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This paper considers the performance of $(j,k)$-regular low-density parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC…
In joint multiuser decoding, a receiver recovers a set of messages from a single noisy aggregate of many simultaneous transmissions. Classical decoders rely on rule-based mechanisms such as successive interference cancellation, joint belief…
Single sequences like Legendre have high linear complexity. Known CDMA families of sequences all have low complexities. We present a new method of constructing CDMA sequence sets with the complexity of the Legendre from new frequency hop…
The everlasting bandwidth limitations in wireless communication networks has directed the researchers' thrust toward analyzing the prospect of overloaded Code Division Multiple Access (CDMA). In this paper, we have proposed a Genetic…
This paper presents a joint typicality framework for encoding and decoding nested linear codes for multi-user networks. This framework provides a new perspective on compute-forward within the context of discrete memoryless networks. In…
Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we…
Sparse Code Multiple Access (SCMA) is a disruptive code-domain non-orthogonal multiple access (NOMA) scheme to enable \color{black}future massive machine-type communication networks. As an evolved variant of code division multiple access…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
In this paper, a distributed turbo-like coding scheme for wireless networks with relays is proposed. We consider a scenario where multiple sources communicate with a single destination with the help of a relay. The proposed scheme can be…
Large-scale multi-input multi-output (MIMO) code domain non-orthogonal multiple access (CD-NOMA) techniques are one of the potential candidates to address the next-generation wireless needs such as massive connectivity, and high…
Cyclic codes have efficient encoding and decoding algorithms over finite fields, so that they have practical applications in communication systems, consumer electronics and data storage systems. The objective of this paper is to give eight…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
We show that for (systematic) linear codes the time complexity of unique decoding is O(n^{2}q^{nRH(delta/2/R)}) and the time complexity of minimum distance decoding is O(n^{2}q^{nRH(delta/R)}). The proposed algorithm inspects all error…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
In this paper, we consider a hierarchical distributed multi-task learning (MTL) system where distributed users wish to jointly learn different models orchestrated by a central server with the help of a layer of multiple relays. Since the…
Sequential decoding, commonly applied to substitution channels, is a sub-optimal alternative to Viterbi decoding with significantly reduced memory costs. In this work, a sequential decoder for convolutional codes over channels that are…
We study the following one-way asymmetric transmission problem, also a variant of model-based compressed sensing: a resource-limited encoder has to report a small set $S$ from a universe of $N$ items to a more powerful decoder (server). The…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…