14 research outputs found
Optimal Sequential Frame Synchronization
We consider the `one-shot frame synchronization problem' where a decoder
wants to locate a sync pattern at the output of a channel on the basis of
sequential observations. We assume that the sync pattern of length N starts
being emitted at a random time within some interval of size A, that
characterizes the asynchronism level between the transmitter and the receiver.
We show that a sequential decoder can optimally locate the sync pattern, i.e.,
exactly, without delay, and with probability approaching one as N tends to
infinity, if and only if the asynchronism level grows as O(exp(N*k)), with k
below the `synchronization threshold,' a constant that admits a simple
expression depending on the channel. This constant is the same as the one that
characterizes the limit for reliable asynchronous communication, as was
recently reported by the authors. If k exceeds the synchronization threshold,
any decoder, sequential or non-sequential, locates the sync pattern with an
error that tends to one as N tends to infinity. Hence, a sequential decoder can
locate a sync pattern as well as the (non-sequential) maximum likelihood
decoder that operates on the basis of output sequences of maximum length A+N-1,
but with much fewer observations.Comment: 6 page
The Strongly Asynchronous Massive Access Channel
This paper considers a Strongly Asynchronous and Slotted Massive Access
Channel (SAS-MAC) where different users transmit a randomly
selected message among ones within a strong asynchronous window
of length blocks, where each block lasts channel uses. A
global probability of error is enforced, ensuring that all the users'
identities and messages are correctly identified and decoded. Achievability
bounds are derived for the case that different users have similar channels, the
case that users' channels can be chosen from a set which has polynomially many
elements in the blocklength , and the case with no restriction on the users'
channels. A general converse bound on the capacity region and a converse bound
on the maximum growth rate of the number of users are derived.Comment: under submissio
Asynchronous Communication: Exact Synchronization, Universality, and Dispersion
Recently, Tchamkerten and coworkers proposed a novel variation of the problem of joint synchronization and error correction. This paper considers a strengthened formulation that requires the decoder to estimate both the message and the location of the codeword exactly. Such a scheme allows for transmitting data bits in the synchronization phase of the communication, thereby improving bandwidth and energy efficiencies. It is shown that the capacity region remains unchanged under the exact synchronization requirement. Furthermore, asynchronous capacity can be achieved by universal (channel independent) codes. Comparisons with earlier results on another (delay compensated) definition of rate are made. The finite blocklength regime is investigated and it is demonstrated that even for moderate blocklengths, it is possible to construct capacity-achieving codes that tolerate exponential level of asynchronism and experience only a rather small loss in rate compared to the perfectly synchronized setting; in particular, the channel dispersion does not suffer any degradation due to asynchronism. For the binary symmetric channel, a translation (coset) of a good linear code is shown to achieve the capacity-synchronization tradeoff.National Science Foundation (U.S.) (Center for Science of Information Grant CCF-0939370
Asynchronous Communication: Capacity Bounds and Suboptimality of Training
Several aspects of the problem of asynchronous point-to-point communication
without feedback are developed when the source is highly intermittent. In the
system model of interest, the codeword is transmitted at a random time within a
prescribed window whose length corresponds to the level of asynchronism between
the transmitter and the receiver. The decoder operates sequentially and
communication rate is defined as the ratio between the message size and the
elapsed time between when transmission commences and when the decoder makes a
decision.
For such systems, general upper and lower bounds on capacity as a function of
the level of asynchronism are established, and are shown to coincide in some
nontrivial cases. From these bounds, several properties of this asynchronous
capacity are derived. In addition, the performance of training-based schemes is
investigated. It is shown that such schemes, which implement synchronization
and information transmission on separate degrees of freedom in the encoding,
cannot achieve the asynchronous capacity in general, and that the penalty is
particularly significant in the high-rate regime.Comment: 27 pages, 8 figures, submitted to the IEEE Transactions on
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