From Möbius Strips to Twisted Toric Codes: A Homological Approach to Quantum Low Density Parity Check Codes

In the past few years, the search for good quantum low density parity check (qLDPC) codes suddenly took flight, and many different constructions of these codes have since been presented, including many product constructions. As these code constructions have a natural interpretation in the language of homology, this thesis studies the interplay...

Firmware Updates Over The Air for LoRa using Random Linear Network Coding

LoRaWAN is a public Wireless Sensor network with excellent properties like being long-range, low-energy radios and resulting in long battery life. Devices are connected to this network through gateways, and they will run in that deployment for years without replacement. Therefore, bugs and security issues in such devices' firmware are present...

The Stopping Set Property and the Iterative Decoding Performance of Binary Block Codes on BSC and AWGN Channel

In the field of Error Correcting Coding (ECC), the concept of ''stopping set'' recently became a hot topic. A stopping set for a parity-check matrix is the set of bits which would cause the iterative decoding progress in Binary Erasure Channel (BEC) to ''stop'' when it is erased. It has already been proved in several papers that the decoding...

New Decoding Methods for LDPC Codes on Error and Error-Erasure Channels

We present new low complexity decoders for LDPC codes by improving existing methods.