In distributed storage systems (DSSs), the optimal tradeoff between node storage and repair bandwidth is an important issue for designing distributed coding strategies to ensure large scale data reliability. The capacity of DSSs is obtained as a function of node storage and repair bandwidth parameters, characterizing the tradeoff. There are lots of works on DSSs with clusters (racks) where the repair bandwidths from intra-cluster and cross-cluster are differentiated. However, separate nodes are also prevalent in the realistic DSSs, but the works on DSSs with clusters and separate nodes (CSN-DSSs) are insufficient. In this paper, we formulate the capacity of CSN-DSSs with one separate node for the first time where the bandwidth to repair a separate node is of cross-cluster. Consequently, the optimal tradeoff between node storage and repair bandwidth are derived and compared with cluster DSSs. A regenerating code instance is constructed based on the tradeoff. Furthermore, the influence of adding a separate node is analyzed and formulated theoretically. We prove that when each cluster contains R nodes and any k nodes suffice to recover the original file (MDS property), adding an extra separate node will keep the capacity if R|k, and reduce the capacity otherwise.
The storage and repair bandwidth tradeoff is an important issue in distributed storage systems (DSSs) where large scale data are stored in multiple nodes with erasure coding to ensure reliability. There are lots of studies on the DSS model with multiple clusters where the repair bandwidths from intra-cluster and cross-cluster nodes are differentiated to improve repair efficiency based on the realistic network topological structures. At the same time, separate nodes are also prevalent due to the variety of practical networks, but the work on the cluster DSS model with multiple separate nodes is insufficient, which is a main motivation of this paper. We formulate the tradeoff bound between storage repair bandwidth for a heterogeneous DSS model consisting of clusters and separate nodes by analyzing the min-cuts of heterogeneous information flow graphs corresponding to the orders of failed nodes. Additionally, the tradeoff bounds are investigated in multiple aspects when the repair bandwidth constraints and the amount of separate nodes vary, respectively. Moreover, a class of regenerating codes are illustrated to achieve the tradeoff in the heterogeneous cases.
Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, suboptimal source coding and joint source-channel coding, constrains among successive codewords may be utilized to improve decoding performance. In this paper, list decoding is used to correct the undetected errors. The benefit proportion of the correction is obviously improved especially on Hamming codes and Reed-Muller codes, which achieves about 40% in some cases. But this improvement is significant only after the selection of final codewords from the lists based on the constrains among the successive transmitted codewords. The selection algorithm is investigated here to complete the list decoding program in the application of Markov context model. The performance of the algorithm is analysed and a lower bound of the correctly selected probability is derived to determine the proper context length.
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