Laurie L. Joiner

Arbitrary waveform DDFS utilizing Chebyshev polynomials interpolation

A new technique of arbitrary waveform direct digital frequency synthesis (DDFS) is introduced. In this method, one period of the desired periodic waveform is divided into m sections, and each section is approximated by a series of Chebyshev polynomials up to degree d. By expanding the resultant Chebyshev polynomials, a power series of degree d is produced. The coefficients of this power series are obtained by a closed-form direct formula. To reconstruct the desired signal, the coefficients of the approximated power series are placed in a small ROM, which delivers the coefficients to the inputs of a digital system. This digital system contains digital multipliers and adders to simulate the desired polynomial, as well as a phase accumulator for generating the digital time base. The output of this system is a reconstructed signal that is a good approximation of the desired waveform. The accuracy of the output signal depends on the degree of the reconstructing polynomial, the number of subsections, the wordlength of the truncated phase accumulator output, as well as the word length of the DDFS system output. The coefficients are not dependent on the sampling frequency; therefore, the proposed system is ideal for frequency sweeping. The proposed method is adopted to build a traditional DDFS to generate a sinusoidal signal. The tradeoff between the ROM capacity, number of sections, and spectral purity for an infinite output wordlength is also investigated.

Decoding binary BCH codes

BCH codes are powerful error-correcting codes. Algorithms used for decoding must be able to find the error locations, and for nonbinary codes, the error magnitudes. One of the most efficient algorithms for decoding BCH codes is Berlekamps algorithm. To find the error locations the algorithm must solve a set of t equations in t unknowns. This paper explores, for binary BCH codes, a new method that uses half of the unknowns to determine the other unknowns, thus solving t/2 equations in t/2 unknowns. However, because of the reduced number of equations, the algorithm only iterates half the number of times. The performance of the new algorithm is shown to be superior to both Berlekamps algorithm and a simplified algorithm in terms of execution times, which includes the field multiplications and additions and required memory.

Soft decision decoding of BCH codes using error magnitudes

An efficient method for soft decision decoding of binary BCH codes using error magnitude calculations its presented. The 2t syndromes for a t-error correcting BCH code are used to solve 2t modified error magnitude type equations to obtain maximum likelihood decoding.

Adaptive rate coding using convolutional codes for asynchronous code division multiple access communications over slowly fading channels

This paper presents a method of code rate adaptation using punctured convolutional codes for direct sequence spread spectrum communication systems over slowly fading channels. A blind channel estimation technique is used to estimate the nature of the multi-user channel at the detector (before the decoder). The path gains obtained from the channel estimation technique are used to adapt the code rates. Punctured codes derived from a specific rate 1/2 (M=4) mother code are used to provide error protection corresponding to the actual channel state. The upper and lower bounds on the bit error probability and the upper bound on the error event probability are derived for hard-decision and soft-decision decoding over Rayleigh and Rician fading channels. The throughput gains obtained using the adaptive scheme and the performances of the punctured codes are studied.

Fast error magnitude evaluations for Reed-Solomon codes

A fast algorithm for the evaluation of error magnitudes for Reed-Solomon codes is obtained here in terms of the error locations and syndromes. This fast algorithm is compared to the Forney algorithm (1965) in terms of required additions and multiplications and implementation speed.

Delay Based Congestion Detection and Admission Control for Voice quality in enterprise or carrier controlled IP Networks

Reservations based admission control, using Multi-protocol Label Switching (MPLS) is the leading method being considered by traditional carriers for maintaining Quality of Service (QoS) when deploying Voice over Internet Protocol (VoIP). In this research we explore an alternative to reservations based admission control called Delay Based Congestion Detection and Admission Control (DBCD/AC), a form of Endpoint Admission Control. DBCD/AC is a method for edge devices, such as media gateways, to detect impending congestion in the core based on delay measurements and analysis. When impending congestion is detected, the edge devices refuse new incoming connections to the media gateways to mitigate the congestion. This research examines the characteristics of DBCD/AC and finds that DBCD/AC is a promising alternative to a reservations based admission control approach for enterprise or carrier controlled IP Networks.

Variable energy adaptation for asynchronous CDMA communications over slowly fading channels

In this paper, a detailed theoretical analysis of variable energy adaptation in an asynchronous code division multiple access (A-CDMA) system is discussed. Rayleigh and Rician frequency-selective slowly fading channels are considered. The receiver, capable of measuring the received signal energy-to-noise ratio, provides the transmitter with the necessary signal-to-noise ratio measurement to control the transmitter energy through a noise-free feedback channel. System parameters such as fading margin and mean transmitter energy gain are calculated for both Rayleigh and Rician fading channels as a function of the probability of error specification and the probability of unsatisfactory operation.

Performance of punctured convolutional codes in asynchronous CDMA communications under perfect phase-tracking conditions

In this paper, the performance of punctured convolutional codes of short constraint lengths is discussed. The punctured codes are used to provide error protection to a particular user in an asynchronous code division multiple access (A-CDMA) system. Perfect channel estimation is assumed at the receiver. A slow fading Rician or Rayleigh channel is assumed. Maximum likelihood decoding through a Viterbi algorithm is used to decode the received symbols. Soft decision decoding for perfect phase tracking of the received signal is considered. Analytical bounds, which are useful in predicting the performance of the A-CDMA system are derived and plotted for the cases of infinite and finite channel memory. The upper bounds with Viterbi decoding are derived and plotted for the various punctured codes considered. The simulated results are found to agree very well with their upper bounds and predicted results.

Improved performance of reduced M-ary orthogonal signaling using Reed-Solomon codes

This paper presents a comparison of communication systems using different signal constellation sizes and Reed-Solomon code sizes with different rates so that the overall required bandwidth is the same for each system. In these comparisons the channel symbol size is smaller than the code symbol size, so that a code symbol contains parts of more than one channel symbol. Thus, the normal assumption of independent code symbols does not apply. Instead consideration must be taken to obtain the best arrangement of channel symbols in each code symbol. Analytical expressions are derived to compare the bit error probability performance of comparable systems based on individual codewords.

Sequential decoding of Reed-Solomon codes in an incremental redundancy system

A method of soft-decision decoding of Reed-Solomon codes is presented. This method is an iterative procedure where erasures only decoding is performed followed by a sequential procedure to determine the maximum likelihood estimate of the transmitted word. Results are given that compare this new method of soft decision decoding to more traditional soft decision decoding algorithms. The use of the sequential decoding method in an incremental redundancy system is discussed.