Minimum Code Length Research Articles

Polar Code Parameter Recognition Algorithm Based on Dual Space

To improve the performance of polar code parameter recognition in the fields of intelligent communication, communication detection, and network countermeasures, we propose a new recognition scheme for the additive white Gaussian noise (AWGN) channel. The scheme turns parameter recognition problems into hypothetical tests and is effective due to the check relationship between the received codeword and the dual space determined by the correct parameters. First, a sub-matrix is obtained by removing the frozen-bit-index rows of the polar code generator matrix, and then its dual matrix is calculated. To check the relationship of the dual matrix and codewords, the average likelihood ratio of codewords is introduced as a test statistic, and then the corresponding decision threshold is deduced. Next, the degree of conformity of polar code recognition is defined, and the minimum code length and code rate corresponding to the highest degree of conformity are chosen to calculate the index of information-bit positions by a Gaussian approximation (GA) construction algorithm. Finally, the chosen code length, code rate, and corresponding index are provided as the recognition results. Simulation results show that the algorithm can achieve effective parameter recognition in both high-signal-to-noise (SNR) and low-SNR environments, and that the algorithm’s recognition performance increases with decreasing code rate and code length. The parameter recognition rate with a code length of 128 and code rate of 1/5 is close to 100% when the SNR is 4 dB, and the algorithm complexity increases almost linearly with the decreasing code rate and the increasing length of the intercepted data.

Sparse Signal Recovery in MIMO Specular Meteor Radars With Waveform Diversity

Since the 1950s, specular meteor radars (SMRs) have been used to study the mesosphere and lower thermosphere (MLT) dynamics. Atmospheric parameters derived from SMRs are highly dependent on the number of detected meteors and the accuracy of the meteors' locations. Recently, incoherent and coherent multiple-input-multiple-output (MIMO) radar approaches combined with waveform diversity have been proposed to increase the number of detected meteors and to improve time, altitude, and horizontal resolution of the estimated wind fields. The incoherent MIMO approach refers to the addition of new transmit sites (widely separated), whereas the coherent MIMO refers to the addition of new transmit antennas in the same site (closely separated). In both the cases, a different pseudorandom sequence is transmitted from each antenna element. Unfortunately, the addition of new transmit antennas with different code sequences degrades the performance of conventional signal recovery algorithms. This is a consequence of the cross-interference between the transmitted waveforms, making it worse as the number of transmitters increases. In this article, we propose a signal recovery approach based on compressed sensing, taking advantage of the sparse nature of specular meteor echoes. The approach allows the exact recovery of weak echoes even in interference environments. Besides the advantage of the proposed approach to recover the meteor signal, we discuss the optimal selection of the transmitted waveforms and the minimum code length required for exact recovery. Additionally, we propose a modification of the orthogonal matching pursuit algorithm used in sparse problems to make it applicable in real-time analysis of large data. The success of the proposed approach is corroborated using Monte Carlo simulations and real data from a multi-static spread spectrum meteor radar network installed in northern Germany.

Explicit and Efficient WOM Codes of Finite Length

Write-once memory (WOM) is a storage device consisting of binary cells that can only increase their levels. A $t$ -write WOM code is a coding scheme that makes it possible to write $t$ times to a WOM without decreasing the levels of any of the cells. The sum-rate of a WOM code is the ratio between the total number of bits written to the memory during the $t$ writes and the number of cells. It is known that the maximum possible sum-rate of a $t$ -write WOM code is $\log (t+1)$ . This is also an achievable upper bound, both by information-theoretic arguments and through explicit constructions. While existing constructions of WOM codes are targeted at the sum-rate, we consider here two more figures of merit. The first one is the complexity of the encoding and decoding maps. The second figure of merit is the convergence rate , defined as the minimum code length $n(\delta)$ required to reach a point that is $\delta $ -close to the capacity region. One of our main results in this paper is a capacity-achieving construction of two-write WOM codes which has polynomial encoding/decoding complexity while the block length $n(\delta)$ required to be $\delta $ -close to capacity is significantly smaller than existing constructions. Using these two-write WOM codes, we then obtain three-write WOM codes that approach a sum-rate of 1.809 at relatively short block lengths. We also provide several explicit constructions of finite length three-write WOM codes; in particular, we achieve a sum-rate of 1.716 by using only 93 cells. Finally, we modify our two-write WOM codes to construct $\epsilon $ -error WOM codes of high rates and small probability of failure.

On the Capacity of Locally Decodable Codes

A locally decodable code (LDC) maps $K$ source symbols, each of size $L_{w}$ bits, to $M$ coded symbols, each of size $L_{x}$ bits, such that each source symbol can be decoded from $N \leq M$ coded symbols. A perfectly smooth LDC further requires that each coded symbol is uniformly accessed when we decode any one of the messages. The ratio $L_{w}/L_{x}$ is called the symbol rate of an LDC. The highest possible symbol rate for a class of LDCs is called the capacity of that class. It is shown that given $K, N$ , the maximum value of capacity of perfectly smooth LDCs, maximized over all code lengths $M$ , is $C^{*}=N\left ({1+1/N+1/N^{2}+\cdots +1/N^{K-1}}\right)^{-1}$ . Furthermore, given $K, N$ , the minimum code length $M$ for which the capacity of a perfectly smooth LDC is $C^{*}$ is shown to be $M = N^{K}$ . Both of these results generalize to a broader class of LDCs, called universal LDCs. The results are then translated into the context of PIRmax, i.e., Private Information Retrieval subject to maximum (rather than average) download cost metric. It is shown that the minimum upload cost of capacity achieving PIRmax schemes is $(K-1)\log N$ . The results also generalize to a variation of the PIR problem, known as Repudiative Information Retrieval (RIR).

Fingerprinting Codes Under the Weak Marking Assumption

Fingerprinting codes based on the marking assumption provide reliable security against collusion attacks, but lack resilience against channel errors such as symbol erasures or other forms of distortions introduced by transmission over noisy or insecure communication channels. This additional source of distortion errors can be addressed by relaxing the marking assumption. In this paper we examine the restrictions and limitations on the code construction in terms of accusation errors, alphabet size, and the distortion errors under this weaker form of the marking assumption as formulated by Guth and Pfitzmann, also deriving a theoretical minimum lower bound on the code length of $q$ -ary fingerprinting codes. We provide the formulas for applying the already existing binary Tardos code with symmetric accusation function under the weaker form of the marking assumption along with numerical results proving the tightness of the derived bounds. We show that the code is still of asymptotically minimum code length under the relaxation of the marking assumption.

Research on channel-related polar code with an optimum code length for wireless ultraviolet communications

In this paper a polar coding scheme for ultraviolet communication (UVC) systems is proposed and experimentally implemented to address the high path loss propagation, which severely deteriorates the communication performance. Firstly, we analyze the property of the path loss in the optical domain by applying the particle-wave duality to the existing path loss model. Considering the characteristic of the UV channel, we design a polar code with specific channel correlations, and study the computational complexity in terms of the code length. A new theoretical Bhattacharyya upper-bound for the general polar codes is introduced and applied to the UV channel in order to derive a minimum code length without impairing a required bit error rate performance. Numerical simulations and off-line experimental investigations validate the proposed polar coding scheme, which can effectively combat path loss induced performance deterioration with a relatively low computational complexity.

Visible light for communication, indoor positioning, and dimmable illumination: A system design based on overlapping pulse position modulation

In this paper, we design a dimming compatible visible light communication (VLC) system with asynchronous and optimum indoor positioning method in a standard office room in combination with asynchronous and optimum indoor positioning method according to illumination standards under channel constraints. We use overlapping pulse position modulation (OPPM) to support dimming control by changing the code weights. The system parameters such as a valid interval for dimming together with an upper bound for bit rate according to the channel delay spread are investigated. Moreover, considering the dispersive VLC channel and using Monte Carlo (MC) simulations, a method is proposed to determine the minimum code length in different dimming levels in order to achieve a valid bit error rate (BER). Then, the trellis coded modulation (TCM) is suggested to be applied to OPPM in order to take advantage of consequent coding gain which could be up to 3 dB. Finally, in order to enable asynchronously and with high throughput data transmission of LEDs for the purpose of indoor positioning, we propose using one-persistent carrier sense multiple access (CSMA) network protocol. Using received signal strength (RSS) based trilateration, the two dimensional positioning error of around 10cm is verified by the simulation results.

Index Coding With Coded Side-Information

This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as index coding with coded side-information. Our aim is to characterize the minimum index code length that the sender needs to transmit to simultaneously satisfy all user requests. We show that the optimal binary vector index code length is equal to the minimum rank (minrank) of a matrix whose elements consist of the sets of desired packet indices and side- information encoding matrices. This is the natural extension of matrix minrank in the presence of coded side information. Using the derived expression, we propose a greedy randomized algorithm to minimize the rank of the derived matrix.

Bacteria Genome Compression Based on the Weighted Context Model

The genome compression algorithm based on the weighted context model is present in this paper. In this algorithm, the method to construct the weighted context model is discussed. The adaptive code length of the context models are used to determine the values of the corresponding weights of models. In the coding process, the values of these weights are modified in order to achieve the minimum code length and to enhance the compression efficiency. At last, the proposed algorithm is used to the bacteria genome compression. The experiments results indicate that the algorithm present could produce better compression result than the results by other algorithms.

Shorten LDPC Codes with Better Performance

In this paper, the bipartite graphical structure of LDPC codes is studied, some methodology for designing shorten LDPC Codes are presented. The performance evaluation of shorten LDPC codes presented provides easy and effective strategy in selecting appropriate shorten scheme, avoiding the complex encoding and iterative decoding steps. The shorten LDPC codes whose minimum code weight greater and length 4-cycle free have better performance.

Shorten LDPC Codes with Better Performance

In this paper, the bipartite graphical structure of LDPC codes is studied, some methodology for designing shorten LDPC Codes are presented. The performance evaluation of shorten LDPC codes presented provides easy and effective strategy in selecting appropriate shorten scheme, avoiding the complex encoding and iterative decoding steps. The shorten LDPC codes whose minimum code weight greater and length 4-cycle free have better performance.

A fast algorithm for Huffman decoding based on a recursion Huffman tree

This paper focuses on the time efficiency of Huffman decoding. In this paper, we utilize numerical interpretation to speed up the decoding process. The proposed algorithm firstly transforms the given Huffman tree into a recursion Huffman tree. Then, with the help of the recursion Huffman tree, the algorithm has the possibility to decode more than one symbol at a time if the minimum code length is less than or equal to half of the width of the processing unit. When the minimum code length is larger than the half of the width of the processing unit, the proposed method can still increase the average symbols decoded in one table access (thus speeding up the decoding time). In fact, the experimental results of the test files show that the average number of decoded symbols at one time for the proposed method ranges from 1.91 to 2.13 when the processing unit is 10. The experimental comparisons show that, compared to the conventional binary tree search method and the level-compressed Huffman decoding method, the decoding time of the proposed method is a great improvement.

An Analysis of Slepian-Wolf Coding Problem Based on the Asymptotic Normality

Source coding theorem reveals the minimum achievable code length under the condition that the error probability is smaller than or equal to some small constant. In the single user communication system, the source coding theorem was proved for general sources. The class of general source is quite large and it is important result since the result can be applied for a wide class of sources. On the other hand there are several studies to evaluate the achievable code length more precisely for the restricted class of sources by using the restriction. In the multi-user communication system, although the source coding theorem was proved for general correlated sources, there is no study to evaluate the achievable code length more precisely. In this study, we consider the stationary memoryless correlated sources and show the coding theorem for Slepian-Wolf type problem more precisely than the previous result.

A coded beamforming scheme for frequency-flat MIMO fading channels

In this paper, a coded beamforming scheme is considered for frequency-flat multiple-input-multiple-output (MIMO) fading channels. With channel state information (CSI) available at the transmitter, this scheme combines coded modulation (CM) with downlink transmission beamforming to exploit both diversity and coding advantages. In order to identify the appropriate code design criteria, the exact pairwise error probability and bit error rate upper bounds are derived for both frequency-flat slow and fast MIMO Rayleigh fading channels. It is shown that the minimum squared Euclidean distance of the code should be maximised in slow-fading channels, whereas the minimum effective code length and the product distances should be maximised in fast-fading scenarios. This conclusion indicates that the conventional Ungerboeck's trellis-coded modulation codes originally designed for additive white Gaussian noise channels and single-antenna Rayleigh fading channels could be directly utilised in the proposed scheme for slow and fast MIMO fading channels, respectively. This eliminates the need for complicated code design. Simulation results are provided to substantiate the theoretical analysis. For an example, it is demonstrated that a trellis-coded beamforming scheme can outperform the published space-time trellis coded beamforming schemes by up to 4 dB, although it has a simpler encoder structure and requires no specific code design. Interference free is assumed in the analysis, while the impact of the imperfect CSI and antenna correlation on the system error performance is evaluated.

Modeling by MDL criterion for adaptive data compression

AbstractThis paper proposes a high‐performance noiseless data compression model which can compress strings generated by a binary Markov information source without prior knowledge of the source. The adaptive expression of the existing universal codes is described by a model with separated sampler and encoder, and the learning structure of each code and the encoding process are described. Through such a discussion, the intuitive reasons are clarified as to why the codes, despite their asymptotic optimality, do not compress well at the start, pointing out room for improvement. Then, the MDL criterion is introduced into each encoder, to improve the performance, while keeping the sampler fixed. The MDL criterion is an estimation for the minimum code length, including the representation cost of the parameters. Based on this criterion, the Markov order which is to be assumed for each symbol is adaptively determined. Since the same determination can be made at the time of decoding, the unique decodability is guaranteed. In the second half of this paper, more detailed techniques are discussed, and a remarkable improvement is demonstrated by a computer simulation. It is also shown that the sampler of the proposed universal code is of a high‐performance, realizing two kinds of encoders.