THE METHOD OF CORRECTING CODES FORMATION IN THE RESIDUE NUMBER SYSTEM
T.G. Tsavolyk, Vasyl Yatskiv · Науковий вісник НЛТУ України · 2017
The problem of high reliability of data transmission in wireless computer networks becomes more urgent with the widespread development and implementation of wireless technology. One of the approaches to solve this problem is using of correcting codes. A significant amount of correcting codes was developed. They operate in positional number systems and have practical application in wireless communications. It is necessary to highlight the correcting codes that operate in the Residue Number System (RNS). These codes are characterized by high corrective ability and the possibility of adaptive changes in the number and values of check symbols depending on the channel's state. However, the usage of RNS correcting codes requires additional data conversion from the binary system into the RNS. Thus, the aim of the work is to increase the efficiency of correcting codes formation based on Residue Number System. The essence of a proposed method of RNS correcting codes formation is as follows. The transmitted sequence of bits is divided into segments of 4 or 8 bits. Each part of the binary code is associated with prime numbers (modules) pi (p1 2m. The authors present the following results of experimental studies. Firstly, the experimental studies of hardware costs (number of logic gates) and computation time for the check symbols are conducted for different digit capacity of the input data for RNS correcting codes and proposed method for the RNS correcting codes formation. Secondly, the study was conducted using the Quartus software by the Intel (Altera) company. Both known and proposed methods of RNS correcting codes coding are described using the Verilog-HDL, synthesized in Cyclone IV chips. Thirdly, the following parameters were choosen for the experiment: digit capacity of the input data from 16 to 48 bit; the number of information modules – 4; the number of check modules – 1, 2; the modules' values depend on the digit capacity of the message. Finally, the proposed method reduces hardware costs by an average of 20 % and depends on the digit capacity of the input data (block capacity is 8 bit). At the same time, the computation time costs rise by an average of 59 %. However, in the known method the message is represented in Residue Number System, which requires additional time for transformation in positional system. The conclusions are as follows. The proposed method of the RNS correcting codes formation reduces the hardware costs by 20 % depending on the digit capacity of the message and improves performance through the necessary transformation of the messages into RNS. Also the method of forming check symbols will expand the scope of RNS correcting codes usage by processing the messages represented in positional systems.