COMMUNICATION OVER NOISY CHANNELS WITH NO A PRIORI SYNCHRONIZATION INFORMATION.
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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This work is concerned with determining how a lack of synchronization affects the minimum probability of error obtainable when information is transmitted over a noisy communication channel. The channel capacity for discrete memoryless nonsynchronized channels is shown to be the same as the capacity for synchronized channels. By introducing a new form of coding, which allows for a Markov dependency between successive code words, one is able to show that for certain channels the exponents for the nonsynchronized and synchronized channels are equivalent for all rates. For binary channels, bounds on the minimum probability of error are obtained for unconstrained binary codes, as well as for several classes of parity-check codes. These bounds are also used to obtain asymptotic distance properties for the various classes of unsynchronized binary codes. These distance properties are considerably stronger than just statements on the existence of comma-free codes. In particular, we show that for a certain range of rates there exist codes whose minimum distance, in the comma-free sense, is not only greater than one, but actually is proportional to the block length. Author