Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs

An Orbital Construction of Optimum Distance Flag Codes

Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, where $q$ is a prime power and $\mathbb{F}_q$, the finite field of size $q$. In this paper we study the construction on $\mathbb{F}_q^{2k}$ of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension $k$ and maximum distance with a given orbital description, we provide sufficient con…

准最优距离旗码

Quasi-optimum distance flag codes

本文研究了网络编码中的准最优距离旗码，通过部分散布和向日葵提出了适用于任意类型向量的系统性构造方法，并给出了其基数上界及低距离旗码的刻画结果。

基于部分展开的完全旗码新构造

New Constructions of Full Flag Codes Based on Partial Spreads

本文提出基于部分展开的完全旗码新构造，涵盖最优与准最优距离，并给出高效译码算法。

Flag Codes from Planar Spreads in Network Coding

In this paper we study a class of multishot network codes given by families of nested subspaces (flags) of a vector space $\mathbb{F}_q^n$, being $q$ a prime power and $\mathbb{F}_q$ the finite field of $q$ elements. In particular, we focus on flag codes having maximum minimum distance (optimum distance flag codes). We explore the existence of these codes from spreads, based on the good properties of the latter ones. For $n=2k$, we show that optimum distance full flag codes with the largest size are exactly those that can be constructed from a planar spread. We give a precise construction of t…

On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA

We extend the result by Tse and Verdú on the optimum asymptotic multiuser efficiency of randomly spread CDMA with Binary Phase Shift Keying (BPSK) input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a $K$-user system with spreading gain $N$ when $K$ and $N\rightarrow\infty$ and the loading factor, $\frac{K}{N}$, grows logarithmically with $K$ under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high Signal to No…

伪正交随机扩频CDMA的最佳渐近多用户效率

Optimum Asymptotic Multiuser Efficiency of Pseudo-Orthogonal Randomly Spread CDMA

介绍了一种$K$ -用户伪正交（PO）随机扩频CDMA系统，该系统等效于在$K'\leq K$单用户高斯信道子集上传输。在大系统极限下，通过严格推导PO-CDMA的渐近多用户效率（AME），分析了PO-CDMA的高信噪比性能。有趣的是，$K'$优化的PO-CDMA收发机方案产生的AME对于小于0.1的系统负载实际上等于1，并且对于增加的负载下限为1/4。相对于线性多用户检测器的消失的效率，派生的效率是可比的最终CDMA效率实现的棘手的最佳多用户检测器。