4 research outputs found
Sparse Regression Codes for Multi-terminal Source and Channel Coding
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 codes. Codewords are linear combinations of subsets of
columns of a design matrix. These codes were recently introduced by Barron and
Joseph and shown to achieve the channel capacity of AWGN channels with
computationally feasible decoding. They have also recently been shown to
achieve the optimal rate-distortion function for Gaussian sources. In this
paper, we demonstrate how to implement random binning and superposition coding
using sparse regression codes. In particular, with minimum-distance
encoding/decoding it is shown that sparse regression codes attain the optimal
information-theoretic limits for a variety of multi-terminal source and channel
coding problems.Comment: 9 pages, appeared in the Proceedings of the 50th Annual Allerton
Conference on Communication, Control, and Computing - 201
Polar codes for the m-user multiple access channel and matroids
In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arıkan’s polarization technique applied individually to each user will polarize any m-user binary input MAC into a finite collection of extremal MACs. The extremal MACs have a number of desirable properties: (i) the ‘uniform sum rate’1 of the original channel is not lost, (ii) the extremal MACs have rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits; in this sense they are easy to communicate over. Provided that the convergence to the extremal MACs is fast enough, the preceding leads to a low complexity communication scheme that is capable of achieving the uniform sum rate of an arbitrary binary input MAC. We show that this is indeed the case for arbitrary values of m
Polar Codes for the m-User MAC and Matroids
In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arıkan’s polarization technique applied individually to each user will polarize any m-user binary input MAC into a finite collection of extremal MACs. The extremal MACs have a number of desirable properties: (i) the ‘uniform sum rate ’ 1 of the original channel is not lost, (ii) the extremal MACs have rate regions that are not only polymatroids but matroids and thus (iii) their uniform sum rate can be reached by each user transmitting either uncoded or fixed bits; in this sense they are easy to communicate over. Provided that the convergence to the extremal MACs is fast enough, the preceding leads to a low complexity communication scheme that is capable of achieving the uniform sum rate of an arbitrary binary input MAC. We show that this is indeed the case for arbitrary values of m