Abstract-Maximum-distance separable (MDS) convolutional codes have the property that their free distance is maximal among all codes of the same rate and the same degree. In this paper, a class of MDS convolutional codes is introduced whose column distances reach the generalized Singleton bound at the earliest possible instant. Such codes are called strongly-MDS convolutional codes. They also have a maximum or near-maximum distance profile. The extended row distances of these codes will also be discussed briefly.
Abstract-Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds depend on graph structure parameters (like variable degrees, check node degrees, girth) of the Tanner graph and of the underlying proto-graph. Moreover, for several classes of proto-graphs we present explicit QC LDPC code constructions that achieve (or come close to) the respective minimum Hamming distance upper bounds.Because of the tight algebraic connection between QC codes and convolutional codes, we can state similar results for the free Hamming distance of convolutional codes. In fact, some QC code statements are established by first proving the corresponding convolutional code statements and then using a result by Tanner that says that the minimum Hamming distance of a QC code is upper bounded by the free Hamming distance of the convolutional code that is obtained by "unwrapping" the QC code.
Abstract-In this paper the decoding capabilities of convolutional codes over the erasure channel are studied. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance increase.It is shown how this strong minimum distance condition of MDP convolutional codes help us to solve error situations that maximum distance separable (MDS) block codes fail to solve. Towards this goal, two subclasses of MDP codes are defined: reverse-MDP convolutional codes and complete-MDP convolutional codes. Reverse-MDP codes have the capability to recover a maximum number of erasures using an algorithm which runs backward in time. Complete-MDP convolutional codes are both MDP and reverse-MDP codes. They are capable to recover the state of the decoder under the mildest condition. It is shown that complete-MDP convolutional codes perform in many cases better than comparable MDS block codes of the same rate over the erasure channel.
Abstract-The interference in wireless networks is temporally correlated, since the node or user locations are correlated over time and the interfering transmitters are a subset of these nodes. For a wireless network where (potential) interferers form a Poisson point process and use ALOHA for channel access, we calculate the joint success and outage probabilities of n transmissions over a reference link. The results are based on the diversity polynomial, which captures the temporal interference correlation. The joint outage probability is used to determine the diversity gain (as the SIR goes to infinity), and it turns out that there is no diversity gain in simple retransmission schemes, even with independent Rayleigh fading over all links. We also determine the complete joint SIR distribution for two transmissions and the distribution of the local delay, which is the time until a repeated transmission over the reference link succeeds.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.