مسائل میراث حل کرنے کے قدیم اور جدید حسابی طریقوں کا تقابلی جائزہ

Inheritance is a key issue in the Islamic Knowledge base. Its importance has been clarified in Qur’an and Sunnah. The Holy Prophet Muhammad (ﷺ) has referred to it as half of the knowledge and has ordered of seeking inheritance and warned that this will be eliminated first from my Ummah, and also notified that this is volatile nature of knowledge which get lost after memorization if not fully cared and practiced. In the light of above mentioned Hadīths it is worth consideration to make knowledge of Inheritance practicable in everyday life. A reason could be that the arithmetic means used for the solution of Inheritance problems is complicated and time consuming. There it is important to introduce such easy and short arithmetic rules for the solution of Inheritance problem that are easily understandable by both the scholars as well as the common man. This will result in making Inheritance easy to handle and hence will become practicable. In a hadith it is stated that near the day of judgement there will be a conflict between two persons in an Inheritance issue and they will not find a scholar to resolve their problem. In this Article an Introduction and comparison of old and new easy arithmetic principles are made in scholarly manner to introduce new easy methods and draw the attention of the people to such a valuable knowledge and relieve the Phobia of the people regarding it.

Performance Enhancement of Wireless Mobile Adhoc Networks Through Improved Error Correction and Channel Estimation Strategy

PERFORMANCE ENHANCEMENT OF WIRELESS MOBILE ADHOC NETWORKS THROUGH IMPROVED ERROR CORRECTION AND CHANNEL ESTIMATION STRATEGY By Engr. Zeeshan Sabir Mobile Adhoc Networks (MANET) refer to an arrangement of autonomous wireless mobile nodes that show the tendency of freely and dynamically self-organizing into arbitrary and temporary network topologies. A variety of protocols have been implemented in MANET at the Network layer which tend to show different performance in various environments. Three of the most commonly used protocols at the Network Layer in MANET are Destination Sequenced Distance Vector (DSDV) Routing Protocol, Dynamic Source Routing (DSR) Protocol and Adhoc On- Demand Distance Vector (AODV) Routing Protocol. A comprehensive study on the performance evaluation of these three routing protocols have been given in this thesis basing upon the TCP window size using Network Simulator (NS-2.35) with two different types of network traffics. Tool iiCommand Language (TCL) scripting is used to simulate the environment. Orthogonal Frequency Division Multiplexing (OFDM) is the foremost choice for MANET system designers at the Physical Layer due to its inherent property of high data rate transmission that corresponds to its spectral efficiency. One of the problems inherent in OFDM includes its sensitivity to synchronization errors (frequency offsets and symbol time). Most of the present day techniques employing OFDM for data transmission support mobility as one of the primary feature. This mobility causes small Channel Frequency Offsets (CFO) owing to the production of Doppler frequencies. CFO tends to degrade the signal quality making the system design unsuitable for many error sensitive applications. In this work two efficient pilot-assisted channel estimation strategies have been implemented in the proposed model of OFDM. The implemented solutions for channel estimation include Zero Forcing algorithm and modified Least Square channel estimation algorithm. Both these algorithms have been implemented into the proposed environment of OFDM using two different types of pilot insertion methods i.e. block-type and comb-type pilot insertion techniques. Both these techniques have been compared amongst each other and with the already published work as well. iiiAnother serious problem faced by the OFDM based transmission systems is the sensitivity to the noise effects induced by the channel and system. These noise effects tend to increase the BER of the system making it unsuitable for many real-time applications. Turbo Codes have been integrated with the proposed model of OFDM which have the tendency to work in the Forward Error Correction (FEC) manner by not only identifying the erroneous bit locations but also correcting them thus using simplex control information link. The turbo codes have been implemented using parallel concatenation of Recursive Systematic Convolutional (RSC) Codes that tend to introduce redundant information into the user bits in order to mitigate the effects of channel induced noise from the received OFDM symbols. Results have been shown using MATLAB® simulation for changing number of iterations of MAP decoder for five different modulation schemes and are compared. The channel, through which the signal has been passed, is simulated using Stanford University Interim Channel Model parameters. These Channel models are six in number and depict three different real outdoor environments including rural, urban and hilly terrains having low, moderate and high tree densities.