on has the property T(m + 1) = m!, with r(1/2) = VII, r(3/2) = V/2, and T(m + 1/2) It can readily be checked that Vn = Anrn with the definition in Eq. (14.14) yields etc. 4 Channel capacity is conceptually similar to the capacity of transportation means. Thus, if for instance an airplane or a truck can transport 300 passengers or 20 tons, respectively, this corresponds to capacities of 300 passengers or 20 tons per single use of the airplane or of the truck. Using these transportation means several times does not increase the capacity per use, as was also shown in Appendix L. Gaussian channel and Shannon-Hartley theorem capacity theorem, or the band-limited capacity theorem. To recall, SHT or its different appellations relate to Shannon's "second theorem" or "[noisy] channel-capacity theo- rem." As expressed in Eq. (14.17), the SHT provides the maximum bit rate achievable (Cbit/s) given the channel bandwidth, additive noise background, and signal power con- straint, for which information can be transmitted with an arbitrarily small BER. The SHT variant in Eq. (14.18) provides the maximum bit rate achievable per unit of band- width (Hz), under said conditions. The bit rate normalized to bandwidth is referred to as information spectral density, or ISD. The (bit/s)/Hz ISD, is often referred to as spectral efficiency. This would be a correct appellation if the ISD was bounded to a maximum of unity, corresponding to 100% efficiency, or 1 (bit/s)/Hz. However, there are a variety of modulation formats, which make it possible to encode more than 1 bit/s in a single Hz of frequency spectrum, as discussed further on. Regardless of the possible existence of such modulation formats, the SHT states that the ISD is actually unbounded. In the limit of high signal-to-noise ratios (SNR = P/N), we find C 2 log2 (SNR). This result means that every twofold increase (or 3 dB, in the decibel scale5) of the SNR corresponds to an ISD increase of one additional (bit/s)/Hz. For instance, SNR = 210 = 1024 = +30.1 dB corresponds to an ISD o