Modeling neutral evolution using an in nite-allele Markov branching process

We consider an in nite-allele Markov branching process (IAMBP). Our main focus is the frequency spectrum of this process, i.e., the proportion of alleles having a given number of copies at a speci ed time point. We derive the variance of the frequency spectrum, which is useful for interval estimation and hypothesis testing for process parameters. In addition, for a class of special IAMBP with birth and death o spring distribution, we show that the mean of its limiting frequency spectrum has an explicit form in terms of the hypergeometric function. We also derive an asymptotic expression for convergence rate to the limit. Simulations are used to illustrate the results for the birth and death process

Approximately EFX Allocations for Indivisible Chores

In this paper, we study how to fairly allocate a set of m indivisible chores to a group of n agents, each of which has a general additive cost function on the items. Since envy-free (EF) allocations are not guaranteed to exist, we consider the notion of envy-freeness up to any item (EFX). In contrast to the fruitful results regarding the (approximation of) EFX allocations for goods, very little is known for the allocation of chores. Prior to our work, for the allocation of chores, it is known that EFX allocations always exist for two agents or general number of agents with identical ordering cost functions. For general instances, no non-trivial approximation result regarding EFX allocation is known. In this paper, we make progress in this direction by providing several polynomial time algorithms for the computation of EFX and approximately EFX allocations. We show that for three agents we can always compute a 4.45-approximation of EFX allocation. For n>=4 agents, our algorithm always computes a (3n^2-n)-approximation. We also study the bi-valued instances, in which agents have at most two cost values on the chores. For three agents, we provide an algorithm for the computation of EFX allocations. For n>=4 agents, we present algorithms for the computation of partial EFX allocations with at most n-1 unallocated items; and (n-1)-approximation of EFX allocations.Comment: Include new results about partial EFX allocations and improved results regarding approximate EFX allocation

Information-Coupled Turbo Codes for LTE Systems

We propose a new class of information-coupled (IC) Turbo codes to improve the transport block (TB) error rate performance for long-term evolution (LTE) systems, while keeping the hybrid automatic repeat request protocol and the Turbo decoder for each code block (CB) unchanged. In the proposed codes, every two consecutive CBs in a TB are coupled together by sharing a few common information bits. We propose a feed-forward and feed-back decoding scheme and a windowed (WD) decoding scheme for decoding the whole TB by exploiting the coupled information between CBs. Both decoding schemes achieve a considerable signal-to-noise-ratio (SNR) gain compared to the LTE Turbo codes. We construct the extrinsic information transfer (EXIT) functions for the LTE Turbo codes and our proposed IC Turbo codes from the EXIT functions of underlying convolutional codes. An SNR gain upper bound of our proposed codes over the LTE Turbo codes is derived and calculated by the constructed EXIT charts. Numerical results show that the proposed codes achieve an SNR gain of 0.25 dB to 0.72 dB for various code parameters at a TB error rate level of $10^{-2}$, which complies with the derived SNR gain upper bound.Comment: 13 pages, 12 figure