Hybrid weighted symbol-flipping decoding for nonbinary LDPC codes

A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.

Study on cipher propertys of constant weight codes

Constant weight code is an important error-correcting control code in communications. Basic structure of constant weight codes for some arriving at Johnson bound, A（n, 2u, w）, is presented. Some correlative propertys of the codes, the solution of arriving at Johnson bound, and the results on the couple constant code and some constant weight codes are discussed. The conclusion is verified through four examples.

Performance Evaluation of Wavelet Based on Human Visual System

We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function (MTF) of human visual system in the frequency domain. In this paper, we evaluate performance of the constructed wavelet, and compare it with the widely used Daubechies 9 7, Daubechies 9 3 and GBCW 9 7 wavelets. The result shows that coding performance of the constructed wavelet is better than Daubechies 9 3, and is competitive with Daubechies 9 7 and GBCW 9 7 wavelets. Like Daubechies 9 3 wavelet, the filter coefficients of the constructed wavelet are all dyadic fractions, and the tap is less than Daubechies 9 7 and GBCW 9 7. It has an attractive feature in the realization of discrete wavelet transform.

A Depth Video Coding In-Loop Median Filter Based on Joint Weighted Sparse Representation

The existing depth video coding algorithms are generally based on in-loop depth filters, whose performance are unstable and easily affected by the outliers. In this paper, we design a joint weighted sparse representation-based median filter as the in-loop filter in depth video codec. It constructs depth candidate set which contains relevant neighboring depth pixel based on depth and intensity similarity weighted sparse coding, then the median operation is performed on this set to select a neighboring depth pixel as the result of the filtering. The experimental results indicate that the depth bitrate is reduced by about 9% compared with anchor method. It is confirmed that the proposed method is more effective in reducing the required depth bitrates for a given synthesis quality level.

Optimal p-Ary Codes from One-Weight and Two-Weight Codes over IF_p+ vIF_p

This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.

Construction of One-Lee Weight and Two-Lee Weight Codes over IF_p+vIF_p

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.

Some new optimal quaternary constant weight codes

Constant weight codes (CWCs) are an important class of codes in coding theory. Generalized Steiner systems GS(2, k, v, g) were first introduced by Etzion and used to construct optimal nonlinear CWCs over an alphabet of size g+1 with minimum Hamming distance 2k - 3, in which each codeword has length v and weight k. In this paper, Weil's theorem on character sum estimates is used to show that there exists a GS(2,4, v, 3) for any prime v≡1 (mod 4) and v > 13. From the coding theory point of view, an optimal nonlinear quaternary (v, 5,4) CWC exists for such a prime v.

Construction of One-Gray Weight Codes and Two-Gray Weight Codes over Z4+uZ4

This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.

Path Weight Complementary Convolutional Code for Type-Ⅱ Bit-Interleaved Coded Modulation Hybrid ARQ System

Bit-interleaved coded modulation (BICM) is suitable to bandwidth-efficient communication systems. Hybrid automatic repeat request (HARQ) can provide more reliability to high-speed wireless data transmission. A new path weight complementary convolutional (PWCC) code used in the type-Ⅱ BICM-HARQ system is proposed. The PWCC code is composed of the original code and the complimentary code. The path in trellis with large hamming weight of the complimentary code is designed to compensate for the path in trellis with small hamming weight of the original code. Hence, both of the original code and the complimentary code can achieve the performance of the good code criterion of corresponding code rate. The throughput efficiency of the BICM-HARQ system wit PWCC code is higher than repeat code system, a little higher than puncture code system in low signal-to-noise ratio (SNR) values and much higher than puncture code system, the same as repeat code system in high SNR values. These results are confirmed by the simulation.

The Determination on Weight Hierarchies of q-Ary Linear Codes of Dimension 5 in Class IV

The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.

Generalized Steiner Triple Systems with Group Size Ten

Generalized Steiner triple systems, GS(2, 3, n, g) are equivalent to (g+1)-ary maximum constant weight codes (n, 3,3)s. In this paper, it is proved that the necessary conditions for the existence of a GS(2,3, n, 10), namely, n ≡ 0,1 (mod 3) and n ≥ 12, are also sufficient.

UWB multi-pulse position modulation for high data-rate wireless application

A new ultra-wide band （UWB） modulation scheme called L-ary ultra-wide band time hopping multi-pulse position modulation （UWB-TH-MPPM） is proposed for high data-rate wireless application, which can provide better communication performance. The constant weight code is introduced to construct the MPPM signal and the comparison between MPPM and single pulse position modulation （SPPM） is done in three aspects, namely, power efficiency, bandwidth efficiency, and probability of symbol error, respectively. The theoretical analysis and the numerical results show that when the constant weight code is appropriately chosen, MPPM can achieve lower probability of symbol error and higher power efficiency than SPPM at the cost of more bandwidth under the same condition. The proposed MPPM can be a good candidate in UWB system design.

On the Intersection of Binary Linear Codes

For a binary linear code,a new relation between the intersection and(2,2)-separating property is addressed,and a relation between the intersection and the trellis complexity is also given.Using above relations,the authors will apply several classes of binary codes to secret sharing scheme and determine their trellis complexity and separating properties.The authors also present the properties of the intersection of certain kinds of two-weight binary codes.By using the concept of value function,the intersecting properties of general binary codes are described.

Generalized Steiner Triple Systems with Group Size g ≡0, 3 (mod 6)

Generalized Steirier triple systems, GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (n-1)g≡0 (mod 2), n(n-1)g2≡0 (mod 6), and n≥g+2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, g≡0 (mod 6) and g≥12, if there exists a GS(2.3.n.g) for all n, g+2≤n≤7g+13. then the necessary conditions are also sufficient. Next, it is also shown that for any given g, g≡3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, n≡1 (mod 2) and g+2≤n≤7g+6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.