codes
Christian Schindelhauer, Andreas Jakoby, Sven K\"ohler

TL;DR
Cyclone codes are a new type of rateless erasure code combining Pair codes and LT codes, offering efficient encoding/decoding with reduced overhead, applicable to data of arbitrary even length under certain number theory assumptions.
Contribution
They introduce Cyclone codes, integrating cyclic shifts with XOR operations, and demonstrate their efficiency and applicability, including extensions based on the Goldbach conjecture.
Findings
Similar encoding/decoding complexity as LT codes
Overhead is upper-bounded by LT codes
Significantly reduces extra coding symbols in simulations
Abstract
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…
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Error Correcting Code Techniques
