Implementation of BCH Code (n, k) Encoder and Decoder for Multiple Error Correction Control

In this paper we have designed and implemented (15, k) a BCH Encoder and decoder using VHDL for reliable data transfer in AWGN channel with multiple error correction control. The digital logic implementation of binary encoding of multiple error correcting BCH code (15, k) of length n=15 over GF (24) with irreducible primitive polynomial x4+x+1 is organized into shift register circuits. Using the cyclic codes, the reminder b(x) can be obtained in a linear (15-k) stage shift register with feedback connections corresponding to the coefficients of the generated polynomial. Three encoders are designed using VHDL to encode the single, double and triple error correcting BCH code (15, k) corresponding to the coefficient of generated polynomial. Information bit is transmitted in unchanged form up to K clock cycles and during this period parity bits are calculated in the LFSR then the parity bits are transmitted from k+1 to 15 clock cycles. Total 15-k numbers of parity bits with k information bits are transmitted in 15 code word. In multiple error correction method, we have implemented (15, 5 ,3 ) ,(15,7, 2) and (15, 11, 1) BCH encoder and decoder using VHDL and the simulation is done using Xilinx ISE 14.2.