An efficient algorithm synthesizing all shortestq-linearized-feedback shift-registers generating a given sequence of lengthNover a finite field \BBFqmis derived and its correctness is proved. This algorithm, which is a generalization of the Berlekamp-Massey algorithm, has time complexityO(lN)O(N2) operations in \BBFqm, wherelis the linearized complexity of the sequence. The algorithm can be applied for efficiently solving the key equation when decoding Gabidulin codes.

Irregular low-density parity-check (LDPC) codes constructed from small protographs are one of the most powerful LDPC codes. In this paper, we show that the performance of LDPC codes based on small protographs can be further improved by using different transmission energies for every variable node of the protograph. Thus, a protograph is now described by a set of variable nodes, a set of check nodes, edges connecting variable nodes and check nodes, and the transmission energy used for every variable node, which is called the energy distribution. We optimize the energy distribution of protographs by choosing the energy distribution with the highest threshold calculated with a generalization of the discretized density evolution. Furthermore, we show by simulations that the performance of long LDPC codes based on protographs can be improved as expected from the thresholds.

Low-density parity-check (LDPC) codes are very powerful error correction codes for bit-interleaved coded modulation (BICM) schemes. In BICM schemes the bits of one symbol have unequal error protection. In this paper, we show how to improve the performance of given LDPC codes by mapping the variable nodes of certain degree in a special way to the different bit levels. Since the equivalent binary-input component channels for each individual bit level are not symmetric, we use the tool of i.i.d. channel adapters to force symmetry. After that, we optimize the mapping of the LDPC code to the different bit levels by a downhill algorithm that uses a generalized discretized density evolution to calculate the thresholds. We show by thresholds and by simulations that a special mapping of LDPC codes lowers the bit error rates compared to a random mapping of LDPC codes.

The influence of time-varying cyclic delay diversity (TV-CDD) on the channel fading correlation properties is analyzed in this paper. TV-CDD is an attractive transmit diversity technique which increases not only the frequency diversity like pure CDD but also the time diversity in orthogonal frequency division multiplexing (OFDM) based systems. These transmit diversity schemes are characterized by no need of additional complexity at the receiver to exploit the increased transmit diversity. This paper gives first investigations regarding the resulting channel characteristics from TV-CDD and the impact on the system performance. Due to the increased frequency and time selectivity and a larger channel delay, an unintended higher channel estimation effort is possible. Therefore, we analyze the choice of the maximum cyclic delay. We show that the resulting channel for TV-CDD can be seen as an uncorrelated Rayleigh channel (except for the first sub-carrier) for a large maximum cyclic delay. Furthermore, analysis and simulation results demonstrate a feasible choice of small time-varying cyclic delays for guaranteeing the standard conformability of the TV- CDD technique at the receiver without significant performance degradations.

In this paper, we present a construction method based on the progressive edge-growth (PEG) algorithm to design irregular low-density parity-check (LDPC) codes without small stopping sets. We show how to choose the connections in the PEG algorithm when having multiple choices to connect a variable node with a check node. Since preventing small stopping sets also prevents a low minimum distance, our construction method also leads to LDPC codes with a higher minimum distance. Furthermore, we show by simulation that our construction method improves the performance over the binary erasure channel and over the additive white Gaussian noise channel for a low erasure probability and a high signal-to-noise ratio, respectively.

Irregular low-density parity-check (LDPC) codes constructed from small protographs are one of the most powerful LDPC block codes. In this paper, we introduce the convolutional version of these codes. LDPC convolutional codes constructed from protographs have some advantages in comparison to LDPC block codes constructed from protographs, e.g., an effective pipeline decoding. We show that LDPC convolutional codes constructed from protographs have much lower error rates than analogous LDPC block codes with the same complexity and that they operate with low error rates near the Shannon limits even for a relatively small memory size

In this paper, we describe a method, how to optimize the asymptotic puncturing distributions for low-density parity-check codes constructed with different algorithms. Therefore, we generalize the discretized density evolution such that we can take care of the structure of the code. We show by density evolution and by simulations that even for the same degree distributions the optimized asymptotic puncturing distributions vary considerably for different construction algorithms. Furthermore, we demonstrate the performance gain by using the designed puncturing distributions compared to known puncturing distributions

In this paper, permutor design aspects for woven convolutional encoders (WCEs) with outer warp (OW) are discussed. We show how the minimum distance of the overall code can be increased by considering all warp permutors together. A bound on the minimum distance of a code generated by a WCE with OW and designed permutors is presented that considerably exceeds those with known designs.

In this paper, an algorithm for low-density parity-check (LDPC) codes with reduced complexity is presented. The complexity reduction is achieved by calculating a linear function for updating the check nodes in each iteration, instead of an exponential and logarithmic function. The parameters of the linear function are optimized by density evolution. Simulation results show that there is nearly no loss in the performance by using this approximation compared to the exact calculation of the belief propagation decoding algorithm, even for very large block lengths.

This paper describes the decoding of Rank-Codes with different decoding algorithms. A new modified Berlekamp-Massey algorithm for correcting rank errors and column erasures is described. These algorithms consist of two decoding steps. The first step is the puncturing of the code and the decoding in the punctured code. The second step is the column erasure decoding in the original code. Thus decoding step is about half as complex as the known algorithms