Related papers: Sparse Superposition Codes with Binomial Dictionar…
For the additive white Gaussian noise channel with average power constraint, sparse superposition codes, proposed by Barron and Joseph in 2010, achieve the capacity. While the codewords of the original sparse superposition codes are made…
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform.…
For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…
We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that…
For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by…
We study the approximate message-passing decoder for sparse superposition coding on the additive white Gaussian noise channel and extend our preliminary work [1]. We use heuristic statistical-physics-based tools such as the cavity and the…
Sparse superposition codes, or sparse regression codes, constitute a new class of codes which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are…
We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression…
Sparse superposition codes were recently introduced by Barron and Joseph for reliable communication over the AWGN channel at rates approaching the channel capacity. The codebook is defined in terms of a Gaussian design matrix, and codewords…
Recently, a new class of codes, called sparse superposition or sparse regression codes, has been proposed for communication over the AWGN channel. It has been proven that they achieve capacity using power allocation and various forms of…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is…
This paper shows that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense…
A general method of coding over expansions is proposed, which allows one to reduce the highly non-trivial problem of coding over continuous channels to a much simpler discrete ones. More specifically, the focus is on the additive…
Let $W$ be a binary-input memoryless symmetric (BMS) channel with Shannon capacity $I(W)$ and fix any $\alpha > 0$. We construct, for any sufficiently small $\delta > 0$, binary linear codes of block length $O(1/\delta^{2+\alpha})$ and rate…