Among the recent advances in the area of low-density parity-check (LDPC) codes, protograph-based LDPC codes have the advantages of a simple design procedure and highly structured encoders and decoders. These advantages can also be exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. In this dissertation we provide analytical tools which aid the design of protographbased ...

The design of future communication systems with high throughput demands will become a critical task, especially when sophisticated channel coding schemes have to be applied. Low-Density Parity-Check(LDPC) codes are among the most powerful forward error correcting codes, since they enable to get as close as a fraction of a dB from the Shannon limit. A simplified decoding algorithms for decoding ...

The key encapsulation mechanism EDON-K was proposed in response to the call for post-quantum cryptography standardization issued by the National Institute of Standards and Technologies (NIST). This scheme is inspired by the McEliece scheme but uses another family of codes defined over F2128 instead of F2 and is not based on the Hamming metric. It allows significantly shorter public keys than th...

Low-density parity-check (LDPC) codes are widely used in communications due to their excellent practical performance. Error probability of LDPC code under iterative decoding on the binary erasure channel is determined by a class of combinatorial objects, called stopping sets. Stopping sets of small size are the reason for the decoder failures. Stopping redundancy is defined as the minimum numbe...

An area-e±cient high-throughput shift-based LDPC decoder architecture is proposed. The specially designed (512, 1,024) parity-check matrix is e®ective for partial parallel decoding by the min-sum algorithm (MSA). To increase throughput during decoding, two data frames are fed into the decoder to minimize idle time of the check node unit (CNU) and the variable node unit (VNU). Thus, the throughp...

Performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite length LDPC codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by using a recurrent procedure and compared to the empirically found average spectrum for the same ensemble as well as to the empirical average spectrum of the Richardson-Urbanke ens...

Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary qubits. However, while the framework maintains the ability to import any binary or quaternary linear code without sacrificing active error correction power, it...

Low-Density Parity-Check (LDPC) codes are increasingly being considered as good candidates for the nextgeneration FEC codes in high throughput wireless and recording applications. Trapping sets (TSs) are known to cause error floors in regular and irregular low-density parity-check (LDPC) codes. In existing algorithm, namely the Progressive-Edge-Growth Approximate-minimum-Cycle-Set-Extrinsic-mes...

Locally repairable codes have attracted lots of interest in Distributed Storage Systems. If a symbol code can be repaired respectively by t disjoint groups other symbols, each has size at most r, we say that the (r, t)-locality. In this paper, employ parity-check matrix to construct information single-parity t)-locality LRCs. All our attain Singleton-like bound LRCs where repair group contains ...

We report the empirical performance of Gallager’s low density parity check codes on Gaussian channels. We show that performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of Turbo codes. A linear code may be described in terms of a generator matrix G or in terms of a pari...