Cyclone Codes

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 $p-1$ bits, for some prime number $p$. We consider the graph given by code symbols combining two data symbols. If $n/2$ such random pairs are given for $n$ 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.