# Bose-Chaudhuri-Hocquenghem¶

The design of a digital communication system aims to maximize the transmission bit rate, to minimize the probability of bit error, to minimize the required power, or equivalently, to minimize the required carrier-to-noise ratio, to minimize the required system bandwidth and to minimize the system complexity and cost. Satellite Digital Video Broadcasting (DVB) systems are particularly affected by power limitations, therefore ruggedness against noise and interference should be the main design objective, rather than spectrum efficiency [1, 2]. In order to achieve high power efficiency without excessively penalizing the spectrum efficiency, such a system should use noise resistant types of modulation and effective channel codes. Recent trends in satellite communications show an increasing demand of higher-order M-ary modulation schemes. Higher-order M-ary modulation schemes can provide greater spectral efficiency and thus the high data rate required for either digital multimedia applications or other applications such as point-to-point high data rate backbone connectivity and future Earth observation missions requiring downlink data rates exceeding 1 Gbps [1].

BCH codes fall into the group of block codes, where the digital information is transmitted in packets of a K symbols length. Each symbol consists of n bits, and the greatest applicability belongs to the dual BCH codes, where n = 1. The BCH codes are generally represented as BCH, where N is the total number of coded symbols in a packet, and T is the number of repairable symbol errors. For the most common codes N = 2h – 1, where h can be every number which is greater than or equals to 3, and hT = N−K is the number of error protection symbols, or checksum [1].

## References¶

[1] L. Jordanova, L.Laskov, D.Dobrev Influence of BCH and LDPC Code PArameters on the BER Characteristics of Satellie DVB Channels Engineering, Technology & Applied Science Research, Vol4, No 1, 2014 591-595