System and apparatus for error control codes based on layering and linear transformations

Abstract

A powerful new class of methods for encoding digital data for reliable transmission over unreliable communication channels is described. With this method, the message bits are divided into multiple submessages and the bits in each layer are encoded using a standard error correction code to provide a plurality of subcodewords. A first linear transformation is applied to each of the subcodewords. The so-transformed subcodewords from the different submessages are then combined to form a first redundancy block to be transmitted. Additional redundancy blocks are generated by repeating this process on the same message but with jointly related nonidentical sets of linear transformations. The result is a set of codewords for each message which are then used to generate a transmitted waveform in one of several different ways, depending upon the application. For example, the codewords can be used in sequence (temporally) to form a rateless code for transmission over channels of unknown quality, in which case a receiver accumulates as many of the codewords as are necessary to successfully decode. As another example, the codewords can be spatially distributed if the channel has multiple-inputs, as would be the case in a multi-antenna system. As still another example, the codewords can be distributed over subchannels in a frequency-division multiplexing system.