Communication networks are often designed and analyzed assuming tight synchronization among nodes. However, in applications that require communication in the energy-efficient regime of low signal-to-noise ratios, establishing tight synchronization among nodes in the network can result in a significant energy overhead. Motivated by a recent result showing that near-optimal energy efficiency can be achieved over the AWGN channel without requiring tight synchronization, we consider the question of whether the potential gains of cooperative communication can be achieved in the absence of synchronization. We focus on the symmetric Gaussian diamond network and establish that cooperative-communication gains are indeed feasible even with unsynchronized nodes. More precisely, we show that the capacity per unit energy of the unsynchronized symmetric Gaussian diamond network is within a constant factor of the capacity per unit energy of the corresponding synchronized network. To this end, we propose a distributed relaying scheme that does not require tight synchronization but nevertheless achieves most of the energy gains of coherent combining.
The notion of capacity per unit energy was analyzed for the synchronized AWGN channel in @cite_3 . It is shown there that pulse-position modulation achieves the capacity per unit energy of this channel. Single-letter characterizations for the capacity per unit cost for general cost functions and general synchronized discrete memoryless channels were found in @cite_10 . However, these results depend on the channel being memoryless, whereas the channel considered here has memory due to the presence of insertions and deletions. Hence, these results cannot be directly applied here. The pulse-position modulation scheme was generalized for unsynchronized channels in @cite_5 , where it was shown to achieve the capacity per unit energy of the unsynchronized AWGN channel. We point out that, pulse-position modulation itself cannot be extended to the unsynchronized diamond network considered in this paper. Indeed, unless the relays decode the message sent by the transmitter, they end up spending a significant amount of energy forwarding noise. However, requiring the relays to decode the message can also be suboptimal---for instance, when the source-relay channel is weak.
@cite_5 @cite_10 @cite_3
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Communication systems are traditionally designed to have tight transmitter-receiver synchronization. This requirement has negligible overhead in the high-SNR regime. However, in many applications, such as wireless sensor networks, communication needs to happen primarily in the energy-efficient regime of low SNR, where requiring tight synchronization can be highly suboptimal. In this paper, we model the noisy channel with synchronization errors as an insertion deletion substitution channel. For this channel, we propose a new communication scheme that requires only loose transmitter-receiver synchronization. We show that the proposed scheme is asymptotically optimal for the Gaussian channel with synchronization errors in terms of energy efficiency as measured by the rate per unit energy. In the process, we also establish that the lack of synchronization causes negligible loss in energy efficiency. We further show that, for a general discrete memoryless channel with synchronization errors and a general cost function (with a zero-cost symbol) on the input, the rate per unit cost achieved by the proposed scheme is within a factor two of the information-theoretic optimum. Memoryless communication channels with arbitrary alphabets where each input symbol is assigned a cost are considered. The maximum number of bits that can be transmitted reliably through the channel per unit cost is studied. It is shown that, if the input alphabet contains a zero-cost symbol, then the capacity per unit cost admits a simple expression as the maximum normalized divergence between two conditional output distributions. The direct part of this coding theorem admits a constructive proof via Stein's lemma on the asymptotic error probability of binary hypothesis tests. Single-user, multiple-access, and interference channels are studied. >