Channel Coding

Using a conventional design process, these codes need to be tailored specifically to the exact considered transmission setup if they are designed to perform close within the theoretical limits. The varying requirements of modern mobile communication systems (e.g., 5G) and their growing heterogeneity cannot be accounted for by these conventional designs.

An alternative design allowing for highly flexible code rates and block sizes yields a mother code matrix.
The flexible code rate is achieved by information shortening (adding dummy bits) and parity puncturing. These techniques are considered during the design process of the mother code matrix: theoretical performance limits are taken into account for each of the desired code rates. Finally, the matrix is structured in a way that facilitates information shortening and parity puncturing by sorting the to-be-punctured and to-be-shortened columns to the “outside” of the matrix (left and right columns).

LDPC code correction capabilities can be improved by using higher-order Galois fields. In order to efficiently decode these non-linear code words, a decoder was implemented with Nvidia's Compute Unified Device Architecture (CUDA) which supports irregular codes with arbitrary Galois field orders and without the need for a special code structure.

A high speedup can be achieved by employing quasi-cyclic LDPC codes which allow updating multiple neighboring check nodes in parallel without performance loss.

Using the parallel processing capabilities of a GPU efficiently requires ordering the data in a well-considered way, because the (up to) 3-dimensional data is stored in a linear (1-dimensional) memory:

The Digital Fountain protocol allows to produce on the fly a potentially limitless number n of encoded packets (encoded symbols) from the k original packets (input symbols). Furthermore, it enables the recovery of a message that consists of k equal length packets upon the reception of any k(1 + ε) encoded packets, where ε ≥ 0 is a small overhead. In contrast to other incremental redundancy schemes no channel state information or feedback message is required.

For instance, in a multicast scenario with a large number of subscribers, each user listens to the encoded data stream only until having collected sufficiently many encoded packets to be able to decode the original message. This protocol is called a digital fountain due to the analogy to a water fountain which is seen as an unlimited source of water allowing to fill the cups of many at the same time. Similar to filling one's cup by collecting a sufficient number of nameless water drops, the original message should be decodable after collecting sufficiently many encoded packets, i.e., each encoded packet should equally and optimally contribute to the decodability. The corresponding erasure-resilient codes are called (digital) fountain codes or rateless codes. The latter name results from the property that their code rate r = k/n is not determined a priori. If the server transmits long enough, users are not even required to tune in at the same time, but can start their session independently of others. In a traditional setup, however, each user would notify the server of lost packets and request a retransmission. If many users were involved, the server as well as the network would easily become overwhelmed, leading to even more packet losses.