 As a bench- mark, each graph plots the upperbound on P for "uncoded" signalling with optimum diversity. In one sense, this comparison is unfavorable to the con- volutional codes. The optimum diversity structure corresponds to the block repetition code with the code rate Klm that provides the best performance Coding Countermeasures WC PARTIAL-BAND NOISE UNCODED, OPTIMUM DIVERSITY (OPTIMUM REPETITION CODE) DUAL - -1, RATE 1/2 CONVOLUTIONAL CODE DUAL I, RATE 1/3 (7, I/2) BINARY CONVOLUTIONAL CODE CONVOLUTIONAL (7, 1/3) BINARY CONVOLUTIONAL Eb/Nj, dB Figure 2.66. Performance of several convolutional codes and optimum repetition code with FH binary FSK signals in worst case partial-band noise. Odenwalder's binary convolutional codes are particularly effective (e.g., about 5-6 dB better than uncoded signalling with optimum diversity at Pb = 10-5). Assumes soft decision energy detection, linear combining, and perfect side information. WC PARTIAL BAND NOISE ORTHOGONAL CONVOLUTIONAL CODE UNCODED, OPTIMUM DIVERSITY DUAL - 2, RATE 1/2 CONVOLUTIONAL CODE DUAL - 2, RATE 1/3 CONVOLUTIONAL (7, 1/2) 4-ARY CONVOLUTIONAL CODE Eb/Nj, dB Figure 2.67. Same as Figure 2.66, except K = 2. The 4-ary orthogonal convolutional code performs poorly, with an inverse linear characteristic for small P's. Trumpis' optimum constraint length 7 convolutional code for 4-ary orthogonal signalling is about 3.5 dB better than optimum diversity at Pb = 10-5. Non-Coherent Frequency-Hopped Systems WC PARTIAL-BAND NOISE DUAL-3, RATE 1/2 CONVOLUTIONAL CODE ORTHOGONAL CONVOLUTIONAL UNCODED, OPTIMUM DIVERSITY DUAL - 3, RATE 1/3 CONVOLUTIONAL (7, 1/3) 8-ARY CONVOLUTION- AL CODE Eb/Nu,dB Figure 2.68. Same as Figures 2.66 and 2.67, except K = 3. The orthogonal convo- lutional code continues to be ineffective, while the dual-3, rate 1/3 code outperforms the optimum diversity system over Pb's of interest. The best performance is again pro- vided by Trumpis' optimum (7,3) code for 8-ary orthogonal channels. WC PARTIAL-BANDNOISE DUAL- 3, RATE 1/2 CONVOLUTIONAL CODE