On the Minimum Distance Properties of Weighted Nonbinary Repeat Multiple-Accumulate Codes

We consider weighted nonbinary repeat multiple- accumulate (WNRMA) code ensembles obtained from the serial concatenation of a nonbinary rate-1/n repetition code and the cascade of L≥1 accumulators, where each encoder is followed by a nonbinary random weighter. We derive the exact weight enumerator of nonbinary accumulators and subsequently give the weight enumerators for WNRMA code ensembles. We formally prove that the symbol-wise minimum distance of WNRMA code ensembles asymptotically grows linearly with the block length when L≥3 and n≥2, and L = 2 and n≥3, for all powers of primes q ≥ 3 considered, where q is the field size. Thus, WNRMA code ensembles are asymptotically good for these parameters

Transceiver Design with Iterative Decoding of Capacity-Approaching codes over Fading channels

Ph.DDOCTOR OF PHILOSOPH

Introduction to Forward-Error-Correcting Coding

This reference publication introduces forward error correcting (FEC) and stresses definitions and basic calculations for use by engineers. The seven chapters include 41 example problems, worked in detail to illustrate points. A glossary of terms is included, as well as an appendix on the Q function. Block and convolutional codes are covered

Performance of weighted nonbinary repeat-accumulate codes over GF(Q) with Q-ary orthogonal modulation

An approximate upper bound is derived to the maximum likelihood decoding threshold of weighted nonbinary repeat-accumulate (WNRA) codes over GF(q) with q-ary orthogonal modulation and coherent detection over the additive white Gaussian noise channel. As with binary RA codes, WNRA codes show the potential for achieving the channel capacity with decreasing code rate for large enough q.X112sciescopu

Design and analysis of turbo and repeat-accumulate codes over GF(q) with q-ary orthogonal modulation

DoctorQAM과 같이 동기식 검출 (coherent detection)이 필요한 변조방식에서는 위상 추정 오류에 의한 성능 열화를 최소화하기 위해 고가의 안정적인 발진기 혹은 다수의 파일럿 심볼을 필요로 한다. 따라서 직교 변조 (orthogonal modulation)와 비동기식 검출 (noncoherent detection)의 조합 (비동기 직교 변조 방식)은 위상 추정 오류에 의한 성능 열화가 심각한 경우 혹은 저비용 수신기가 필요한 경우에 효과적으로 사용된다.그러나 비동기식 검출 방식으로 인해 직교 비동기 직교 변조 방식은 동기 직교 변조 방식 대비 성능 열화가 크게 발생할 수 있다. 따라서 대역이 제한되지 않는 직교 변조 방식의 채널 용량 달성을 위해서는 동기 직교 변조 방식 또한 고려될 수 있다. 실질적으로 q-ary 주파수 변조 시스템의 CM 채널 용량에 근접하기 위해서는 GF(q)상의 터보 부호 혹은 repeat-accumulate (RA) 부호와 같은 강력한 q-ary 부호화 방식이 필요하다. 따라서, 먼저 본 논문에서는 q-ary 직교 변조를 사용하는 GF(q)상의 병렬 연접 터보 부호의 매우 간단한 설계 방식을 제안한다. 제안하는 설계 방식은 기존의 포괄적 컴퓨터 탐색 방법과는 달리 어떠한 q값과 2보다 큰 어떠한 구속장 길이에 대해서도 체계적인 부호 설계가 가능하게 한다. 그리고 반복 복호 (iterative decoding) 실험결과 제안하는 설계 방식을 사용하여 설계된 GF(q)상의 병렬 연접 터보 부호는 기존의 컴퓨터 탐색 알고리즘으로 설계된 부호와 거의 동일한 성능을 보인다. 또한 설계된 부호는 가산 백색 가우시안 잡음 채널 및 독립적인 레일리 페이딩 채널 하에서 채널 용량에 근접한다.다음으로 본 논문에서는 q-ary 동기 및 비동기 직교 변조 방식 그리고 가산 백색 가우시안 잡음 채널 환경 하에서, 이진 RA 부호의 비이진 확장 형태인 GF(q)상의 가중 비이진 RA (weighted nonbinary RA, WNRA) 부호를 고려한다. WNRA 부호의 근사화된 부호어 무게 분포 (codeword weight distribution)를 구하고 Divsalar의 상계 (upper bound)를 동기식 직교 변조의 경우로 확장 유도하였다. 이를 이용하여 WNRA 부호의 최대 우도 복호 임계 (maximum likelihood decoding threshold)의 근사화를 수행하였다. 전산 실험 결과 유도된 WNRA 부호의 근사 최대 우도 복호 임계값은 부호율이 감소하고 q값이 증가할수록 채널 용량에 근접하게 된다. 이는 동기식 q-ary 직교 변조를 사용하는 GF(q)상의 WNRA 부호 또한 BPSK 변조를 사용하는 이진 RA 부호와 마찬가지로 가산 백색 가우시안 잡음 채널의 채널 용량을 달성할 수 있는 가능성이 있음을 말해준다.마지막으로 본 논문에서는 밀도 진화 (density evolution)하에서 메시지 밀도의 가우시안 근사화를 이용하여 q-ary 직교 변조를 사용하는 GF(q)상의 불균일 WNRA (irregular WNRA, IWNRA) 부호를 설계한다. 기존의 이진 RA 부호에 대한 가우시안 근사화를 비이진의 경우로 확장함으로써 채널 용량에 근접하는 다양한 부호율을 갖는 IWNRA 부호의 설계 방법을 제안한다. 전산 실험 결과 설계된 IWNRA 부호는 가산 백색 가우시안 잡음 채널 환경 및 동기 직교 변조 하에서 채널 용량에 근접하는 것을 확인할 수 있다.With modulation schemes requiring coherent detection such as quadrature-amplitude modulation, expensive, stable oscillators and/or a large number of pilot symbols are required with complex receiver circuitry in order to minimize the performance loss due to carrier phase estimation errors. Hence, the combination of orthogonal modulation with noncoherent detection is especially attractive for cases where low cost receivers are desired and/or when the performance loss due to carrier phase estimation errors is significant.However, due to the noncoherent combining penalty, the performance of orthogonal modulation with noncoherent detection is significantly degraded compared to coherent detection. In order to fully exploit the capacity-achieving performance of orthogonal modulation when the channel is not bandwidth-limited, orthogonal modulation with coherent detection may also be considered.In this thesis, we consider orthogonal frequency-shift keying (FSK) as a form of orthogonal modulation. In order to practically approach the channel capacity with q-ary FSK, powerful q-ary coding schemes such as turbo codes and repeat-accumulate (RA) codes defined over GF(q) are necessary. Hence, first, we propose a very simple design rule for parallel concatenated turbo codes over GF(q) with q-ary orthogonal modulation. Unlike previously proposed exhaustive search methods, the proposed design rule allows straightforward and systematic code designs for any value of q>=2 and any constraint length greater than 2. We demonstrate that parallel concatenated turbo codes over GF(q) designed using the proposed design rule perform nearly identical to conventional codes designed via exhaustive computer search. Computer simulation results are presented for the frame error rate (FER) under AWGN and independent Rayleigh fading channels with both coherent and noncoherent detection. Next, we consider the nonbinary extension of the binary RA codes, i.e., weigh-ted nonbinary RA (WNRA) codes over GF(q) with q-ary orthogonal modulation and coherent detection under the AWGN channel. We derive an approximate codeword weight distribution (CWD) of WNRA codes and extend Divsalar's bound to the case of orthogonal modulation with coherent detection. Then, using the derived CWD and the extended Divsalar's bound, an approximate maximum likelihood (ML) decoding threshold for WNRA codes is derived. Numerical results indicate that the derived approximate ML decoding threshold of WNRA codes approaches channel capacity with decreasing code rate and increasing q. This implies that, as with binary RA codes with BPSK modulation, WNRA codes over GF(q) with q-ary orthogonal modulation and coherent detection also have the potential for achieving channel capacity under the AWGN channel.Finally we design irregular WNRA (IWNRA) codes over GF(q) with q-ary orthogonal modulation using a Gaussian approximation to the distribution of the message vectors under density evolution. Simulation results indicate that the resulting IWNRA codes with a frame length of 2520 information bits achieve an FER of 10^{-1} within 0.55 to 1.18 dB of channel capacity under the AWGN channel with coherent and nonocoherent detection

Coded-OFDM for PLC systems in non-Gaussian noise channels

PhD ThesisNowadays, power line communication (PLC) is a technology that uses the power line grid for communication purposes along with transmitting electrical energy, for providing broadband services to homes and offices such as high-speed data, audio, video and multimedia applications. The advantages of this technology are to eliminate the need for new wiring and AC outlet plugs by using an existing infrastructure, ease of installation and reduction of the network deployment cost. However, the power line grid is originally designed for the transmission of the electric power at low frequencies; i.e. 50/60 Hz. Therefore, the PLC channel appears as a harsh medium for low-power high-frequency communication signals. The development of PLC systems for providing high-speed communication needs precise knowledge of the channel characteristics such as the attenuation, non-Gaussian noise and selective fading. Non-Gaussian noise in PLC channels can classify into Nakagami-m background interference (BI) noise and asynchronous impulsive noise (IN) modelled by a Bernoulli-Gaussian mixture (BGM) model or Middleton class A (MCA) model. Besides the effects of the multipath PLC channel, asynchronous impulsive noise is the main reason causing performance degradation in PLC channels. Binary/non-binary low-density parity check B/NB-(LDPC) codes and turbo codes (TC) with soft iterative decoders have been proposed for Orthogonal Frequency Division Multiplexing (OFDM) system to improve the bit error rate (BER) performance degradation by exploiting frequency diversity. The performances are investigated utilizing high-order quadrature amplitude modulation (QAM) in the presence of non-Gaussian noise over multipath broadband power-line communication (BBPLC) channels. OFDM usually spreads the effect of IN over multiple sub-carriers after discrete Fourier transform (DFT) operation at the receiver, hence, it requires only a simple single-tap zero forcing (ZF) equalizer at the receiver. The thesis focuses on improving the performance of iterative decoders by deriving the effective, complex-valued, ratio distributions of the noise samples at the zeroforcing (ZF) equalizer output considering the frequency-selective multipath PLCs, background interference noise and impulsive noise, and utilizing the outcome for computing the apriori log likelihood ratios (LLRs) required for soft decoding algorithms. On the other hand, Physical-Layer Network Coding (PLNC) is introduced to help the PLC system to extend the range of operation for exchanging information between two users (devices) using an intermediate relay (hub) node in two-time slots in the presence of non-Gaussian noise over multipath PLC channels. A novel detection scheme is proposed to transform the transmit signal constellation based on the frequency-domain channel coefficients to optimize detection at the relay node with newly derived noise PDF at the relay and end nodes. Additionally, conditions for optimum detection utilizing a high-order constellation are derived. The closedform expressions of the BER and average BER upper-bound (AUB) are derived for a point-to-point system, and for a PLNC system at the end node to relay, relay to end node and at the end-to-end nodes. Moreover, the convergence behaviour of iterative decoders is evaluated using EXtrinsic Information Transfer (EXIT) chart analysis and upper bound analyses. Furthermore, an optimization of the threshold determination for clipping and blanking impulsive noise mitigation methods are derived. The proposed systems are compared in performance using simulation in MATLAB and analytical methods.Ministry of Higher Education in Ira

Sparse graph-based coding schemes for continuous phase modulations

The use of the continuous phase modulation (CPM) is interesting when the channel represents a strong non-linearity and in the case of limited spectral support; particularly for the uplink, where the satellite holds an amplifier per carrier, and for downlinks where the terminal equipment works very close to the saturation region. Numerous studies have been conducted on this issue but the proposed solutions use iterative CPM demodulation/decoding concatenated with convolutional or block error correcting codes. The use of LDPC codes has not yet been introduced. Particularly, no works, to our knowledge, have been done on the optimization of sparse graph-based codes adapted for the context described here. In this study, we propose to perform the asymptotic analysis and the design of turbo-CPM systems based on the optimization of sparse graph-based codes. Moreover, an analysis on the corresponding receiver will be done

Signal optimization for Galileo evolution

Global Navigation Satellite System (GNSS) are present in our daily lives. Moreover, new users areemerging with further operation needs involving a constant evolution of the current navigationsystems. In the current framework of Galileo (GNSS European system) and especially within theGalileo E1 Open Service (OS), adding a new acquisition aiding signal could contribute to providehigher resilience at the acquisition phase, as well as to reduce the time to first fix (TTFF).Designing a new GNSS signal is always a trade-off between several performance figures of merit.The most relevant are the position accuracy, the sensitivity and the TTFF. However, if oneconsiders that the signal acquisition phase is the goal to design, the sensitivity and the TTFF havea higher relevance. Considering that, in this thesis it is presented the joint design of a GNSS signaland the message structure to propose a new Galileo 2nd generation signal, which provides ahigher sensitivity in the receiver and reduce the TTFF. Several aspects have been addressed inorder to design a new signal component. Firstly, the spreading modulation definition must considerthe radio frequency compatibility in order to cause acceptable level of interference inside the band.Moreover, the spreading modulation should provide good correlation properties and goodresistance against the multipath in order to enhance the receiver sensitivity and to reduce theTTFF. Secondly, the choice of the new PRN code is also crucial in order to ease the acquisitionphase. A simple model criterion based on a weighted cost function is used to evaluate the PRNcodes performance. This weighted cost function takes into account different figures of merit suchas the autocorrelation, the cross-correlation and the power spectral density. Thirdly, the design ofthe channel coding scheme is always connected with the structure of the message. A joint designbetween the message structure and the channel coding scheme can provide both, reducing theTTFF and an enhancement of the resilience of the decoded data. In this this, a new method to codesign the message structure and the channel coding scheme for the new G2G signal isproposed. This method provides the guideline to design a message structure whose the channelcoding scheme is characterized by the full diversity, the Maximum Distance Separable (MDS) andthe rate compatible properties. The channel coding is essential in order to enhance the datademodulation performance, especially in harsh environments. However, this process can be verysensitive to the correct computation of the decoder input. Significant improvements were obtainedby considering soft inputs channel decoders, through the Log Likelihood Ratio LLRs computation.However, the complete knowledge of the channel state information (CSI) was usually considered,which it is infrequently in real scenarios. In this thesis, we provide new methods to compute LLRlinear approximations, under the jamming and the block fading channels, considering somestatistical CSI. Finally, to transmit a new signal in the same carrier frequency and using the sameHigh Power Amplifier (HPA) generates constraints in the multiplexing design, since a constant orquasi constant envelope is needed in order to decrease the non-linear distortions. Moreover, themultiplexing design should provide high power efficiency to not waste the transmitted satellitepower. Considering the precedent, in this thesis, we evaluate different multiplexing methods,which search to integrate a new binary signal in the Galileo E1 band while enhancing thetransmitted power efficiency. Besides that, even if the work is focused on the Galileo E1, many ofthe concepts and methodologies can be easily extended to any GNSS signa