Net coding gain of some rate 1/2 block codes

Using the concept of net coding gain (NCG), we measure the benefits of using a class of rate 1/2 codes in error control systems. A bounded distance decoder for group codes is assumed. The NCG can be compared with other expedients such as increasing transmitted signal power. Although the codes are used in conjunction with phase and frequency modulation systems, the technique is valid for any binary modulation system to which the binomial distribution of errors applies. Using the weight distribution of the codes considered, the net coding gain is computed for (8, 4), (16, 8), (24, 12), (32, 16), (40, 20), (48, 24), (56, 28), (64, 32) and (72, 36) codes. These are self-dual codes with weights divisible by four. All codes except the (72, 36) are known to exist. It is shown that significant coding gains can be obtained with these codes. Decoding algorithms have been described previously in the literature.