The limitations to delay-insensitivity in asynchronous circuits
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Implementation of delay-insensitive (DI) or unordered codes is the subject of this paper. We present two different architectures for decoding systematic DI codes: (a) an enumeration-based decoder, and (b) a comparison-based decoder. We argue that enumeration-based decoders are often impractical for many realistic codes. Comparison-based decoders that detect arrival of a code word by comparing the received check bit with check bits evaluated using the received data are practical but suffer from the following limitation. If the decoder is to be implemented using asynchronous logic, i.e., if the gate and wire delays are arbitrary (unbounded but finite), then it is impossible to design a comparison-based decoder for any code that is more efficient than a dual-rail code. In other words, the encoded word must contain at least twice as many bits as the data. The paper shows that comparison-based decoders for codes that have the requisite level of redundancy can be implemented using asynchronous logic. The paper also shows that, by relaxing the delay assumptions, it is possible to implement decoders for delay-insensitive codes that are more efficient than dual-rail codes.