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Hybrid in-band on-channel (IBOC) broadcasting systems for digital audio radio have the capability of simultaneously transmitting analog FM and digital audio of CD-like quality. Due to fading and interference in the already-crowded FM band, the signal design for the hybrid IBOC system is very challenging. It has been proposed to use a method of double sideband transmission where the digital information is transmitted by means of orthogonal frequency-division multiplexing (OFDM) on both sides of the analog host FM and where the digital information can be recovered when one sideband is partially or even totally lost. This leads to an interesting channel coding problem, where we search for optimal pairs of high-rate codes that form good combined low-rate codes, which are better than classic code combining techniques. Furthermore, we also search for rate-compatible punctured convolutional codes which can be used for two-level unequal error protection (UEP) of digital audio. Since some of the tones in the multitone modem (OFDM) are more exposed to interference than others, optimal assignments of convolutional code bits to tones depending on their spectral position are also found. A large number of new codes with memory 6 and 8 are presented both for equal error protection and UEP.