On the Peak-to-Mean Envelope Power Ratio of Phase-Shifted Binary Codes

The peak-to-mean envelope power ratio (PMEPR) of a code employed in orthogonal frequency-division multiplexing (OFDM) systems can be reduced by permuting its coordinates and by rotating each coordinate by a fixed phase shift. Motivated by some previous designs of phase shifts using suboptimal methods, the following question is considered in this paper. For a given binary code, how much PMEPR reduction can be achieved when the phase shifts are taken from a 2^h-ary phase-shift keying (2^h-PSK) constellation? A lower bound on the achievable PMEPR is established, which is related to the covering radius of the binary code. Generally speaking, the achievable region of the PMEPR shrinks as the covering radius of the binary code decreases. The bound is then applied to some well understood codes, including nonredundant BPSK signaling, BCH codes and their duals, Reed-Muller codes, and convolutional codes. It is demonstrated that most (presumably not optimal) phase-shift designs from the literature attain or approach our bound.Comment: minor revisions, accepted for IEEE Trans. Commun

A New Achievable Rate Region for Multiple-Access Channel with States

The problem of reliable communication over the multiple-access channel (MAC) with states is investigated. We propose a new coding scheme for this problem which uses quasi-group codes (QGC). We derive a new computable single-letter characterization of the achievable rate region. As an example, we investigate the problem of doubly-dirty MAC with modulo-$4$ addition. It is shown that the sum-rate $R_1+R_2=1$ bits per channel use is achievable using the new scheme. Whereas, the natural extension of the Gel'fand-Pinsker scheme, sum-rates greater than $0.32$ are not achievable.Comment: 13 pages, ISIT 201

Binary and Ternary Quasi-perfect Codes with Small Dimensions

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.Comment: 4 page

Asymmetric Lee Distance Codes for DNA-Based Storage

We consider a new family of codes, termed asymmetric Lee distance codes, that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a quaternary alphabet, although the results carry over to other alphabet sizes; furthermore, symbol confusability is dictated by their underlying binary representation. Our contributions are two-fold. First, we demonstrate that the new distance represents a linear combination of the Lee and Hamming distance and derive upper bounds on the size of the codes under this metric based on linear programming techniques. Second, we propose a number of code constructions which imply lower bounds

Tables of subspace codes

One of the main problems of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least $d$ over $\mathbb{F}_q^n$, where the dimensions of the codewords, which are vector spaces, are contained in $K\subseteq\{0,1,\dots,n\}$. In the special case of $K=\{k\}$ one speaks of constant dimension codes. Since this (still) emerging field is very prosperous on the one hand side and there are a lot of connections to classical objects from Galois geometry it is a bit difficult to keep or to obtain an overview about the current state of knowledge. To this end we have implemented an on-line database of the (at least to us) known results at \url{subspacecodes.uni-bayreuth.de}. The aim of this recurrently updated technical report is to provide a user guide how this technical tool can be used in research projects and to describe the so far implemented theoretic and algorithmic knowledge.Comment: 44 pages, 6 tables, 7 screenshot