Performance Study of BCH Error Correcting Codes Using the Bit Error Rate Term BER

Abstract

The quality of a digital transmission is mainly dependent on the amount of errors introduced into the transmission channel. The codes BCH (Bose-Chaudhuri-Hocquenghem) are widely used in communication systems and storage systems. In this paper a Performance study of BCH error correcting codes is proposed. This paper presents a comparative study of performance between the Bose-Chaudhuri-Hocquenghem codes BCH (15, 7, 2) and BCH (255, 231, 3) using the bit error rate term (BER). The channel and the modulation type are respectively AWGN and PSK where the order of modulation is equal to 2. First, we generated and simulated the error correcting codes BCH (15, 7, 2) and BCH (255, 231, 3) using Math lab simulator. Second, we compare the two codes using the bit error rate term (BER), finally we conclude the coding gain for a BER = 10-4.

An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes

“…From this figure we deduce that the BER performances of PHR-BM far exceed the HSDec and DND decoders. In the Figure 7.we present a comparison between HSDec [22], ARDecGA [21], BERT [6] and the proposed combination PHR-BM for the BCH (15,7,5) code. From this figure, we can deduce that our decoder PHR-BM passes remarkably the HSDec, ARDecGA and BERT decoders for this code.…”

“…They are just applicable for Quadratic Residue (QR) codes. By exploiting the Bit Error Rate Term, El ghayyaty et al [6] have published a performances study of BCH error correcting codes and they gave a comparative study between the BCH (15,7,2) and BCH(255, 231, 3) codes. In [7], quadratic residue codes were discussed over a defined ring.…”

Machine learning for decoding linear block codes: case of multi-class logistic regression model

“…To show the efficiency of our decoding model, we have compared its performances with other existing decoders. In Figure 11, we present the performances of the LRDec, ARDecGA [11] and BERT [12] decoders for the BCH code (15,7,5). Thanks to the comparisons listed above, the LRDec for the code BCH (15, 7, 5) has proved to be the best decoder in terms of performance and efficiency.…”

“…For the same purpose, as shown in Figure 12, the LRDec and the HSDec [9] have the same performance in the code BCH (31, 16, 7). What is more, in Figure 13, we have compared the performance of LRDec with HSDec for a new class of binary code, the QR code (23,12,7), and the results have shown that the RLDec is more efficient than HSDec.…”

“…After that, we will expose different obtained results for linear codes. Finally, we will compare and discuss them with other existing decoders' results (e,g: HSDEC [9]- [10], ARdecGA [11] and BERT [12]). In addition to this, in contrast to other decoders, our LRDec is has been successfully applied to another kind of linear codes which is named quadratic residual code (QR).…”