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Register a new userA Coding Theory Perspective on Multiplexed Molecular Profiling of Biological Tissues
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High-throughput and quantitative experimental technologies are experiencing rapid advances in the biological sciences. One important recent technique is multiplexed fluorescence in situ hybridization (mFISH), which enables the identification and localization of large numbers of individual strands of RNA within single cells. Core to that technology is a coding problem: with each RNA sequence of interest being a codeword, how to design a codebook of probes, and how to decode the resulting noisy measurements? Published work has relied on assumptions of uniformly distributed codewords and binary symmetric channels for decoding and to a lesser degree for code construction. Here we establish that both of these assumptions are inappropriate in the context of mFISH experiments and substantial decoding performance gains can be obtained by using more appropriate, less classical, assumptions. We propose a more appropriate asymmetric channel model that can be readily parameterized from data and use it to develop a maximum a posteriori (MAP) decoders. We show that false discovery rate for rare RNAs, which is the key experimental metric, is vastly improved with MAP decoders even when employed with the existing sub-optimal codebook. Using an evolutionary optimization methodology, we further show that by permuting the codebook to better align with the prior, which is an experimentally straightforward procedure, significant further improvements are possible.
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Regular perturbation is applied to space-division multiplexing (SDM) on optical fibers and motivates a correlated rotation-and-additive noise (CRAN) model. For S spatial modes, or 2S complex-alphabet channels, the model has 4S(S+1) hidden independent real Gauss-Markov processes, of which 2S model phase noise, 2S(2S-1) model spatial mode rotation, and 4S model additive noise. Achievable information rates of multi-carrier communication are computed by using particle filters. For S=2 spatial modes with strong coupling and a 1000 km link, joint processing of the spatial modes gains 0.5 bits/s/Hz/channel in rate and 1.4 dB in power with respect to separate processing of 2S complex-alphabet channels without considering CRAN.
A major hurdle in machine learning is scalability to massive datasets. One approach to overcoming this is to distribute the computational tasks among several workers. textit{Gradient coding} has been recently proposed in distributed optimization to compute the gradient of an objective function using multiple, possibly unreliable, worker nodes. By designing distributed coded schemes, gradient coded computations can be made resilient to textit{stragglers}, nodes with longer response time comparing to other nodes in a distributed network. Most such schemes rely on operations over the real or complex numbers and are inherently numerically unstable. We present a binary scheme which avoids such operations, thereby enabling numerically stable distributed computation of the gradient. Also, some restricting assumptions in prior work are dropped, and a more efficient decoding is given.
We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by the ratio of the adversarys successful guessing probability after and before eavesdropping the codeword, maximized over all possible source distributions. Such measurement under the basic adversarial model where the adversary makes a single guess and allows no distortion between its estimator and the true sequence is known as the maximum min-entropy leakage or the maximal leakage in the literature. We develop a single-letter characterization of the optimal normalized leakage under the basic adversarial model, together with an optimum-achieving scalar stochastic mapping scheme. An interesting observation is that the optimal normalized leakage is equal to the optimal compression rate with fixed-length source codes, both of which can be simultaneously achieved by some deterministic coding schemes. We then extend the leakage measurement to generalized adversarial models where the adversary makes multiple guesses and allows certain level of distortion, for which we derive single-letter lower and upper bounds.
In this paper, a sparse Kronecker-product (SKP) coding scheme is proposed for unsourced multiple access. Specifically, the data of each active user is encoded as the Kronecker product of two component codewords with one being sparse and the other being forward-error-correction (FEC) coded. At the receiver, an iterative decoding algorithm is developed, consisting of matrix factorization for the decomposition of the Kronecker product and soft-in soft-out decoding for the component sparse code and the FEC code. The cyclic redundancy check (CRC) aided interference cancellation technique is further incorporated for performance improvement. Numerical results show that the proposed scheme outperforms the state-of-the-art counterparts, and approaches the random coding bound within a gap of only 0.1 dB at the code length of 30000 when the number of active users is less than 75, and the error rate can be made very small even if the number of active users is relatively large.
This paper investigates the application of physical-layer network coding (PNC) to Industrial Internet-of-Things (IIoT) where a controller and a robot are out of each others transmission range, and they exchange messages with the assistance of a relay. We particularly focus on a scenario where the controller has more transmitted information, and the channel of the controller is stronger than that of the robot. To reduce the communication latency, we propose an asymmetric transmission scheme where the controller and robot transmit different amount of information in the uplink of PNC simultaneously. To achieve this, the controller chooses a higher order modulation. In addition, the both users apply channel codes to guarantee the reliability. A problem is a superimposed symbol at the relay contains different amount of source information from the two end users. It is thus hard for the relay to deduce meaningful network-coded messages by applying the current PNC decoding techniques which require the end users to transmit the same amount of information. To solve this problem, we propose a lattice-based scheme where the two users encode-and-modulate their information in lattices with different lattice construction levels. Our design is versatile on that the two end users can freely choose their modulation orders based on their channel power, and the design is applicable for arbitrary channel codes.
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