Coding for Frequency-Hopped Spread-Spectrum Communication with Partial-Band Interference--Part II: Coded Performance

The performance of codes in a frequency-hopped spreadspectrum communication system with partial-band interference is investigated. The performance measure considered is the decoded bit error probability. A simplified interference model and worst-case partial-band Gaussian noise interference model is considered with the interference noise statistically independent of the transmitted signal. We consider soft decision receivers with side information and hard decision receivers with and without side information.     

Concatenated coding for frequency-hop spread-spectrum withpartial-band interference

Concatenated coding techniques are applied to slow frequency-hop packet radio communications for channels with partial-band interference. Binary orthogonal signaling (e.g., binary FSK) is employed with noncoherent demodulation, Reed-Solomon codes are employed for the outer code while both block and convolutional codes are considered for the inner code. Hard-decision and soft decision decoding methods are considered for the inner codes. A method is devised for estimating the reliability of the outer Reed-Solomon code symbols, and this estimate is used to determine which code symbols should be erased. Comparisons are made between the performance of concatenated codes and the performance of Reed-Solomon codes alone     

Bayesian methods for erasure insertion in frequency-hopcommunication systems with partial-band interference

The erasure of unreliable symbols improves the performance of most types of error-control coding if a good method is used to decide which symbols should be erased. Bayesian decision theory is employed to obtain such a method for use in frequency-hop communications with Reed-Solomon coding and errors-and-erasures decoding. The performance of frequency-hop communications with Bayesian erasure insertion is analyzed for channels with both partial-band and wideband Gaussian noise. The Bayesian technique is compared with Viterbi's ratio-threshold test, and these are compared to receivers that do not erase and use errors-only decoding. Comparisons are also made with receivers that erase all the symbols that are affected by the partial-band interference. When interference is strong, large coding gains result from the Bayesian method, and error probabilities are reduced by several orders of magnitude     

Hermitian codes for frequency-hop spread-spectrum packet radio networks

Hermitian codes are an attractive alternative to Reed-Solomon codes for use in frequency-hop spread-spectrum packet radio networks. For a given alphabet size, a Hermitian code has a much longer block length than a Reed-Solomon code. This and other considerations suggest that Hermitian codes may be superior for certain applications. Analytical results are developed for the evaluation of the packet error probability for frequency-hop transmissions using Hermitian coding. We find there are several situations for which Hermitian codes provide much lower packet error probabilities than can be obtained with Reed-Solomon codes. In general, as the code rate decreases or the symbol alphabet size increases, the relative performance of Hermitian codes improves with respect to Reed-Solomon codes. Performance evaluations are presented for an additive white Gaussian noise channel and for certain partial-band interference channels, and the packet error probability is evaluated for both errors-only and errors-and-erasures decoding.     

Performance of fast frequency-hopped MFSK receivers with linear andself-normalization combining in a Rician fading channel withpartial-band interference

An error probability analysis is performed for both self-normalized and conventional M-ary orthogonal frequency-shift-keying (MFSK) noncoherent receivers using fast frequency-hopped (FFH) spread-spectrum waveforms transmitted over a Rician fading channel with partial-band interference. The self-normalization receiver uses a nonlinear combination procedure to minimize performance degradation due to partial-band interference. The performance of the conventional receiver is significantly degraded by worst-case partial-band interference regardless of the modulation order or number of hops per data symbol used, while the self-normalization receiver can provide a significant immunity to worst-case partial-band interference for many channel conditions when diversity is used, provided the signal-to-thermal-noise ratio is large enough to minimize degradation due to nonlinear combining losses. The improvement afforded by higher modulation orders is dependent on channel conditions     

Erasure insertion in frequency-hop communications with fading andpartial-band interference

The use of block coding and errors-and-erasures decoding can enhance performance substantially in frequency-hop communication systems, provided that a good scheme is employed to determine which symbols to erase. In this paper, methods for determining erasures derived from Bayesian decision theory are applied to the mitigation of fading and partial-band interference. The performance of receivers using the Bayesian technique is compared with that of receivers that make erasure decisions using Viterbi's (1982) ratio-threshold test. The performance of hard-decision demodulation and the theoretical performance of receivers with access to perfect side information are also compared. It is found that the Bayesian receiver provides the best performance, and that error probabilities for the Bayesian receiver are lower than those for hard-decision demodulation by as much as six orders of magnitude     

Forced sequence sequential decoding: a concatenated coding systemwith iterated sequential inner decoding

We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low as E_b/N₀=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported by simulation results that are also extended to other parameters     

Linear programming-based optimization of the distance spectrum of linear block codes

We describe an approach for the identification of good distance spectra for possibly existing binary linear block codes based on linear programming and the MacWilliams-Delsarte (1977, 1972) identities. Specifically, the linear program is defined by an expression characterizing the performance of a potential code in terms of its distance spectrum and constraints imposed by the MacWilliams-Delsarte identities. Using the union bound to characterize performance, our results suggest that the best distance spectrum is not a function of signal-to-noise ratio (SNR) above the cutoff rate SNR and also suggest the existence of several unknown, good codes. Characterizing the performance using the maximum spectral error component of the union bound suggests spectral thinning with decreasing SNR.     

Multiple Accessing for the Collision Channel Without Feedback

We consider asynchronous multiple accessing without feedback over the collision channel. Redundant coding is used to overcome user interference which causes erasures for collided packets. The channel has a sum capacity of e^-1and a sum cutoff rate of 0.295. The best codes are long constraint length rate 1/3 convolutional encoders which achieve a sum throughput up to the sum cutoff rate using an easy-to-implement forward search decoding algorithm. In the presence of additive Gaussian noise, the same redundant coding can save, at hardly any extra cost, about 6 dB of signal-to-noise ratio.     

Benchmarking Iterative Receivers for BICM Multi-Carrier Systems Against Capacity Bounds

In this paper, we analyze iterative receivers for bit-interleaved coded modulation (BICM) multi-carrier systems and compare them against theoretical capacity bounds for the channel, coded modulation, and BICM. We map the theoretical capacity bounds into bit-error rate (BER) versus average signal-to-noise ratio per bit plots to simplify the comparison between the theoretical capacity bounds and simulated BER curves. As BER simulations show, iterative receivers with code doping or spreading reach the turbo-cliff within 1 or 0.3dB of the independent Rayleigh fading channel capacity. While the iterative receiver with spreading is closer to the channel capacity than the one with code doping, the later one can eliminate the residual bit-errors after the turbo-cliff. We further present a combinatorial analysis of the distribution of the spread symbol constellation for Walsh-Hadamard spreading codes used in a BICM multi-carrier system to explain the above results.     

Multiple accessing for the collision channel without feedback

We consider asynchronous multiple accessing without feedback over the collision channel. Redundant coding is used to overcome user interference which causes erasures for collided packets. The channel has a sum capacity of e^-1and a sum cutoff rate of 0.295. The best codes are long constraint length rate 1/3 convolutional encoders which achieve a sum throughput up to the sum cutoff rate using an easy-to-implement forward search decoding algorithm. In the presence of additive Gaussian noise, the same redundant coding can save, at hardly any extra cost, about 6 dB of signal-to-noise ratio.     

基于最大余弦比的LDPC码闭集识别

为改善低信噪比条件下LDPC码闭集识别的性能,本文提出了一种基于最大余弦比的软判决识别算法。该算法在分析了最大均值似然比算法存在的问题的基础上,利用LDPC码的编码结构特点,将识别过程归结为二元域中线性关系的检测问题;同时引入能够有效表征线性编码约束关系成立可能性大小的余弦检验函数,基于正确校验矩阵与错误校验矩阵下的余弦检验函数统计特性不同的事实,将两种情况下的余弦比作为编码器判定依据,从而实现低信噪比下LDPC码闭集的有效识别。仿真结果表明,在信噪比为0dB条件下,算法能够可靠识别出常用的IEEE802.16e协议中LDPC码,同时与现有算法相比,算法性能提升近1dB。      

A Theoretical Evaluation of Parallel Interference Cancellation in M-Ary Orthogonal Modulated Asynchronous DS-CDMA System Over Multipath Rayleigh Fading Channels

In this paper, we tackle the problem of theoretical evaluation for the multistage parallel interference cancellation (PIC) scheme in a direct-sequence code division multiple access (DS-CDMA) system with orthogonal modulation and long scrambling codes. The studied system operates on the reverse link in a time varying multipath Rayleigh fading channel. By applying the Central Limit Theorem and some other approximations to multiple access interference (MAI) and intersymbol interference (ISI), as well as assuming identically distributed chips from a single interferer, the bit error rate (BER) performance of the PIC scheme at any stage can be recursively computed from the signal-to-noise ratio, number of users, the number of path per user, processing gain of the CDMA system, and the average received power of each path. For completeness, the BER expression is derived for chip synchronous and chip asynchronous systems over both equal and unequal power multipath channels. The proposed analysis is validated by the Monte Carlo simulations and proved to be reasonably accurate, and it gives insight into the performance and capacity one can expect from PIC-based receivers under different situations. For instance, the analytical results can be used to examine the convergence property, multipath diversity gains, and near-far resistance of the PIC scheme.     

Throughput analysis of a slotted frequency-hop multiple-accessnetwork

A link throughput analysis is presented for a slotted frequency-hop multiple-access (FHMA) packet radio network (PRN) operating in the presence of background noise, partial-band noise jamming, and partial-band tone jamming. The PRN consists of an arbitrary number of transceivers arranged in a paired-off topology. Forward error-correction coding is used for packet protection. M-ary FSK modulation is used with hard-decision decoding. Expressions are derived for the link throughput in terms of the channel cutoff rate and capacity. The dependency of the optimal processing gain, code rate, and jamming fraction on the population size, traffic intensity, bit energy to background noise ratio, and bit energy to jammer noise ratio is examined in detail. It is shown that a properly designed (optimized) PRN using random-access FHMA offers a significantly larger heavy-load throughput than a random-access frequency-division multiple-access PRN     

On the cutoff rate of a discrete memoryless channel with(d, k)-constrained input sequences

The cutoff rate of a discrete memoryless channel whose output sequences are from a (d, k) encoder is investigated. A rational rate (d, k) encoder is considered as a finite state machine and maximum-likelihood decoding is used to compute the cutoff rate. Some commonly used (d, k) codes, such as the rate 1/2 (1, 3) code with a two-state encoder, the IBM rate 2/3 (1, 7) code having a five-state encoder, and the IBM rate 1/2 (2, 7) code with a seven-state encoder, are used to illustrate the cutoff rate computation. Results are presented for both the binary symmetric channel (BSC) and the Gaussian noise channel. The performance of a decoder designed for noiseless transmission of (1, 3) code is compared to that of a maximum-likelihood decoder for the (1, 3) code. It is also shown that for the case of the Gaussian noise channel, a gain of about 1.7 dB in signal-to-noise ratio is possible by using 3-bit soft decisions over hard decisions     

A new family of 2D wavelength/time codes with large cardinality for incoherent spectral amplitude coding OCDMA networks and analysis of its performance

A new family of two-dimensional wavelength/time codes (2D-W/T-MQC/MQCs) and its system structure of encoder/decoder are proposed, which is based on tunable optical fiber delay lines (TOFDLs) and fiber Bragg gratings (FBGs). Multiple-access interference (MAI) can fully be eliminated by using a wavelength/time balanced detector structure at the receivers. Furthermore, the performance of the system is also analyzed by taking into account the phase-induced intensity noise (PIIN), shot noise, and thermal noise. The simulation results reveal that the new code family possesses higher signal-to-noise ratio (SNR) and lower bit-error rate (BER) than the family of one-dimensional spectral amplitude coding modified quadratic congruence codes (1D-SAC-MQCs) and that of the two-dimensional wavelength/spatial M-matrices codes (2D-W/S-M-Matrices) so that a larger number of subscribers can be supported simultaneously. Additionally, the 2D-W/T-MQC/MQC system requires less signal power for each light source under the same error-free condition. As a result, the network based on the new code family will support more active users and utilize the frequency bandwidth more efficiently.     

Parallel acquisition of multicarrier direct-sequence spread-spectrum signals in fading and partial-band interference

The frequency diversity of multicarrier direct-sequence signaling can potentially offer robust performance in frequency-selective channels. The paper focuses on the acquisition of multicarrier signals in channels containing fading and partial-band interference. The maximum-likelihood decision rule for parallel acquisition in frequency-selective fading and partial-band interference is derived. Several simpler, near-optimal decision rules are also discussed. The performance of these decision rules is compared to that of equal-gain combining for multicarrier acquisition. Results show that the decision rules designed specifically for partial-band interference give significantly better performance. Methods of acquisition with a limited number of correlators are also discussed. Finally, the potential benefits of estimating the signal strength on each subcarrier prior to acquisition are examined.     

Source-optimized irregular repeat accumulate codes with inherent unequal error protection capabilities and their application to scalable image transmission.

The common practice for achieving unequal error protection (UEP) in scalable multimedia communication systems is to design rate-compatible punctured channel codes before computing the UEP rate assignments. This paper proposes a new approach to designing powerful irregular repeat accumulate (IRA) codes that are optimized for the multimedia source and to exploiting the inherent irregularity in IRA codes for UEP. Using the end-to-end distortion due to the first error bit in channel decoding as the cost function, which is readily given by the operational distortion-rate function of embedded source codes, we incorporate this cost function into the channel code design process via density evolution and obtain IRA codes that minimize the average cost function instead of the usual probability of error. Because the resulting IRA codes have inherent UEP capabilities due to irregularity, the new IRA code design effectively integrates channel code optimization and UEP rate assignments, resulting in source-optimized channel coding or joint source-channel coding. We simulate our source-optimized IRA codes for transporting SPIHT-coded images over a binary symmetric channel with crossover probability p. When p = 0.03 and the channel code length is long (e.g., with one codeword for the whole 512 x 512 image), we are able to operate at only 9.38% away from the channel capacity with code length 132380 bits, achieving the best published results in terms of average peak signal-to-noise ratio (PSNR). Compared to conventional IRA code design (that minimizes the probability of error) with the same code rate, the performance gain in average PSNR from using our proposed source-optimized IRA code design is 0.8759 dB when p = 0.1 and the code length is 12800 bits. As predicted by Shannon's separation principle, we observe that this performance gain diminishes as the code length increases.     

Performance analysis and design criteria for finite-alphabet source-channel codes

Efficient compression of finite-alphabet sources requires variable-length codes (VLCs). However, in the presence of noisy channels, error propagation in the decoding of VLCs severely degrades performance. To address this problem, redundant entropy codes and iterative source-channel decoding have been suggested, but to date, neither performance bounds nor design criteria for the composite system have been available. We calculate performance bounds for the source-channel system by generalizing techniques originally developed for serial concatenated convolutional codes. Using this analysis, we demonstrate the role of a recursive structure for the inner code and the distance properties of the outer code. We use density evolution to study the convergence of our decoders. Finally, we pose the question: Under a fixed rate and complexity constraint, when should we use source-channel decoding (as opposed to separable decoding)? We offer answers in several specific cases. For our analysis and design rules, we use union bounds that are technically valid only above the cutoff rate, but interestingly, the codes designed with union-bound criteria perform well even in low signal-to-noise ratio regions, as shown by our simulations as well as previous works on concatenated codes.     

Probability of Error Analyses of a BFSK Frequency-Hopping System with Diversity Under Partial-Band Jamming Interference--Part II: Performance of Square-Law Nonlinear Combining Soft Decision Receivers

In this paper, error probability analyses are performed for a binary frequency-shift-keying (BFSK) system employingLhop/bit frequency-hopping (FH) spread-spectrum waveforms transmitted over a partial-band Gaussian noise jamming channel. The performance results for two types of square-law nonlinear combining soft decision receivers under worst-case partial-band jamming are presented. The receivers employ, prior to combining, nonlinear weighting strategies of 1) adaptive gain control and 2) soft limiting (clipping) of the detector output of each channel of the dehopped waveform. Both thermal noise and jamming are included in the analyses. It is shown in the paper that a diversity gain for error rate improvement is realizable for nonlinear combining receivers provided that the noncoherent combining loss is less dominant than the jamming power reduction realized by the weighting strategy. Performance comparisons between linear and nonlinear combining receivers are presented.