Interval Modulation Coding

Abstract

In this paper we introduce a new paradigm for storage and communication. We call this paradigm Interval Modulation Coding. Both in the context of communication and storage, one needs to measure the elapsed time between voltage transitions or voltage pulses. Conventionally, this measurement is made by a clock, by counting clock pulses. Analog circuits (or clocks of higher frequency) can also be used to measure elapsed time. And in this case the set of permissible time intervals no longer has to consist of consecutive integer multiples of the clock period but can be chosen in accordance with a probabilistic model of measurement error. We will show that this can potentially provide substantial improvements in terms of bandwitdth and storage density over coding techniques deployed in real storage and communication systems. We provide a mechanism for encoding and decoding data based on variable length to variable length prefix free codes. We show that such codes can be constructed using integer linear programming. From a theoretical standpoint, we study the linear programming relaxation of the integer linear program associated with code construction. We provide an efficient algorithm for determining if the linear programming relaxation is feasible and an efficient algorithm for solving the linear programming relaxation, assuming it is feasible.

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