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By Martin S Roden

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2: Information-bit error probability for binary block coherent PSK. 3: Information-bit error probability for Reed-Solomon Modulation is coherent PSK or noncoherent MFSK. 17 codes and codes. 18 CHAPTER 1. CHANNEL CODES are used. For the binary channel symbols, (1-34) and the lower bound in (1-33) are used. For the chosen values of the best performance at is obtained if the code rate is Further gains result from increasing and hence the implementation complexity. Although the figure indicates the performance advantage of Reed-Solomon codes with MFSK, there is a major bandwidth penalty.

Although the figure indicates the performance advantage of Reed-Solomon codes with MFSK, there is a major bandwidth penalty. Let B denote the bandwidth required for an uncoded binary PSK signal. If the same data rate is accommodated by using uncoded binary frequeny-shift keying (FSK), the required bandwidth for demodulation with envelope detectors is approximately 2B. For uncoded MFSK using frequencies, the required bandwidth is because each symbol represents bits. If a Reed-Solomon code is used with MFSK, the required bandwidth becomes Code Metrics for Orthogonal Signals For orthogonal symbol waveforms, matched filters are needed, and the observation vector is where each is an row vector of matched-filter output samples for filter with components Suppose that symbol of codeword uses unitenergy waveform where the integer is a function of and If codeword is transmitted over the AWGN channel, the received signal for symbol can be expressed in complex notation as where is independent, zero-mean, white Gaussian noise with two-sided power spectral density is the carrier frequency, and is the phase.

1. BLOCK CODES 21 To determine the maximum-likelihood metric for making a hard decision on each symbol, we set and drop the subscript in (1-57) and (1-61). We find that the maximum-likelihood symbol metric is for coherent MFSK and for noncoherent MFSK, where the index ranges over the symbol alphabet. Since the latter function increases monotonically and is a constant, optimal symbol metrics or decision variables for noncoherent MFSK are or for Metrics and Error Probabilities for MFSK Symbols For noncoherent MFSK, baseband matched-filter is matched to the unit-energy waveform where If is the received signal, a downconversion to baseband and a parallel set of matched filters and envelope detectors provide the decision variables The orthogonality condition (1-52) is satisfied if the adjacent frequencies are separated by where is a nonzero integer.

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