Search

We propose a new coding scheme using only one lattice that, under lattice decoding, achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel, when the signal-to-noise ratio SNR > 3. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which additionally involves a quantization-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error (MMSE) lattice decoding is almost the same as that of Poltyrev's coding over an infinite lattice, for any rate up to the AWGN channel capacity.

This paper considers cyclic DNA codes of arbitrary length over the ring R = F2[u]/(u4 - 1). A mapping is given between the elements of R and the alphabet {A, C, G, T} which allows the additive stem distance to be extended to this ring. Then, cyclic codes over R are designed such that their images under the mapping are also cyclic or quasi-cyclic of index 2 with designed hybridization energy. The hybridization energy and additive distance are shown to be functions of the neighborhood energy.

The minimum energy, and, more generally, the minimum cost, to transmit one bit of information has been recently derived for bursty communication when information is available infrequently at random times at the transmitter. This result assumes that the receiver is always in the listening mode and samples all channel outputs until it makes a decision. If the receiver is constrained to sample only a fraction f>0 of the channel outputs, what is the cost penalty due to sparse output sampling? Remarkably, there is no penalty: regardless of f>0 the asynchronous capacity per unit cost is the same as under full sampling, ie, when f=1. There is not even a penalty in terms of decoding delay---the elapsed time between when information is available until when it is decoded. This latter result relies on the possibility to sample adaptively; the next sample can be chosen as a function of past samples. Under non-adaptive sampling, it is possible to achieve the full sampling asynchronous capacity per unit cost, but the decoding delay gets multiplied by 1/f. Therefore adaptive sampling strategies are of particular interest in the very sparse sampling regime., Submitted to the IEEE Transactions on Information Theory