Based on the covert communication framework, we consider a covert queueing problem that has a Markovian statistic. Willie jobs arrive according to a Poisson process and require service from server Bob. Bob does not have a queue for jobs to wait and h
ence when the server is busy, arriving Willie jobs are lost. Willie and Bob enter a contract under which Bob should only serve Willie jobs. As part of the usage statistic, for a sequence of N consecutive jobs that arrived, Bob informs Willie whether each job was served or lost (this is the Markovian statistic). Bob is assumed to be violating the contract and admitting non-Willie (Nillie) jobs according to a Poisson process. For such a setting, we identify the hypothesis testing to be performed (given the Markovian data) by Willie to detect the presence or absence of Nillie jobs. We also characterize the upper bound on arrival rate of Nillie jobs such that the error in the hypothesis testing of Willie is arbitrarily large, ensuring covertness in admitting Nillie jobs.
In distributed machine learning (DML), the training data is distributed across multiple worker nodes to perform the underlying training in parallel. One major problem affecting the performance of DML algorithms is presence of stragglers. These are no
des that are terribly slow in performing their task which results in under-utilization of the training data that is stored in them. Towards this, gradient coding mitigates the impact of stragglers by adding sufficient redundancy in the data. Gradient coding and other straggler mitigation schemes assume that the straggler behavior of the worker nodes is identical. Our experiments on the Amazon AWS cluster however suggest otherwise and we see that there is a correlation in the straggler behavior across iterations. To model this, we introduce a heterogeneous straggler model where nodes are categorized into two classes, slow and active. To better utilize training data stored with slow nodes, we modify the existing gradient coding schemes with shuffling of the training data among workers. Our results (both simulation and cloud experiments) suggest remarkable improvement with shuffling over existing schemes. We perform theoretical analysis for the proposed models justifying their utility.
We consider a distributed storage system which stores several hot (popular) and cold (less popular) data files across multiple nodes or servers. Hot files are stored using repetition codes while cold files are stored using erasure codes. The nodes ar
e prone to failure and hence at any given time, we assume that only a fraction of the nodes are available. Using a cavity process based mean field framework, we analyze the download time for users accessing hot or cold data in the presence of failed nodes. Our work also illustrates the impact of the choice of the storage code on the download time performance of users in the system.
This work proposes a tractable estimation of the maximum a posteriori (MAP) threshold of various families of sparse-graph code ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GE
XIT) function, first proposed by Measson et al. We consider the transmission over non-binary complex-input additive white Gaussian noise channel and extend the existing results to obtain an expression for the GEXIT function. We estimate the MAP threshold by applying the Maxwell construction to the obtained approximate EBP-GEXIT charts for various families of low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC, and serially concatenated turbo codes (SC-TC). When codewords of SC-TC are modulated using Gray mapping, we also explore where the spatially-coupled belief propagation (BP) threshold is located with respect to the previously computed MAP threshold. Numerical results indicate that the BP threshold of the spatially-coupled SC-TC does saturate to the MAP threshold obtained via EBP-GEXIT chart.
The problem of identifying whether the family of cyclic codes is asymptotically good or not is a long-standing open problem in the field of coding theory. It is known in the literature that some families of cyclic codes such as BCH codes and Reed-Sol
omon codes are asymptotically bad, however in general the answer to this question is not known. A recent result by Nelson and Van Zwam shows that, all linear codes can be obtained by a sequence of puncturing and/or shortening of a collection of asymptotically good codes~cite{Nelson_2015}. In this paper, we prove that any linear code can be obtained by a sequence of puncturing and/or shortening of some cyclic code. Therefore the result that all codes can be obtained by shortening and/or puncturing cyclic codes leaves the possibility open that cyclic codes are asymptotically good.
