FT is the number of symbols in a coded block, or the number of sub-carriers used in an OFDMA system and P(.) is an invertible function. In the case of the mutual information-based ESM, the function P(.) is derived from the constrained capacity, whereas in the case of EESM, the function P(.) is derived from the Chernoff bound on the probability of error. The accuracy of a mutual information-based metric depends on the equivalent channel over which this metric is defined. The capacity is defined as the mutual information based on a Gaussian channel with Gaussian distributed inputs. The modulation constrained capacity is the mutual information of a symbol channel, i.e., constrained by the input symbols drawn from a complex set. The computation of the mutual information per coded bit can be derived from the received symbol-level mutual information which is regarded as Received Bit mutual Information Rate (RBIR) link-to-system mapping. An alternative approach directly arrives at the bit-level mutual information and is known as the Mean Mutual Information per Bit (MMIB) PHY abstraction method. The procedure of the MI ESM approach is illustrated in Figure 12-4. Given a set of N received encoder symbol SINRs from the 'In the theory of probability and stochastic processes, the Chernoff bound provides exponentially decreasing bounds (asymptotic) on tail distributions of sums of independent random variables, compared to the first or second moment-based tail bounds such as Markov's inequality or Chebyshev inequality, which only yield power-law bounds on tail decay. Let X1, X2 Xn denote discrete and independent random variables with probability p > 1/2. Then, the probability of simultaneous occurrence of more than n/2 of the events XK has an exact value P, where P = - The Chernoff bound provides a lower bound for P given by P > 1 - exp[-2n(p - 1/2)2]. The Chernoff bound applies to a class of random variables and provides an exponential fall-off of probability with distance from the mean. The critical condition that is needed 