Design of Geometric Molecular Bonds

An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the affinity of the DNA base A for T, but not for C, G, or another A. Recent experimental breakthroughs in DNA nanotechnology demonstrate that a particular nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the ends of any pair of DNA double-helices) can be used to create specific "macrobonds" by careful geometric arrangement of many nonspecific blunt ends, motivating the need for sets of macrobonds that are orthogonal: two macrobonds not intended to bind should have relatively low binding strength, even when misaligned. To address this need, we introduce geometric orthogonal codes that abstractly model the engineered DNA macrobonds as two-dimensional binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung, Salehi, and Wei. The main technical difference is the importance of 2D geometry in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and Multi-Scale Communication

Bounds for DNA codes with constant GC-content

We derive theoretical upper and lower bounds on the maximum size of DNA codes of length n with constant GC-content w and minimum Hamming distance d, both with and without the additional constraint that the minimum Hamming distance between any codeword and the reverse-complement of any codeword be at least d. We also explicitly construct codes that are larger than the best previously-published codes for many choices of the parameters n, d and w.Comment: 13 pages, no figures; a few references added and typos correcte

Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading MIMO channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upperbound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January 2006 - First review: June 200