Parsing a sequence of qubits

We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication such as a self-synchronizing quantum network where one can hop into the channel at any time, catch the next coming quantum information with a label indicating the sender, and reply by routing her quantum information with control qubits for quantum switches all without assuming prior frame synchronization between users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication in the IEEE Transactions on Information Theor

Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures

We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these sequences. We point out sufficient conditions under which the variable-length coding and its inverse preserve asymptotic mean stationarity. Moreover, conditions for preservation of shift-invariant $\sigma$-fields and the finite-energy property are discussed and the block entropies for stationary means of coded processes are related in some cases. Subsequently, we apply certain of these results to construct a stationary nonergodic process with a desired linguistic interpretation.Comment: 20 pages. A few typos corrected after the journal publicatio

Codes for protection from synchronization loss and additive errors

Codes for protection from synchronization loss and additive error

Comma-free Codes Over Finite Alphabets

Comma-free codes have been widely studied in the last sixty years, from points of view as diverse as biology, information theory and combinatorics. We develop new methods to study comma-free codes achieving the maximum size, given the cardinality of the alphabet and the length of the words. Specifically, we are interested in counting the number of such codes. We provide (two different proofs for) a closed-formula. The approach introduced is further developed to tackle well-known sub-families of comma-free codes, such as self-complementary and (generalisations of) non-overlapping codes. We also study codes that are not contained in strictly larger ones. For instance, we determine the maximal size of self-complementary comma-free codes and the number of codes reaching the bound. We provide a characterisation of-letter non-overlapping codes (over an alphabet of cardinality n), which allows us to devise the number of such codes that are not contained in any strictly larger one. Our approach mixes combinatorial and graph-theoretical arguments

Interactive specification of data displays

On-line graphical language for computer data displa

Condons and Codes

In this paper we assemble a few ingredients that are remotely connected to each other, but governed by the rule of coding theory ([1], [12]) and formal language theory, i.e. cyclic codes and DNA codes. Our interest arose from the remark that there exist both linear and circular DNAs in higher living organisms. We state the theory of codes in a wide sense due to [1] in order to understand the circular DNAs while we state rudiments of formal language theory as a means to interpret genes. We hope this will be a starter for unifying two approaches depending on the theory of codes and that of formal language