Network and Storage Coding

Coding for networks and storage has become recently an important application in order to increase the throughput in networks and to minimize the loss of data and the data rates when lost data have to be recovered by redundant data from other storage devices.

The lecture starts with a survey of decoding Reed-Solomon (RS) codes beyond half the minimum distance by interleaving, power, and list decoding. A particular focus will be on the decoding by modul minimization exploiting the weak Popov form. Then rank metric codes, especially Gabidulin codes and subspace codes are described and their application in network coding is discussed. Such codes are used in random linear network coding which is defined and analyzed.

The coding for non-volatile memories uses masking for stuck cells and error correction as well as so called rewriting codes. Code constructions and their anaysis will be given.

Coding for insertions and deletions is explained and the Varshamov-Tenengolts codes are introduced. The substitution correction is explained. Then locally repairable codes for distributed storage will be described and the connection to majority logic decoding will be established.

• Decoding of Reed-Solomon codes beyond half the minimum distance; modul minimization, weak Popov form, power decoding, list decoding, interleaved RS codes, burst error correction
• Rank metric codes, subspace codes and applications to network coding, linearized polynomials, skew polynomials, Gabidulin codes, error correction in networks
• Coding for flash memories, non-volotile memories, memory with defects, write-once memories, cyclic codes
• Coding for insertions and deletions, Varshamov-Tenengolts codes
• Coding for distributed data storage, locally repairable codes, regeneration codes