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In certain communications problems, such as remote telemetry, it is important that any operations performed at the transmitter be of a simple nature, while operations performed at the receiver can frequently be orders of magnitude more complex. Channel coding is well matched to such situations while conventional source coding is not. To overcome this difficulty of usual source coding, we propose using a convolutional encoder for joint source and channel encoding. When the channel is noiseless this scheme reduces to a convolutional source code that is simpler to encode than any other optimal noiseless source code known to date. In either case, decoding can be a minor variation on sequential decoding.