Vladimir B. Balakirsky

Joint source-channel coding with variable length codes

We consider an information transmission scheme where a stream of messages is encoded using a variable length code, and the code sequence, obtained as a concatenation of codewords, is transmitted over a noisy discrete memoryless channel. The decoder constructs a stream of estimates of the messages. Note that the problems that concern the use of variable length codes for transmission over noisy channels also appear if the code is used only for source encoding since any channel coding scheme cannot reduce the level of noise up to zero. We propose a convolutional-type decoding algorithm assuming that: (1) the total length of the transmitted code sequence is known to the decoder and (2) decoding delay is allowed and the decoder constructs a maximum likelihood estimate of the whole stream of messages.

A converse coding theorem for mismatched decoding at the output of binary-input memoryless channels

An upper bound on the maximal transmission rate over binary-input memoryless channels, provided that the decoding decision rule is given, is derived. If the decision rule is equivalent to the maximum-likelihood decoding (matched decoding), then the bound coincides with the channel capacity. Otherwise (mismatched decoding), it coincides with a known lower bound.

Construction of uniquely decodable codes for the two-user binary adder channel

A construction of uniquely decodable codes for the two-user binary adder channel is presented. The rates of the codes obtained by this construction are greater than the rates guaranteed by the Coebergh van den Braak and van Tilborg construction and these codes can be used with simple encoding and decoding procedures.

Potential performance of PLC systems composed of several communication links

We consider data transmission over a bus system composed of several communication links. All users of the system simultaneously receive transmitted signals with different reliabilities depending on their distance from the sender. Two possible ways of organizing communication are analyzed. The first algorithm includes transmission in a few steps, where each step is devoted to a reliable delivery of the message from one intermediate user to another one. All other users exclude themselves from the system for this step. The second algorithm assumes that all users of the system are active all the time, and they receive side information from communication of intermediate users, which allows them to reduce uncertainty about the original message. Lower bounds on the time needed to deliver a message over the system that follow from the capacity arguments for both methods are given. These bounds are illustrated by numerical examples.

Privacy Amplification Theorem for Noisy Main Channel

Secret key agreement protocol between legal parties based on reconciliation and privacy amplification procedure has been considered in [2]. The so called privacy amplification theorem is used to estimate the amount of Shannons information leaking to an illegal party (passive eavesdropper) about the final key. We consider a particular case where one of the legal parties (Alice) sends to another legal party (Bob) a random binary string x through a binary symmetric channel (BSC) with bit error probability ?m while an eavesdropper (Eve) receives this string through an independent BSC with bit error probability ?w. We assume that ?m < ?w and hence the main channel is superior to the wire-tap channel. To reconcile the strings between legal parties Alice sends to Bob through noiseless channel the check string y based on some good error correcting code. Since this transmission is completely public Eve can eavesdrop it and therefore this extra information has to be taken into account in an estimation of the information leaking to Eve about the final key. In [3] an inequality has been proved to upper bound the information of Eve in such scenario. The main contribution of the running paper is to improve this inequality and hence to enhance the privacy amplification theorem. We present also bounds for the probability of false reconciliation when the check symbols of the linear code are transmitted through noiseless channel. The presented results can be very useful when considering the non-asymptotic case.

Joint Source-Channel Coding Using Variable-Length Codes

We address the problem of joint source-channel coding when variable-length codes are used for information transmission over a discrete memoryless channel. Data transmitted over the channel are interpreted as pairs (mk,tk), where mk is a message generated by the source and tk is a time instant when the transmission of the kth codeword begins. The decoder constructs an estimate of the transmitted sequence of pairs, and the kth decoding error is introduced as the event that the pair (mk,tk) does not belong to this sequence. We describe the maximum likelihood decoding algorithm and prove a lower bound on the exponent of the decoding error probability. For a subclass of discrete memoryless sources and discrete memoryless channels, this bound is asymptotically tight.

On the performance of permutation codes for multi-user communication

Considers a system of information transmission for T pairs of users (sender, receiver) numbered 1,..., T, which can be viewed as an extension of the T-user M-frequency noiseless multiple access channel model Each of the T senders uses the same input alphabet of M integers and the idle symbol. The output of the channel at each time instant is a symbol identifying which subset of integers occurred as input to the channel.

Mathematical model for constructing passwords from biometrical data

Summary We propose a probabilistic model for constructing passwords on the basis of outcomes of biometrical measurements. An algorithm for the transformation of biometrical data to passwords is given. Performance of the authentication scheme is evaluated by the compression factor, the false acceptance/rejection rates, the probability distribution over the set of passwords, and the probability of a correct guess of the input biometrical data mapped to the known password. An application of the results to the DNA measurements is presented. Copyright

On the Performance of Permutation Codes for Multi-User Communication

Permutation coding for multi-user communication schemes that originate from the Fast Frequency Hopping/Multiple Frequency Shift Keying modulation is investigated. Each sender is either passive or sends some signal formed as the concatenation of M elementary signals having M different specified frequencies. There is also a jammer, who can introduce disturbances. A single disturbance is either sending the signal that contains all M frequencies at a certain time instant or sending some elementary signal at all time instants. Each receiver receives a vector of M sets, where a set at each time instant contains a fixed frequency if and only if the corresponding elementary signal was sent by either some sender or the jammer. The task of the receiver is to uniquely decode the message of his sender. We present regular constructions of permutation codes for this scheme given the following parameters: the number of frequencies, number of pairs (sender, receiver), number of messages per sender, and maximum number of disturbances of the jammer.

Hashing of databases based on indirect observations of Hamming distances

We describe hashing of databases as a problem of information and coding theory. It is shown that the triangle inequality for the Hamming distances between binary vectors may essentially decrease the computational efforts of a search for a pattern in a database. Introduction of the Lee distance in the space, which consists of the Hamming distances, leads to a new metric space where the triangle inequality can be effectively used.