In the channel code detection problem, given a sequence of noise-affected codewords generated by an unknown code, the aim is to identify the correct channel code from the given set of potential codes. This problem has many applications in military spectrum surveillance and in cognitive radios. In this paper, we consider the situation when the set of potential channel codes consists of two linear block codes and propose a deep learning based classification approach for the corresponding code detection problem. In this work, we propose data processing strategies suitable for linear block codes that reduce the amount of data required to train the deep neural network classifier. This however comes at the cost of having a lower probability of detection. For the proposed data processing strategies, we analytically obtained the optimal probability of correct detection that one can hope to achieve using any neural network classifier. The proposed results are validated numerically using a variety of examples.

The maximum a posteriori (MAP) threshold corresponds to the fundamental limit that one can hope to achieve with the given channel code ensemble. Apart from theoretical interests, finding this limit is also desirable sincespatial-coupledcode ensembles approach this MAP threshold due to phenomenon termed asthreshold saturation. However finding this MAP threshold, in general, is known to be computationally prohibitive. This work proposes a tractable method for estimating the MAP threshold for various families of sparse-graph code ensembles over non-binary complex-input additive white Gaussian noise (AWGN) channel. Towards this, we provide a method to approximate the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) chart and estimate the MAP threshold by applying theMaxwell constructionto it. To illustrate the validity of our method, we study spatial coupling for serially-concatenated turbo-codes and numerically observe threshold saturation of these codes to the MAP thresholds estimated via our method.

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 are 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.

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 nodes 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.

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 hence 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.

We investigate the problem of estimating the maximum a posteriori (MAP) threshold for serially concatenated turbo codes. First, we provide a method to compute this MAP threshold using a numerical approximation of the EBP-GEXIT chart and the Maxwell construction. Second, we explore where the spatially coupled belief propagation (BP) threshold is located with respect to the previously computed MAP threshold and analyze the saturation phenomenon of such schemes. Simulation results indicate that the BP threshold of the spatially coupled turbo-codes saturates to the MAP threshold obtained using the EBP-GEXIT chart.

This work proposes a tractable evaluation of the maximum a posteriori (MAP) threshold of sparse-graph ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) function, first proposed by Measson et al. The approximation allows to find a MAP threshold in such numerically involved cases as the binary-input additive white Gaussian noise (AWGN) channel, graph ensembles with general component codes and/or irregularities. The paper contains examples of estimations of the MAP thresholds in the case of irregular low-density parity-check (LDPC), generalized LDPC, and doubly generalized LDPC codes ensembles. Our estimations are confirmed by numerical simulations.

Given a sequence of noise-affected codewords of an unknown channel code, the problem of blind reconstruction of channel codes consists of identifying this unknown channel code. This problem has many applications in military surveillance and cognitive radios. In this paper, we study this problem for the case when the noise is introduced by the binary erasure channel (BEC) and the unknown channel code is a binary cyclic code of known length. We provide an algorithm to find the generator polynomial of the unknown cyclic code. We also provide an analysis of our algorithm where we provide a lower bound on the probability of correctly identifying the factors of the generator polynomial.

The problem of identifying the channel code from a received sequence of noise-affected codewords is known as the blind reconstruction of channel codes. Blind reconstruction of channel codes is an important problem in military surveillance applications to identify the channel code used by an adversary. In this paper, we consider the problem of the blind reconstruction of the binary cyclic codes of unknown length from an unsynchronized bitstream (i.e., when the location of codeword boundaries is not known). For the blind reconstruction of cyclic codes, it is sufficient to identify the correct synchronization, the length, and the factors of the generator polynomial of the code. Toward this, we study the distribution of the syndromes (remainders) of the received polynomials with respect to a candidate factor of the generator polynomial. We prove that the probability of zero syndrome is maximum when all the parameters are correct. Using this result, the problem of the blind reconstruction of cyclic codes is formulated and solved as a hypothesis testing problem.

Channel codebook detection is of interest in cognitive paradigm or security applications. A binary hypothesis testing problem is considered, where a receiver has to detect the channel-code from two possible choices upon observing noise-affected codewords through a communication channel. For analytical tractability, it is assumed that the two channel-codes are linear block codes with identical block-length. In a first, this work studies the likelihood ratio test for minimizing the error probability in this detection problem. In an asymptotic setting, where a large number of noise-affected codewords are available for detection, the Chernoff information characterizes the error probability. A lower bound on the Chernoff information, based on the parameters of the two hypothesis, is established. Further, it is shown that if likelihood based efficient (generalized distributive law or BCJR) bit-decoding algorithms are available for the two codes, then the likelihood ratio test for the code-detection problem can be performed in a computationally feasible manner.

In this paper, we consider the problem of distinguishing the noisy codewords of a known binary linear block code from a random bit sequence. We propose to use the generalized likelihood ratio test (GLRT) to solve this problem. We also give a formula to find approximate number of codewords required and compare our results with an existing method.