Spatially Coupled Sparse Regression Codes for Single- and Multi-user Communications

Sparse regression codes (SPARCs) are a class of channel codes for efficient communication over the single-user additive white Gaussian noise (AWGN) channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear combinations of columns of an i.i.d. Gaussian design matrix, and the user message is encoded in the indices of those columns. Techniques such as power allocation and spatial coupling have been proposed to improve the performance of low-complexity iterative decoding algorithms such as approximate message passing (AMP). In this thesis we investigate spatially coupled SPARCs, where the design matrix has a block- wise band-diagonal structure, and modulated SPARCs, which generalise standard SPARCs by introducing modulation to the encoding of user messages. We introduce a base matrix framework which provides a unified way to construct power allocated and spatially coupled design matrices, and propose AMP decoders for modulated SPARCs constructed using base matrices. We prove that phase shift keying modulated and spatially coupled SPARCs with AMP decoding asymptotically achieve the capacity of the (complex) AWGN channel. We also show via numerical simulations that they can achieve lower error rates than standard coded modulation schemes at finite code lengths. A sliding window AMP decoder is proposed for spatially coupled SPARCs that significantly reduces the decoding latency and complexity. We then investigate coding schemes based on random linear models and AMP decoding for the multi-user Gaussian multiple access channel in the asymptotic regime where the number of users grows linearly with the code length. For a fixed target error rate and message size per user (in bits), we obtain the exact trade-off between energy-per-bit and the user density achievable in the large system limit. We show that a coding scheme based on spatially coupled Gaussian matrices and AMP decoding achieves near-optimal trade-off for a large range of user densities. To the best of our knowledge, this is the first efficient coding scheme to do so in this multiple access regime. Moreover, the spatially coupled coding scheme has a practical interpretation: it can be viewed as block-wise time-division with overlap.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2021

Author dc:creator

• Hsieh, Kuan

Advisor dc:contributor.advisor

• Venkataramanan, Ramji

• error correcting codes
• digital communications
• signal processing
• information theory

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/8fabf77d-fe82-422a-ba5d-a432addedbef/download
• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0001-7500-9980

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/323267