A data distribution system has a number of data processing devices interconnected by data transmission media. At least one of the data processing devices transmit data to other data processing devices in the system. The transmitting data processing system includes memory for storing the data to be transmitted, programmable data processing circuitry, and data transmission apparatus for transmitting an encoded representation of the stored message as a sequence of data packets. Priority data, stored in the memory, represents a plurality of assigned priority levels for specified portions of the stored message such that portions of the stored message have respective assigned priority levels. A data encoding program generates an encoded representation of the stored message that includes, for each portion of the stored message, a level of redundant data corresponding to the priority level assigned to that portion of the stored message. As a result, the encoded representation of the stored message includes different levels of redundant data for the different portions of the stored message. Each receiving data processing system includes memory for storing received data, programmable data processing circuitry, and data receiving apparatus for receiving at least a portion of the transmitted data packets. A data decoding program generates a decoded representation of the received data stream. The data decoding program decodes different portions of the received encoded data in accordance with the different levels of redundant data included in the received data stream.