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A 32 kbit/s rate per channel would double the capacity of digital links compared with 62 kbit/s standard PCM and permit digital techniques to be used throughout in telecommunication networks. The requirements imposed on a coding scheme for long-haul telephone transmission are reviewed. Besides the minimal complexity of implementation, the toll-quality level, the capability of handling signals other than speech, a crucial feature is the non cumulation of degradations in successive coding-decoding processes. An ADPCM coder is proposed ; in the implementation with finite precision arithmetic, both adapted quantization step sizes and prediction filter outputs track in coder and decoder. Experimental results show that the 32 kbit/s scheme outperforms 56 kbit/s PCM for speech in several aspects and is adequate for data transmission up to 4800 bit/s.