tions quality. Error Control Coding 1.0E + 00 1.0E-01 1.0E-02 No coding 1.0E-03 1.0E-04 coding 1.0E - 05 Eb/No (dB) Figure 6.12 Hamming (7,4) BER performance Error correcting code BERs are generally drawn against a normalised SNR measure, EIN 0 This is to account for the fact that extra non-information bits are used to facilitate error correction. The extra power consumed to transmit these bits needs to be taken into consideration. E is the energy per information bit and N 0 is noise power per unit of bandwidth. The relation between SNR and EINo can be written as: STATE where B is the signal bandwidth and f is the source information rate. The improvement in BER resulting from error correction is called 'coding gain' and is the main metric for evalu- ating an FEC code's efficacy. The coding efficiency also depends on the number of extra bits added: this is indicated by the coding rate or the ratio of information bits to the total trans- mitted. For example the Hamming (7,4) code has a coding rate of 4/7. The effect of FEC coding in reducing BLER is twofold. One is the reduction of underlying BER which reduces the overall probability of erroneous reception. The other is skewing the error events to burst errors. As Hamming (7,4) code can correct all single-bit errors, block error events are multiple-error events, and therefore the overall number of erroneously received blocks decreases. Shannon Limit As shown in Chapter 3, Shannon's capacity formula calculates the amount of information that may be carried over a band-limited channel. The theorem's application to error correction cod- ing shows that if transmission rate is less than channel capacity, then one can design FEC codes to provide arbitrary small error rates at a certain EINo level. This EINo level is known as the Shannon limit, and is a function of coding rate. Broadband Telecommunications Technologies and Management Table 6.1 Shannon limit for common coding rates Coding rate Shannon limit: EIN (dB) Source: Ref. [6] Historically the Shannon limit has been 