Algebraic lower bounds on the free distance of convolutional codes

A new module structure for convolutional codes is introduced and used to establish further links with quasi-cyclic and cyclic codes. The set of finite weight codewords of an (n,k) convolutional code over F_q is shown to be isomorphic to an F_q[x]-submodule of F_q ⁿ[x], where F_q ⁿ[x] is the ring of polynomials in indeterminate x over F_q ⁿ, an extension field of F_q. Such a module can then be associated with a quasi-cyclic code of index n and block length nL viewed as an F_q[x]-submodule of F_q ⁿ[x]/langx^L-1rang, for any positive integer L. Using this new module approach algebraic lower bounds on the free distance of a convolutional code are derived which can be read directly from the choice of polynomial generators. Links between convolutional codes and cyclic codes over the field extension F_q ⁿ are also developed and Bose-Chaudhuri-Hocquenghem (BCH)-type results are easily established in this setting. Techniques to find the optimal choice of the parameter L are outlined     

Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications

In this paper we present a unified way to determine the values and their multiplicities of the exponential sums Sigma_xisinF(q)zeta_p ^Tr(af(x)+bx)(a,bisinF_q,q=p^m,pges3) for all perfect nonlinear functions f which is a Dembowski-Ostrom polynomial or p = 3,f=^x(3(k)+1)/2 where k is odd and (k,m)=1. As applications, we determine (1) the correlation distribution of the m-sequence {a_lambda=Tr(gamma^lambda)}(lambda=0,1,...) and the sequence {b_lambda=Tr(f(gamma^lambda))}(lambda=0,1,...) over F_p where gamma is a primitive element of F_q and (2) the weight distributions of the linear codes over F_p defined by f.     

On lowest density MDS codes

Let F_q denote the finite field GF(q) and let h be a positive integer. MDS (maximum distance separable) codes over the symbol alphabet F_q^b are considered that are linear over F _q and have sparse (“low-density”) parity-check and generator matrices over F_q that are systematic over F_q^b. Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an F_q-linear MDS code over F_q^b, along with upper bounds on the length of any MDS code that attains those lower bounds. A construction is presented that achieves those bounds for certain redundancy values. The building block of the construction is a set of sparse nonsingular matrices over F_q whose pairwise differences are also nonsingular. Bounds and constructions are presented also for the case where the systematic condition on the parity-check and generator matrices is relaxed to be over F_q, rather than over F_q^b     

Graded pseudomorphic channel AlInP/AlInAs/GaInAs HEMTs with highchannel breakdown voltage

Reports effects of the composition grading of the channel on the device characteristics of Al_0.48In_0.52As/Ga_1-xIn_xAs pseudomorphic HEMTs. Systematic studies reveal that the modification of the quantum-well channel by grading the composition considerably changes the channel breakdown (BV_ds) and output conductance (G₀ ) characteristics. HEMTs with graded Ga_1-xIn_xAs channel (from x=0.7 to x=0.6) exhibited significantly improved BV_ds (11V) and g₀ (40 mS/mm) compared with HEMTs with uniform composition (x=0.7) in the channel (BV_ds=4V and g₀=80 mS/mm)     

Extremely high transconductance Ge/Si0.4Ge0.6p-MODFET's grown by UHV-CVD

Ge-channel modulation-doped field-effect transistors (MODFET's) with extremely high transconductance are reported. The devices were fabricated on a compressive-strained Ge/Si_0.4Ge_0.6 heterostructure with a Hall mobility of 1750 cm²/Vs (30,900 cm²/Vs) at room temperature (77 K). Self-aligned, T-gate p-MODFET's with L_g=0.1 μm displayed an average peak extrinsic transconductance (g(m_ext)) of 439 mS/mm, at a drain-to-source bias voltage (V_ds) of -0.6 V, with the best device having a value of g(m_ext)=488 mS/mm. At 77 K, values as high as g(m_ext)=687 mS/mm were obtained at a bias voltage of only V_ds=-0.2 V. These devices also displayed a unity current gain cutoff frequency (f_T) of 42 GHz and maximum frequency of oscillation (f_max) of 86 GHz at V_ds=-0.6 V and -1.0 V, respectively     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

Optimal quaternary linear codes of dimension five

Let d_q(n,k) be the maximum possible minimum Hamming distance of a q-ary [n,k,d]-code for given values of n and k. It is proved that d₄ (33,5)=22, d₄(49,5)=34, d₄ (131,5)=96, d₄(142,5)=104, d₄(147,5)=108, d ₄(152,5)=112, d₄(158,5)=116, d₄(176,5)⩾129, d₄(180,5)⩾132, d₄(190,5)⩾140, d₄(195,5)=144, d₄(200,5)=148, d₄(205,5)=152, d₄(216,5)=160, d₄(227,5)=168, d₄(232,5)=172, d₄(237,5)=176, d₄(240,5)=178, d₄(242,5)=180, and d₄(247,5)=184. A survey of the results of recent work on bounds for quaternary linear codes in dimensions four and five is made and a table with lower and upper bounds for d₄(n,5) is presented     

有限域上最优码的一种新的构造方法

基于域F_p^m上一类特殊的矩阵,定义了环R(_p^m,k)=F_p^m[u]/k>到F_p^p_mj的一个新的Gray映射,其中u^k=0、p为素数、j为正整数且p^j－1+1≤k≤p^j.得到了环R(_p^m,k)上码长为任意长度N的(1+u)常循环码的Gray象是F_p^m上长为p^jN的保距线性循环码,并给出了Gray象的生成多项式,构造了F₃,F₅和F₇上的一些最优线性循环码.     

New families of almost perfect nonlinear power mappings

A power mapping f(x)=x^d over GF(pⁿ) is said to be differentially k-uniform if k is the maximum number of solutions x∈GF(pⁿ) of f(x+a)-f(x)=b where a, b∈GF(pⁿ ) and a≠0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings     

Sort-and-match algorithm for soft-decision decoding

Let a q-ary linear (n, k) code C be used over a memoryless channel. We design a decoding algorithm Ψ_N that splits the received block into two halves in n different ways. First, about √N error patterns are found on either half. Then the left- and right-hand lists are sorted out and matched to form codewords. Finally, the most probable codeword is chosen among at most n√N codewords obtained in all n trials. The algorithm can be applied to any linear code C and has complexity order of n³√N. For any N⩾q^n-k, the decoding error probability P_N exceeds at most 1+q^n-k/N times the probability P_Ψ (C) of maximum-likelihood decoding. For code rates R⩾1/2, the complexity order q^n-k/2 grows as square root of general trellis complexity q^min{n-k,k}. When used on quantized additive white Gaussian noise (AWGN) channels, the algorithm Ψ_N can provide maximum-likelihood decoding for most binary linear codes even when N has an exponential order of q^n-k     

Emission cross sections and spectroscopy of Ho3+ laserchannels in KGd(WO4)2 single crystal

The spectroscopic properties of Ho³⁺ laser channels in KGd(WO₄)₂ crystals have been investigated using optical absorption, photoluminescence, and lifetime measurements. The radiative lifetimes of Ho³⁺ have been calculated through a Judd-Ofelt (JO) formalism using 300-K optical absorption results. The JO parameters obtained were Ω₂=15.35×10^-20 cm², Ω ₄=3.79×10^-20 cm², Ω₆ =1.69×10^-20 cm². The 7-300-K lifetimes obtained in diluted (8·10¹⁸ cm^-3) KGW:0.1% Ho samples are: τ(⁵F₃)≈0.9 μs, τ( ⁵S₂)=19-3.6 μs, and τ(⁵F₅ )≈1.1 μs. For Ho concentrations below 1.5×10²⁰ cm^-3, multiphonon emission is the main source of non radiative losses, and the temperature independent multiphonon probability in KGW is found to follow the energy gap law τ_ph ^-1(0)=βexp(-αΔE), where β=1.4×10^-7 s^-1, and α=1.4×10³ cm. Above this holmium concentration, energy transfer between Ho impurities also contributes to the losses. The spectral distributions of the Ho³⁺ emission cross section σ_EM for several laser channels are calculated in σ- and π-polarized configurations. The peak a σ_EM values achieved for transitions to the ⁵I₈ level are ≈2×10^-20 cm² in the σ-polarized configuration, and three main lasing peaks at 2.02, 2.05, and 2.07 μm are envisaged inside the ⁵I₇→⁵I₈ channel     

CMOS equaliser for compensating sinc(x) distortion of video D/Aconverters

The authors describe the design and CMOS realisation of a new g _m-C amplitude equaliser for correcting sinc(x) distortion in video D/A converters. Simulated and measured results demonstrate how the equaliser is used to correct distortion in D/A converters with F_s =13.5 MHz to ⩽0.08 dB ripple over 5 MHz bandwidth. Fabricated using a 0.8 μm CMOS process, the equaliser occupies 0.7 mm² and dissipates 20 mW from a 5 V supply     

Erasure, list, and detection zero-error capacities for low noiseand a relation to identification

For the discrete memoryless channel (χ, y, W) we give characterizations of the zero-error erasure capacity C_er and the zero-error average list size capacity C_al in terms of limits of suitable information (respectively, divergence) quantities (Theorem 1). However, they do not “single-letterize.” Next we assume that χ⊂y and W(x|x)>0 for all x∈χ, and we associate with W the low-noise channel W_ϵ, where for y ⁺(x)={y:W(y|x)>0} W_ϵ(y|x)={1, if y=x and |y⁺(x)|=1 1-ϵ, if y=x and |y⁺(x)|>1 e/|y ⁺(x)|-1, if y≠x. Our Theorem-2 says that as ε tends to zero the capacities C_er(W_ε) and C_al (W_ε) relate to the zero-error detection capacity C _de(W). Our third result is a seemingly basic contribution to the theory of identification via channels. We introduce the (second-order) identification capacity C_oid for identification codes with zero misrejection probability and misacceptance probability tending to zero. Our Theorem 3 says that C_oid equals the zero-error erasure capacity for transmission C_er     

Minimum-weight codewords as generators of generalized Reed-Mullercodes

We establish the range of values of ρ, where 0⩽ρ⩽m(q-1), for which the generalized Reed-Muller code R_Fq(ρ, m) of length q^m over the field F_q of order q is spanned by its minimum-weight vectors     

A New Family of Ternary Almost Perfect Nonlinear Mappings

A mapping f(x) from GF(pⁿ) to GF(pⁿ) is differentially k-uniform if k is the maximum number of solutions x isin GF(pⁿ) of f(x+a) - f(x) = b, where a, b isin GF(pⁿ) and a ne 0. A 2-uniform mapping is called almost perfect nonlinear (APN). This correspondence describes new families of ternary APN mappings over GF(3ⁿ), n>3 odd, of the form f(x) = ux^d + x^{d 2} where d₁ = (3^n-1)/2 - 1 and d₂ = 3ⁿ - 2.     

Power performance of InP-based single and double heterojunctionbipolar transistors

The microwave and power performance of fabricated InP-based single and double heterojunction bipolar transistors (HBTs) is presented. The single heterojunction bipolar transistors (SHBTs), which had a 5000 Å InGaAs collector, had BV_CEO of 7.2 V and J_Cmax of 2×10⁵ A/cm². The resulting HBTs with 2×10 μm² emitters produced up to 1.1 mW/μm2 at 8 GHz with efficiencies over 30%. Double heterojunction bipolar transistors (DHBTs) with a 3000-Å InP collector had a BV_CEO of 9 V and J_{c max} of 1.1×10⁵ A/cm², resulting in power densities up to 1.9 mW/μm² at 8 GHz and a peak efficiency of 46%. Similar DHBTs with a 6000 Å InP collector had a higher BV_CEO of 18 V, but the J _{c max} decreased to 0.4×10⁵ A/cm² due to current blocking at the base-collector junction. Although the 6000 Å InP collector provided higher f_max and gain than the 3000 Å collector, the lower J_{c max} reduced its maximum power density below that of the SHBT wafer. The impact on power performance of various device characteristics, such as knee voltage, breakdown voltage, and maximum current density, are analyzed and discussed     

Phase-noise analysis of MEMS-based circuits and phase shifters

The effect of Brownian, acceleration, acoustic, and power-supply noise on MEMS based circuits has been calculated for MEMS.-based circuits (phase shifters, delay circuits). The calculations are done for capacitive shunt MEMS switches and metal-to-metal contact series MEMS switches. It is found that these effects result in both an amplitude and phase noise, with the phase noise being around 100× larger than the amplitude noise. The phase noise due to Brownian motion is negligible for MEMS switches with k ≃ 1.0 N/m, g₀ > 2 μm, Q > 0.5, and f₀ ≃ 50 kHz. The effect of acceleration and acoustic noise is negligible for a total acceleration noise of 10 g or less and a total acoustic noise of 74-dB sound pressure level. The power-supply noise depends on the bias conditions of the MEMS element, but is negligible for MEMS switches with a bias voltage of 0 V and a total noise voltage of 0.1 V or less. It is also found that metal-to-metal contact series switches result in much less phase noise than standard capacitive shunt switches. The phase noise increases rapidly for low spring-constant bridges (k = 0.24 N/m), low-height bridges, and bridges with a large mechanical damping (Q < 0.3). Also, varactor-based designs result in 30-40 dB more phase noise than switch-based circuits. This paper proves that microwave passive circuits built using MEMS switches (with a proper mechanical design) can be used in most commercial and military applications without any phase-noise penalty     

Measurement of self-phase modulation of amplified spontaneousemission: the role of second-order degree of coherence in determiningthe Kerr effect

We have experimentally characterized the self-phase-modulation-induced spectral broadening of continuous-wave amplified spontaneous emission (ASE) propagating in dispersion-shifted fiber samples. Experimental results for polarized and unpolarized beams show a dependence of the Kerr effect on the second-order degree of coherence of light g₁₁⁽²⁾(0). In particular, the difference in second-order statistics for laser and ASE light must be properly accounted for when estimating the Kerr effect for a reliable modeling of transmission in long-haul amplified optical links. Whenever the g₁₁⁽²⁾(0)=2 value for ASE light cannot be properly reproduced in simulated transmission, an enhanced value for the Kerr coefficient n₂ with respect to the coherent light case, must be used in computing the effects of self-phase modulation for the ASE portion of light     

Circuit performance of CMOS technologies with silicon dioxide andreoxidized nitrided oxide gate dielectrics

The circuit performance of CMOS technologies with silicon dioxide (SiO₂) and reoxidized nitrided oxide (RONO) gate dielectrics over the normal regime of digital circuit operation, i.e. V_GS⩽5 V and B_DS⩽5 V, is discussed. The simulation of a simple CMOS inverter has shown that the SiO₂ inverter consistently outperforms the RONO inverter over temperatures ranging from 300 to 100 K. This can be attributed mainly to the significantly lower μ_p (hole mobility) of RONO p-channel devices. At 300 K, μ_p(RONO) is 14-8% smaller than μ_p(SiO₂) over the entire range of gate biases, while μ_n(RONO) (electron mobility of n-channel RONO devices) is also smaller than μ_n(SiO₂) and reaches only 96% of μ_n(SiO₂) at V_GS=5 V. At 100 K, μ_n(RONO)/μ_n (SiO₂) at V_GS=5 V is increased to 1.10, however, μ_p(RONO)/μ_p(SiO₂) at V_GS=5 V is degraded to 0.59. The dependence of circuit performance on the supply voltage has also been evaluated for the RONO and SiO₂ inverters     

Fresnel-integral approximation

In diffraction analysis, an approximation to K_-(x)=1/(√π)e^ix(2)+iπ/4∫_x ^∞e^-it(2) dt, (0-(x), suitable for computation with a hand-held computer, such as the HP-288