Soft-decision demodulation design for COVQ over white, colored, andISI Gaussian channels

In this work, the design of a q-bit (scalar and vector) soft-decision demodulator for Gaussian channels with binary phase-shift keying modulation is investigated. The demodulator is used in conjunction with a soft-decision channel-optimized vector quantization (COVQ) system. The COVQ is constructed for an expanded (q>1) discrete channel consisting of the concatenation of the modulator, the Gaussian channel, and the demodulator. It is found that as the demodulator resolution q increases, the capacity of the expanded channel increases, resulting in an improvement of the COVQ performance. Consequently, the soft-decision demodulator is designed to maximize the capacity of the expanded channel. Three Gaussian channel models are considered as follows: (1) additive white Gaussian noise channels; (2) additive colored Gaussian noise channels; and (3) Gaussian channels with intersymbol interference. Comparisons are made with (a) hard-decision COVQ systems, (b) COVQ systems which utilize interleaving, and (c) an unquantized (q=∞) soft-decision decoder proposed by Skoglund and Hedelin (1999). It is shown that substantial improvements can be achieved over COVQ systems which utilize hard decision demodulation and/or channel interleaving. The performance of the proposed COVQ system is comparable with the system by Skoglund and Hedelin-though its computational complexity is substantially less     

Soft-decision differential phase detection of turbo-coded M-ary CPFSK signals over Ricean channels

The performance of turbo codes is examined over the Ricean fading channel with soft-decision differential phase detection (DPD). M-ary continuous phase frequency-shift keying (CPFSK) signaling and puncturing of the coded sequence are considered to achieve bandwidth efficient communication. The effects of the number of phase decision regions, fading conditions, number of states of the constituent codes, and code rate are examined. A bit error rate upper bound is developed, which is useful at low values of bit error probability where computer simulations are lengthy. Significant gains using soft-decision DPD over hard-decision DPD and conventional noncoherent detection are reported.     

Performance of sphere decoding of block codes

A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We focus on analyzing the performance of sphere decoding of linear block codes. We analyze the performance of soft-decision sphere decoding on AWGN channels and a variety of modulation schemes. A hard-decision sphere decoder is a bounded distance decoder with the corresponding decoding radius. We analyze the performance of hard-decision sphere decoding on binary and q-ary symmetric channels. An upper bound on the performance of maximum-likelihood decoding of linear codes defined over F_q (e.g. Reed- Solomon codes) and transmitted over q-ary symmetric channels is derived and used in the analysis.We then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes. The tradeoff between the performance and complexity of a sphere decoder is then discussed.     

Bit-by-bit soft-decision decoding of trellis-coded M-DPSKmodulation

We present a simple soft-decision decoding method for use with trellis-coded M-ary differential phase-shift keying (M-DPSK). The demodulator assigns a separate confidence level to each bit associated with an M-ary symbol, and these confidence levels are based only on the phase of the received symbol. Decoding is performed by the standard soft-decision Viterbi decoder that is normally used for binary modulation. Our soft-decision decoder is much simpler to implement than the typical trellis decoder, but we show that the performance is approximately the same     

COVQ for MAP hard-decision demodulated channels

We design a channel optimized vector quantizer (COVQ) for symbol-by-symbol maximum a posteriori (MAP) hard-decision demodulated channels. The main objective is to exploit the non-uniformity of the indices representing the quantized source via the MAP decoder and iteratively optimize the overall discrete channel (at the symbol level) jointly with the quantizer. We consider memoryless Gaussian and Gauss-Markov sources transmitted over a binary phase-shift keying modulated Rayleigh fading channel. Our scheme has less encoding computational and storage complexity (particularly for noisy channel conditions) than both conventional and soft-decision COVQ systems, which use hard-decision and soft-decision maximum likelihood demodulation, respectively. Furthermore, it provides a notable signal-to-distortion ratio gain over the former system, and in some cases it matches or outperforms the latter one.     

How often is hard-decision decoding enough?

The problem of decoding binary linear block codes has received much attention; the two extremes are optimal, high-complexity soft-decision (or maximum-likelihood) decoding and lower performance, much lower complexity hard-decision (or algebraic) decoding. This article considers a class of decoders which first implements hard-decision decoding; second, tests to see if that is enough, that its result matches the result of soft-decision decoding; and third, continues to search if a match is not found. The advantage of such a testing procedure is that if the hard-decision decoding result is found to be enough (called a success for the test), then the computational effort expended by the decoder is low. The performance, as measured by the probability of a success, of a variety of simple tests of the hard-decision codeword are analyzed     

Soft-decision COVQ for turbo-coded AWGN and Rayleigh fadingchannels

A robust soft-decision channel-optimized vector quantization (COVQ) scheme for turbo coded additive white Gaussian noise (AWGN) and Rayleigh fading channels is proposed, The log likelihood ratio (LLR) generated by the turbo decoder is exploited via the use of a q-bit scalar soft-decision demodulator. The concatenation of the turbo encoder, modulator, AWGN channel or Rayleigh fading channel, turbo decoder, and q-bit soft-decision demodulator is modeled as an expanded discrete memoryless channel (DMC). A COVQ scheme for this expanded discrete channel is designed. Numerical results indicate substantial performance improvements over traditional tandem coding systems, COVQ schemes designed for hard-decision demodulated turbo coded channels (q=1), as well as performance gains over a recent soft decoding COVQ scheme by Ho (see IEEE Commun. Lett., vol.3, p.208-10, 1999)     

Diversity and coding for FH/MFSK systems with fading and jamming.II. Selective diversity

For pt.1 see ibid., vol.COM-35, p.1329-41 (1987). A performance evaluation is presented for selective diversity with feedback for frequency-hopping M-ary frequency-shift-keyed systems operating over Rayleigh faded channels in the presence of partial-band noise and partial-band tone jamming. The behavior of uncoded and coded systems is studied. For coded systems, the performance is evaluated for hard-decision receivers without channel state information and soft-decision receivers with perfect jammer state information. The results demonstrate that the performance of uncoded FH/MFSK with selective diversity is unacceptable. However, this diversity technique can offer definite improvements for coded FH/MFSK systems. Specifically, the effectiveness of selective diversity signaling depends on the provision of a feedback channel between the transmitter and receiver to provide the transmitter with the fading gains of the independently faded channels. To obtain an improvement from the selective diversity signaling scheme described here, there must be multiple independently faded channels between the transmitter and receiver. If not, the performance of the selective diversity signaling scheme will be identical to the performance of FH/MFSK without diversity     

Algebraic soft-decision decoding of Reed-Solomon codes

A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed. This list-decoding algorithm is algebraic in nature and builds upon the interpolation procedure proposed by Guruswami and Sudan(see ibid., vol.45, p.1757-67, Sept. 1999) for hard-decision decoding. Algebraic soft-decision decoding is achieved by means of converting the probabilistic reliability information into a set of interpolation points, along with their multiplicities. The proposed conversion procedure is shown to be asymptotically optimal for a certain probabilistic model. The resulting soft-decoding algorithm significantly outperforms both the Guruswami-Sudan decoding and the generalized minimum distance (GMD) decoding of Reed-Solomon codes, while maintaining a complexity that is polynomial in the length of the code. Asymptotic analysis for alarge number of interpolation points is presented, leading to a geo- metric characterization of the decoding regions of the proposed algorithm. It is then shown that the asymptotic performance can be approached as closely as desired with a list size that does not depend on the length of the code.     

LTE中PDCCH有效控制信道元素的软判决检测算法

在LTE系统的PDCCH盲检中,检测信道中的有效控制信道元素（CCE）是一种常用的盲检加速方法。对于有效CCE的检测,基于硬判决的能量检测与融合判决相结合的方法是一种常用手段,但随着信道环境的下降这种方法的可靠性也会大幅降低。为了确保低较差信道条件下的可靠性和提高算法性能,本文提出了一种基于软判决的有效CCE检测算法。利用奈曼-皮尔逊准则推导出满足系统可靠性需求的最佳软判决检测阈值,降低错检概率,提高了原有检测方法的性能。本文推导了判决的软信息形式,给出检测的软判决门限。仿真结果证明了理论推导的正确性。与硬判决相比,如系统在SNR = -2dB,漏警率均为0.15时,软判决虚警率降低了82%,表明所提算法可以有效保证检测的低漏警率并降低虚警的发生概率。      

Low complexity iterative decoding for bit-interleaved coded modulation

Bit-interleaved coded modulation with iterative decoding (ID) is an effective scheme for both AWGN and fading channels because it simultaneously realizes large Euclidean distance and high diversity. In the literature, ID schemes with hard-decision feedback (HDF), as well as soft-decision feedback (SDF), have been investigated. While HDF/ID exhibits a performance inferior to SDF/ID, it is much simpler to implement. To enhance the performance of HDF/ID with moderate additional complexity, we propose a uniform soft-decision feedback ID (USF/ID) scheme. The proposed scheme is applicable in both single antenna and multiple antenna communication systems. The simulation results verify that it achieves impressive performance gain over HDF/ID and has a practically more attractive implementation than SDF/ID, especially for complexity-constrained wireless applications.     

Bounds on the bit error probability of a linear cyclic code overGF(2l) and its extended code

An upper bound on the bit-error probability (BEP) of a linear cyclic code over GF(2^l) with hard-decision (HD) maximum-likelihood (ML) decoding on memoryless symmetric channels is derived. Performance results are presented for Reed-Solomon codes on GF(32), GF(64), and GF(128). Also, a union upper bound on the BEP of a linear cyclic code with either hard- or soft-decision ML decoding is developed, as well as the corresponding bounds for the extended code of a linear cyclic code. Using these bounds, which are tight at low bit error rate, the performance advantage of soft-decision (SD) ML and HD ML over bounded-distance (BD) decoding is established     

基于双向逐幸存路径处理的空时格形码软判决自适应解码

本文提出一种针对TDMA下行链路的空时格形码自适应解码算法.为充分利用下行链路相邻时隙前导序列中的正交导引信号,该解码算法采用了双向逐幸存路径处理技术——正向处理利用基于当前时隙前导序列的自适应信道估计实现正向解码,并将软判决结果传递给反向处理模块;以正向软判决为先验知识,反向处理利用基于下一时隙前导序列的自适应信道估计实现反向解码,并将反向软判决作为最终结果输出.计算机仿真结果表明:在存在卷积外码的情况下,与基于最大似然序列检测的单向硬判决解码相比,基于所提出算法的软判决解码在多普勒频移小于60赫兹的时变信道中可提供1～2dB的增益.     

Cutoff rates of multichannel MFSK and DPSK signals in mobilesatellite communications

This paper studies the coded performance of multichannel MFSK and DPSK signalings in mobile satellite environments characterized by various kinds of multipath fading. Rician, Rician/lognormal, and a convex combination of Rician and Rician/lognormal or Rayleigh/lognormal distributions are used to model these communication channels. We investigate the minimum average signal-energy-to-noise ratio required to yield a cutoff rate that is greater than or equal to a given code rate. Also examined are system design issues such as the effect of quantization and metric conversion, the choice between binary codes and M-ary symbol codes, the optimization of the diversity order and the signal size, and the order of deinterleaving and diversity combining. Numerical examples are given to answer concerns raised by these issues     

Soft decision-directed MAP estimate of fast Rayleigh flat fading channels

An iterative receiver with soft-decision feedback is derived by using the expectation-maximization algorithm for maximum a posteriori estimate of fast Rayleigh flat fading channels. Simulation results indicate that in a fast fading environment, the derived receiver can perform better than an iterative receiver with hard-decision feedback.     

Soft-decision COVQ for Rayleigh-fading channels

A channel-optimized vector quantizer (COVQ) scheme that exploits the channel soft-decision information is proposed. The scheme is designed for stationary memoryless Gaussian and Gauss-Markov sources transmitted over BPSK-modulated Rayleigh-fading channels. It is demonstrated that substantial coding gains of 2-3 dB in channel signal-to-noise ratio (SNR) and 1-1.5 dB in source signal-to-distortion ratio (SDR) can be achieved over COVQ systems designed for discrete (hard-decision demodulated) channels     

Architecture and Implementation of an Interpolation Processor for Soft-Decision Reed–Solomon Decoding

Reed-Solomon codes are powerful error-correcting codes that can be found in many digital communications standards. Recently, there has been an interest in soft-decision decoding of Reed-Solomon codes, incorporating reliability information from the channel into the decoding process. The Koetter-Vardy algorithm is a soft-decision decoding algorithm for Reed-Solomon codes which can provide several dB of gain over traditional hard-decision decoders. The algorithm consists of a soft-decision front end to the interpolation-based Guruswami-Sudan list decoder. The main computational task in the algorithm is a weighted interpolation of a bivariate polynomial. We propose a parallel architecture for the hardware implementation of bivariate interpolation for soft-decision decoding. The key feature is the embedding of both a binary tree and a linear array into a 2-D array processor, enabling fast polynomial evaluation operations. An field-programmable gate array interpolation processor was implemented and demonstrated at a clock frequency of 23 MHz, corresponding to decoding rates of 10-15 Mb/s     

A Moment-Generating Function (MGF) Derivative-Based Unified Analysis of Incoherent Diversity Reception of M-ary Orthogonal Signals over Independent and Correlated Fading Channels

Exact, closed-form, error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician, and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. In addition, a concise, derivative formula is derived for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (DPSK) signals. All of these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signaling over generalized fading channels with arbitrary parameters.     

Iterative receivers with bit-level cancellation and detection for MIMO-BICM systems

The multiple-input multiple-output (MIMO) detection in the iterative receiver is investigated for a modulation of square constellation. For computationally efficient MIMO detection, we employ the hard-decision bit-level cancellation (BLC) to reduce the dimension of the MIMO detection as it has advantages over the symbol-level cancellation: 1) it can provide better performance and 2) the extrinsic bit information can be directly used for the BLC. A set of reliably decoded bits from the channel decoder in iterations is used for hard-decision BLC to approximate the maximum a posteriori probability (MAP) detection under the partial MAP detection principle. For the bits that are not canceled, the ing using projection is employed to approximate the MAP detection. This approach is applicable for a lower order modulation. For a higher order modulation, the minimum mean square error (MMSE) filtering with soft-decision cancellation (SC) is applied to further mitigate the bits that are not canceled.     

Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.