Weight Codes Research Articles

Joint Error-Dimming Control Using Constant Weight Coding in Visible Light Communication Systems

To enhance commercial implementation, visible light communication (VLC) should facilitate dimming control and reliable data transmission simultaneously, where users can adjust the brightness levels arbitrarily. Constant weight code (CWC) based dimming method can achieve higher spectral efficiency, but the codewords need further selection to exponentially map the massage. In this paper, based on CWC, we proposed a method to achieve dimming control as well as improve error performance via optimizing the average Hamming distance of the codeword set. Simulation results show that the optimal codeword set can achieve better error performance.

The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s

Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples.

Two-dimensional multi-service code for spectral/spatial optical CDMA system

A new two-dimensional(spectral/spatial) optical code division multiple access is developed by using one-dimensional Multi-Service code. The spectral/spatial proposed system can suppress the multiple access interference (MAI) by using the MAI cancellation property. The numerical analysis shows that two-dimensional multi-service code has a better performance compared to one-dimensional multi-service, two-dimensional perfect difference (2D-PD), two-dimensional Hybrid «flexible cross correlation/modified double weight» (2D-FCC/MDW)and two-dimensional extended enhanced double weight (2D-extended-EDW) codes; It accommodates 1.5, 2.5 and 3.3 times the maximum number of simultaneous users allocated by 2D-PD, 2D-FCC/MDW and 2D-Extended-EDW codes, respectively. By keeping the similar code length and increasing the spatial code length, the capacity and the available data rate are enhanced; also, the effective transmitted power and spectral width are decreased. The transit from 1D to 2D enhances around three times the system capacity.

New Classes of p-Ary Few Weight Codes

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $$R=\mathbb {F}_p+u\mathbb {F}_p+\cdots +u^{k-1}\mathbb {F}_{p},$$ with $$u^k=0,$$ are constructed that generalize the construction of Shi et al. (IEEE Commun. Lett. 20(12):2346–2349, 2016), which is the special case of $$p=k=2.$$ These codes are defined as trace codes. In some cases of their defining sets, they are abelian. Their homogeneous weight distributions are computed by using exponential sums. In particular, in the two-weight case, we give some conditions of optimality of their Gray images by using the Griesmer bound. Their dual homogeneous distance is also given. The codewords of these codes are shown to be minimal for inclusion of supports, a fact favorable to an application to secret sharing schemes.

Essential idempotents and codes of constant weight

In this note, we prove that a binary linear code of constant weight is equivalent to a cyclic code which is either generated by an essential idempotent or a repetition code of a code of this kind.

Compact Constant Weight Coding Engines for the Code-Based Cryptography

We present here a more memory efficient method for encoding binary information into words of prescribed length and weight. Existing solutions either require complicated float point arithmetic or additional memory overhead, making it a challenge for resource constrained computing environment. The solution we propose here solves these problems yet obtains better coding efficiency by a memory efficient approximation of the critical intermediate value in constant weight coding. For the time being, the design presented in this brief is the most compact one for any code-based encryption schemes.

Spectral/spatial optical CDMA code based on Diagonal Eigenvalue Unity

Abstract A new two dimensional Diagonal Eigenvalue Unity (2D-DEU) code is developed for the spectral⧹spatial optical code division multiple access (OCDMA) system. It has a lower cross correlation value compared to two dimensional diluted perfect difference (2D-DPD), two dimensional Extended Enhanced Double Weight (2D-Extended-EDW) codes. Also, for the same code length, the number of users can be generated by the 2D-DEU code is higher than that provided by the others codes. The Bit Error Rate ( BER ) numerical analysis is developed by considering the effects of shot noise, phase induced intensity noise (PIIN), and thermal noise. The main result shows that BER is strongly affected by PIIN for the higher source power. The 2D-DEU code performance is compared with 2D-DPD, 2D-Extended-EDW and two dimensional multi-diagonals (2D-MD) codes. This comparison proves that the proposed 2D-DEU system outperforms the related codes.

Optimal cyclic quaternary constant‐weight codes of weight three

AbstractA cyclic code is a cyclic q‐ary code of length n, constant weight w and minimum distance d. Let denote the largest possible size of a cyclic code. The pure and mixed difference method plays an important role in the determination of upper bound on . By analyzing the distribution of odd mixed and pure differences, an improved upper bound on is obtained for . A new construction based on special sequences is provided and the exact value of is almost completely determined for all d and n except when and . Our constructions reveal intimate connections between cyclic constant weight codes and special sequences, particularly Skolem‐type sequences.

A generic method to construct zero-difference balanced functions

Zero-difference balanced (ZDB) function plays an important role in communication field. In this paper, we propose a generic method to construct ZDB functions on generic algebraic rings. Using this method, we construct many new ZDB functions and retrieve some existing ZDB functions in a much simpler way. Moreover, new applications of the constructed ZDB functions, such as constructing optimal constant weight codes and optimal frequency-hopping sequences, are presented.

Constructions of cyclic quaternary constant-weight codes of weight three and distance four

A cyclic $$(n,d,w)_q$$ code is a cyclic q-ary code of length n, constant-weight w and minimum distance d. A cyclic $$(n,d,w)_q$$ code with the largest possible number of codewords is said to be optimal. Optimal nonbinary cyclic $$(n,d,w)_q$$ codes were first studied in our recent paper (Lan et al. in IEEE Trans Inf Theory 62(11):6328–6341, 2016). In this paper, we continue to discuss the constructions of optimal cyclic $$(n,4,3)_q$$ codes. We establish the connection between cyclic $$(n,4,3)_{q}$$ codes and $$q-1$$ mutually orbit-disjoint cyclic (n, 3, 1) difference packings (briefly (n, 3, 1)-CDPs). For the case of $$q=4$$ , we construct three mutually orbit-disjoint (n, 3, 1)-CDPs by constructing a pair of strongly orbit-disjoint (n, 3, 1)-CDPs, which are obtained from Skolem-type sequences. As a consequence, we completely determine the number of codewords of an optimal cyclic $$(n,4,3)_{4}$$ code.

A Spectral-Efficient Transmission Scheme for Dimmable Visible Light Communication Systems

Dimming control is of vital importance for visible light communication (VLC) systems. Conventional dimmable transmission schemes based on compensation are spectrally inefficient. In this paper, we propose the use of two techniques, i.e., time-sharing and superposition, to construct spectral-efficient dimmable transmission schemes. For VLC systems with on–off keying (OOK) signaling, we present a general framework to construct dimmable transmission scheme by time-sharing among different dimming control codes. Arbitrary dimming target is achieved by adjusting the proportion of each dimming control code. We, then, give a practical construction of dimming control codes with semi-constant weight codes. We obtain optimal proportions of the semi-constant weight codes, which maximize the asymptotic spectral efficiency using linear programming. We also compute achievable rates of the proposed scheme under different dimming targets and different signal-intensity-to-noise-amplitude ratios. To achieve higher spectral efficiency ( $>$ 1.0 (b/s)/Hz), we present a dimmable multilevel transmission scheme based on superposition. In the proposed scheme, the first $\ell$ $-1$ levels adopt traditional OOK modulation, whereas the $\ell$ th level adopts the dimmable transmission scheme for OOK modulation. The transmitted signal is formed by superimposing modulated signals of the $\ell$ levels. Analysis shows that the proposed scheme achieves a higher spectral efficiency than the state-of-the-art schemes. Hence, it provides an attractive candidate for dimmable VLC systems with demanding spectral efficiency.

New explicit binary constant weight codes from Reed–Solomon codes

Binary constant weight codes have important applications in various topics and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose an improvement of the Ericson–Zinoviev construction of binary constant weight codes from q-ary codes. By applying this improvement to Reed–Solomon codes, some new or optimal binary constant weight codes are presented. In particular new binary constant weight codes A(64,10,8)≥4112 and A(64,12,8)≥522 are constructed. We also give explicitly constructed binary constant weight codes which improve the Gilbert and the Graham–Sloane lower bounds asymptotically in a small range of parameters. Some new binary constant weight codes constructed from algebraic-geometric codes by applying our this improvement are also presented.

Classification of optimal conflict-avoiding codes of weights 6 and 7

A conflict-avoiding code is used to guarantee that each transmitting user can send at least one packet successfully within a fixed period of time, provided that at most k out of M potential users are active simultaneously in a multiple-access collision channel. The number of codewords in a conflict-avoiding code determines the number M of potential users that can be supported in a system. That is why codes of the maximum cardinality for given parameters (optimal codes) are of interest. In this paper we determine the values of the maximum cardinality and classify up to multiplier equivalence optimal conflict-avoiding codes for 6 and 7 active users and given small lengths.

High Performance with Avalanche Photodiode in Wavelength/Time Optical Code Division Multiple Access

In order to increase the number of users as increasing the data rate and transmission distance, then to reduce the impact of multi-access interference (MAI) and the effect of phase-induced intensity noise (PIIN). This study proposed the utilizing of an avalanche photodiode (APD) on two-dimension optical code division multiple access (2-D OCDMA). APD detector is more sensitive than positive-intrinsic-negative (PIN) photodiode, due to its inherent gain that increases the signal to noise ratio (SNR) of the system by amplifying the received signal prior to proceeding to next stage. In this research, an improvement of realizable system capacity APD performance of different gain applied for Wavelength/Time modified double weight (MDW) code for cardinality, bit error rates (BER) and noise interference are analyzed. MATLAB is utilized as a software for theoretical results to study the APD gain effect upon the probability density function (PDF) and SNR performance. The results in very good approval indicate that 95.45% cardinality improvements compare to 2-D MDW code with PIN at 1.25 Gbps data bit rate. The Psr = -14 dBm for 500 active users by using APDs with gain =5, but 5 dBm effective receive power for PIN error floor 10-9 for 500 users. The usage of APD over (PIN) photodiode provides a high performance for a long transmission distance and high data bit rate that improved in the simulation for real environment by using the Optiwave software version 11.0. Seemingly, the system supports more no. of users, less bit error rate, and large data rate transmission.

A new series of optimal tight conflict-avoiding codes of weight [formula omitted

In this article, a construction of an optimal tight conflict-avoiding code of length 3dpe and weight 3 is shown for d≡1(mod3), e∈N and a prime p≡3(mod8) with p≠3, assuming that p is a non-Wieferich prime if e≥2. This is a new series of optimal conflict-avoiding code for which the number of codewords can be exactly determined.

Withdrawn article: Simulation Realization of 2-D Wavelength/Time System Utilizing MDW Code for OCDMA System

This paper presented a realization of Wavelength/Time (W/T) Two-Dimensional Modified Double Weight (2-D MDW) code for Optical Code Division Multiple Access (OCDMA) system based on Spectral Amplitude Coding (SAC) approach. The MDW code has capability to suppress Phase-Induce Intensity Noise (PIIN) and minimizing the Multiple Access Interference (MAI) noises. At the permissible BER 10 -9 , the 2-D MDW (APD) had shown minimum effective received power (P sr ) = -71 dBm that can be obtained at the receiver side as compared to 2-D MDW (PIN) only received -61 dBm. The results show that 2-D MDW(APD) has better performance in achieving same BER with longer optical fiber length and with less effective received power (P sr ). Also, the BER from the result shows that MDW code has capability to suppress PIIN ad MAI.

Simulation realization of 2-D wavelength/time system utilizing MDW code for OCDMA system

This paper presents a realization of Wavelength/Time (W/T) Two-Dimensional Modified Double Weight (2-D MDW) code for Optical Code Division Multiple Access (OCDMA) system based on Spectral Amplitude Coding (SAC) approach. The MDW code has the capability to suppress Phase-Induce Intensity Noise (PIIN) and minimizing the Multiple Access Interference (MAI) noises. At the permissible BER 10-9 , the 2-D MDW (APD) had shown minimum effective received power (Psr ) = -71 dBm that can be obtained at the receiver side as compared to 2-D MDW (PIN) only received -61 dBm. The results show that 2-D MDW (APD) has better performance in achieving same BER with longer optical fiber length and with less received power (Psr ). Also, the BER from the result shows that MDW code has the capability to suppress PIIN ad MAI.

Optimal conflict-avoiding codes for 3, 4 and 5 active users

Conflict-avoiding codes are used in multiple-access collision channels without feedback. The number of codewords in a conflict-avoiding code is the number of potential users of the channel. That is why codes with maximum cardinality (optimal codes) for given parameters are of interest. In this paper we classify, up to multiplier equivalence, all optimal conflict-avoiding codes of weights 3, 4, and 5 and given small lengths. We also determine some previously unknown values of the maximum cardinality of conflict-avoiding codes of weights 4 and 5.

Constructing Large Girth QC Protograph LDPC Codes Based on PSD-PEG Algorithm

For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. In this paper, we first derive a lower bound on the lifting degree to achieve a large girth lifted graph. Then, motivated by the cycle searching and girth maximizing features of the progressive edge-growth (PEG) algorithm, we introduce the permutation shifts determining (PSD) PEG algorithm, which can construct large girth base graph and determine the optimal permutation shifts, simultaneously. It is shown that the computational complexity of PSD-PEG algorithm is much lower than that of the PEG algorithm and the PEG-QC algorithm for the same codeword length. Furthermore, we show that the PSD-PEG algorithm can also be used to construct nonbinary QC protograph LDPC codes without low weight codes. Simulation results show that the binary and nonbinary QC protograph LDPC codes constructed by the PSD-PEG algorithm have good bit error rate performance and frame error rate performance over the additive white Gaussian noise channel.

New Optimal Constant Weight Codes from Difference Balanced Functions

New Optimal Constant Weight Codes from Difference Balanced Functions