294,353 research outputs found

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

    Full text link
    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

    From coordinate subspaces over finite fields to ideal multipartite uniform clutters

    Full text link
    Take a prime power qq, an integer n≥2n\geq 2, and a coordinate subspace S⊆GF(q)nS\subseteq GF(q)^n over the Galois field GF(q)GF(q). One can associate with SS an nn-partite nn-uniform clutter C\mathcal{C}, where every part has size qq and there is a bijection between the vectors in SS and the members of C\mathcal{C}. In this paper, we determine when the clutter C\mathcal{C} is ideal, a property developed in connection to Packing and Covering problems in the areas of Integer Programming and Combinatorial Optimization. Interestingly, the characterization differs depending on whether qq is 2,42,4, a higher power of 22, or otherwise. Each characterization uses crucially that idealness is a minor-closed property: first the list of excluded minors is identified, and only then is the global structure determined. A key insight is that idealness of C\mathcal{C} depends solely on the underlying matroid of SS. Our theorems also extend from idealness to the stronger max-flow min-cut property. As a consequence, we prove the Replication and τ=2\tau=2 Conjectures for this class of clutters.Comment: 32 pages, 6 figure

    Selfish Bin Covering

    Get PDF
    In this paper, we address the selfish bin covering problem, which is greatly related both to the bin covering problem, and to the weighted majority game. What we mainly concern is how much the lack of coordination harms the social welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and several other new equilibria. For each equilibrium, the corresponding PoA and PoS are given, and the problems of computing an arbitrary equilibrium, as well as approximating the best one, are also considered.Comment: 16 page

    Submodular Minimization Under Congruency Constraints

    Full text link
    Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint types under which SFM remains efficiently solvable. The arguably most relevant non-trivial constraint class for which polynomial SFM algorithms are known are parity constraints, i.e., optimizing only over sets of odd (or even) cardinality. Parity constraints capture classical combinatorial optimization problems like the odd-cut problem, and they are a key tool in a recent technique to efficiently solve integer programs with a constraint matrix whose subdeterminants are bounded by two in absolute value. We show that efficient SFM is possible even for a significantly larger class than parity constraints, by introducing a new approach that combines techniques from Combinatorial Optimization, Combinatorics, and Number Theory. In particular, we can show that efficient SFM is possible over all sets (of any given lattice) of cardinality r mod m, as long as m is a constant prime power. This covers generalizations of the odd-cut problem with open complexity status, and with relevance in the context of integer programming with higher subdeterminants. To obtain our results, we establish a connection between the correctness of a natural algorithm, and the inexistence of set systems with specific combinatorial properties. We introduce a general technique to disprove the existence of such set systems, which allows for obtaining extensions of our results beyond the above-mentioned setting. These extensions settle two open questions raised by Geelen and Kapadia [Combinatorica, 2017] in the context of computing the girth and cogirth of certain types of binary matroids
    • …
    corecore