Minimum Coding Rate Research Articles

Эффективный выбор основания кода при первичном кодировании

Modern advances in microelectronics and the widespread use of computer technology for the purpose of software implementation of various telecommunication and information devices are a reliable justification for the representation of messages from various sources in digital form, that is, in the form of appropriate code combinations, which are essentially numbers in a certain number system. Considering the effective primary coding of messages from the source, they strive to achieve, first of all, the coding rate as close as possible to the entropy of the source, which was proved in the well-known theorems of Claude Shannon, which substantiated this position regarding the minimum value of the average length of the code combination. Since different messages from the source appear, as a rule, with different probabilities, it is possible to achieve the minimum coding rate using non-uniform coding methods, for example, according to the algorithm proposed by David Huffman. In an effort to achieve the minimum encoding rate, one should also take into account the complexity of the implementation of the primary encoding device, take into account the number of elements that will be required for its practical implementation, and so on. Based on this, the effectiveness of one or another method of primary coding is determined not by one, but by a number of factors that often contradict each other. One of these factors is the choice of the code base, which makes it possible to optimize the costs of the practical implementation of the primary coding method, which was the subject of consideration in this paper

Reliable OFDM Data Transmission with Pilot Tones and Error-Correction Coding in Shallow Underwater Acoustic Channel

The performance of Underwater Acoustic Communication (UAC) systems are strongly related to the specific propagation conditions of the underwater channel. Horizontal, shallow-water channels are characterised by extremely disadvantageous transmission properties, due to strong multipath propagation and refraction phenomena. The paper presents the results of communication tests performed during a shallow, inland-water experiment with the use of a laboratory model of a UAC system implementing the Orthogonal Frequency-Division Multiplexing (OFDM) technique. The physical layer of data transmission is partially configurable, enabling adaptation of the modulation and channel coding parameters to the specific propagation conditions. The communication tests were preceded by measurement of the UAC channel transmission properties. Based on the estimated transmission parameters, four configurations of OFDM modulation parameters were selected, and for each of them, communication tests were performed with the use of two Error-Correction Coding (ECC) techniques. In each case, the minimum coding rate was determined for which reliable data transmission with a Bit Error Rate (BER) of less than 10 − 4 is possible.

Source-Channel Secrecy for Shannon Cipher System

Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of $2^{mR_{L}}$ reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity lossy equivocation , which is proved to be the minimum optimistic one-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for infinitely many blocklengths ) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proved to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product, optimistic lossy source coding has also been addressed.

Entropy-based evaluation of context models for wavelet-transformed images.

Entropy is a measure of a message uncertainty. Among others aspects, it serves to determine the minimum coding rate that practical systems may attain. This paper defines an entropy-based measure to evaluate context models employed in wavelet-based image coding. The proposed measure is defined considering the mechanisms utilized by modern coding systems. It establishes the maximum performance achievable with each context model. This helps to determine the adequateness of the model under different coding conditions and serves to predict with high precision the coding rate achieved by practical systems. Experimental results evaluate four well-known context models using different types of images, coding rates, and transform strategies. They reveal that, under specific coding conditions, some widely-spread context models may not be as adequate as it is generally thought. The hints provided by this analysis may help to design simpler and more efficient wavelet-based image codecs.

Natural type selection in adaptive lossy compression

Consider approximate (lossy) matching of a source string /spl sim/P, with a random codebook generated from reproduction distribution Q, at a specified distortion d. Previous work determined the minimum coding rate R/sub 1/=R(P, Q, d) for this setting. We observe that for a large word length and with high probability, the matching codeword is typical with a distribution Q/sub 1/ which is different from Q. If a new random codebook is generated /spl sim/Q/sub 1/, then the source string will favor codewords which are typical with a new distribution Q/sub 2/, resulting in a minimum coding rate R/sub 2/=R(P, Q/sub 1/, d), and so on. We show that the sequences of distributions Q/sub 1/, Q/sub 2/,... and rates R/sub 1/, R/sub 2/,..., generated by this procedure, converge to an optimum reproduction distribution Q*, and the rate-distortion function R(P, d), respectively. We also derive a fixed rate-distortion slope version of this natural type selection process. In the latter case, an iteration of the process stochastically simulates an iteration of the Blahut-Arimoto (1972) algorithm for rate-distortion function computation (without recourse to prior knowledge of the underlying source distribution). To strengthen these limit statements, we also characterize the steady-state error of these procedures when iterating at a finite string length. Implications of the main results provide fresh insights into the workings of lossy variants of the Lempel-Ziv algorithm for adaptive compression.