Model-based coding, described by John Pierce in 1961, has great potential to reduce the volume of information that needs to be transmitted in moving big data, without loss of information, from one place to another, or in lossless communications via the internet. Compared with ordinary compression methods, this potential advantage of model-based coding in the transmission of data arises from the fact that both the transmitter ("Alice") and the receiver ("Bob") are equipped with a grammar for the kind of data that is to be transmitted, which means that, to achieve lossless transmission of a body of data from Alice and Bob, a relatively small amount of information needs to be sent. Preliminary trials indicate that, with model-based coding, the volume of information to be sent from Alice to Bob to achieve lossless transmission of a given body of data may be less than $6\%$ of the volume of information that needs to be sent when ordinary compression methods are used. Until recently, it has not been feasible to convert John Pierce's vision into something that may be applied in practice. Now, with the development of the "SP theory of intelligence" and its realisation in the "SP computer model", there is clear potential to realise the three main functions that will be needed: unsupervised learning of a grammar for the kind of data that is to be transmitted using a relatively powerful computer that is independent of Alice and Bob; the encoding by Alice of any one example of such data in terms of the grammar; and, with the grammar, decoding of the encoding by Bob to retrieve the given example. It appears now to be feasible, within reasonable timescales, to bring these capabilities to a level where they may be applied to the transmission of realistically large bodies of data.