Message Encoding for Spread and Orbit Codes

Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been well-studied for their error correction capability and transmission rate, but the question of how to encode messages has not been investigated. In this work we show how the message space can be chosen for a given code and how message en- and decoding can be done.Comment: Submitted to IEEE International Symposium on Information Theory 201

Zero-error Slepian-Wolf Coding of Confined Correlated Sources with Deviation Symmetry

In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming Codes for Multiple Sources, to Matrix Partition Codes and use the latter to efficiently compress the target sources. We further show that every perfect or linear-optimal code is a Matrix Partition Code. We also present some conditions when Matrix Partition Codes are perfect and/or linear-optimal. Detail discussions of Matrix Partition Codes on Hamming sources are given at last as examples.Comment: submitted to IEEE Trans Information Theor

A Coupled Compressive Sensing Scheme for Unsourced Multiple Access

This article introduces a novel paradigm for the unsourced multiple-access communication problem. This divide-and-conquer approach leverages recent advances in compressive sensing and forward error correction to produce a computationally efficient algorithm. Within the proposed framework, every active device first partitions its data into several sub-blocks, and subsequently adds redundancy using a systematic linear block code. Compressive sensing techniques are then employed to recover sub-blocks, and the original messages are obtained by connecting pieces together using a low-complexity tree-based algorithm. Numerical results suggest that the proposed scheme outperforms other existing practical coding schemes. Measured performance lies approximately $4.3$~dB away from the Polyanskiy achievability limit, which is obtained in the absence of complexity constraints

Cyclic division algebras: a tool for space-time coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank. Extensive work has been done on Space–Time coding, aiming at finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to improve the design of good codes. The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes