List Decoding with Double Samplers

We develop the notion of "double samplers", first introduced by Dinur and Kaufman [Proc. 58th FOCS, 2017], which are samplers with additional combinatorial properties, and whose existence we prove using high dimensional expanders. We show how double samplers give a generic way of amplifying distance in a way that enables efficient list-decoding. There are many error correcting code constructions that achieve large distance by starting with a base code $C$ with moderate distance, and then amplifying the distance using a sampler, e.g., the ABNNR code construction [IEEE Trans. Inform. Theory, 38(2):509--516, 1992.]. We show that if the sampler is part of a larger double sampler then the construction has an efficient list-decoding algorithm and the list decoding algorithm is oblivious to the base code $C$ (i.e., it runs the unique decoder for $C$ in a black box way). Our list-decoding algorithm works as follows: it uses a local voting scheme from which it constructs a unique games constraint graph. The constraint graph is an expander, so we can solve unique games efficiently. These solutions are the output of the list decoder. This is a novel use of a unique games algorithm as a subroutine in a decoding procedure, as opposed to the more common situation in which unique games are used for demonstrating hardness results. Double samplers and high dimensional expanders are akin to pseudorandom objects in their utility, but they greatly exceed random objects in their combinatorial properties. We believe that these objects hold significant potential for coding theoretic constructions and view this work as demonstrating the power of double samplers in this context

Doctor of Philosophy

dissertationThe continuous growth of wireless communication use has largely exhausted the limited spectrum available. Methods to improve spectral efficiency are in high demand and will continue to be for the foreseeable future. Several technologies have the potential to make large improvements to spectral efficiency and the total capacity of networks including massive multiple-input multiple-output (MIMO), cognitive radio, and spatial-multiplexing MIMO. Of these, spatial-multiplexing MIMO has the largest near-term potential as it has already been adopted in the WiFi, WiMAX, and LTE standards. Although transmitting independent MIMO streams is cheap and easy, with a mere linear increase in cost with streams, receiving MIMO is difficult since the optimal methods have exponentially increasing cost and power consumption. Suboptimal MIMO detectors such as K-Best have a drastically reduced complexity compared to optimal methods but still have an undesirable exponentially increasing cost with data-rate. The Markov Chain Monte Carlo (MCMC) detector has been proposed as a near-optimal method with polynomial cost, but it has a history of unusual performance issues which have hindered its adoption. In this dissertation, we introduce a revised derivation of the bitwise MCMC MIMO detector. The new approach resolves the previously reported high SNR stalling problem of MCMC without the need for hybridization with another detector method or adding heuristic temperature scaling terms. Another common problem with MCMC algorithms is an unknown convergence time making predictable fixed-length implementations problematic. When an insufficient number of iterations is used on a slowly converging example, the output LLRs can be unstable and overconfident, therefore, we develop a method to identify rare, slowly converging runs and mitigate their degrading effects on the soft-output information. This improves forward-error-correcting code performance and removes a symptomatic error floor in bit-error-rates. Next, pseudo-convergence is identified with a novel way to visualize the internal behavior of the Gibbs sampler. An effective and efficient pseudo-convergence detection and escape strategy is suggested. Finally, the new excited MCMC (X-MCMC) detector is shown to have near maximum-a-posteriori (MAP) performance even with challenging, realistic, highly-correlated channels at the maximum MIMO sizes and modulation rates supported by the 802.11ac WiFi specification, 8x8 256 QAM. Further, the new excited MCMC (X-MCMC) detector is demonstrated on an 8-antenna MIMO testbed with the 802.11ac WiFi protocol, confirming its high performance. Finally, a VLSI implementation of the X-MCMC detector is presented which retains the near-optimal performance of the floating-point algorithm while having one of the lowest complexities found in the near-optimal MIMO detector literature

Accessing Accelerator Parameters with Mathematica via the Passerelle

To access the control system of the accelerators in the PS Complex at CERN from an office PC running Mathematica in a Windows environment, the package PasserelleUtils has been implemented. This package is based on the functions provided by the Passerelle, a bridge between office PCs and the accelerator control system at CERN running Linux. It allows read and write access by executing synchronous function calls to accelerator parameters directly from Mathematica. The seamless integration of data from the accelerators into the powerful mathematical programming and graphics environment of Mathematica facilitates their analysis and post-processing. Parameter settings can be derived and sent to the accelerator equipment directly in Mathematica. Dedicated functions allow for easy read access to vector tables and sampler data as used to control and operate equipment in the PS Complex. Furthermore, it removes limitations inherent to the conventional way of using EXCEL to exploit the functions of the Passerelle. This note can be referred to as a manual of the PasserelleUtils package. After a brief introduction to its functionality, a detailed description of all functions provided is given. Several simple examples illustrate the usefulness

A sticky HDP-HMM with application to speaker diarization

We consider the problem of speaker diarization, the problem of segmenting an audio recording of a meeting into temporal segments corresponding to individual speakers. The problem is rendered particularly difficult by the fact that we are not allowed to assume knowledge of the number of people participating in the meeting. To address this problem, we take a Bayesian nonparametric approach to speaker diarization that builds on the hierarchical Dirichlet process hidden Markov model (HDP-HMM) of Teh et al. [J. Amer. Statist. Assoc. 101 (2006) 1566--1581]. Although the basic HDP-HMM tends to over-segment the audio data---creating redundant states and rapidly switching among them---we describe an augmented HDP-HMM that provides effective control over the switching rate. We also show that this augmentation makes it possible to treat emission distributions nonparametrically. To scale the resulting architecture to realistic diarization problems, we develop a sampling algorithm that employs a truncated approximation of the Dirichlet process to jointly resample the full state sequence, greatly improving mixing rates. Working with a benchmark NIST data set, we show that our Bayesian nonparametric architecture yields state-of-the-art speaker diarization results.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS395 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding

We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions. Important performance measures for a coding scheme are its maximum tolerable error rate $\rho$, communication complexity $N$, and computational complexity. We give the first coding scheme for the standard setting which performs optimally in all three measures: Our randomized non-adaptive coding scheme has a near-linear computational complexity and tolerates any error rate $\delta < 1/4$ with a linear $N = \Theta(n)$ communication complexity. This improves over prior results which each performed well in two of these measures. We also give results for other settings of interest, namely, the first computationally and communication efficient schemes that tolerate $\rho < \frac{2}{7}$ adaptively, $\rho < \frac{1}{3}$ if only one party is required to decode, and $\rho < \frac{1}{2}$ if list decoding is allowed. These are the optimal tolerable error rates for the respective settings. These coding schemes also have near linear computational and communication complexity. These results are obtained via two techniques: We give a general black-box reduction which reduces unique decoding, in various settings, to list decoding. We also show how to boost the computational and communication efficiency of any list decoder to become near linear.Comment: preliminary versio

차세대 자동차용 카메라 데이터 통신을 위한 비대칭 동시 양방향 송수신기의 설계

학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2022.2. 정덕균.본 학위 논문에서는 차세대 자동차용 카메라 링크를 위해 높은 속도의 4레벨 펄스 진폭 변조 신호와 낮은 속도의 2레벨 펄스 진폭 변조 신호를 통신하는 비대칭 동시 양방향 송수신기의 설계 기술에 대해 제안하고 검증되었다. 첫번째 프로토타입 설계에서는, 10B6Q 직류 밸런스 코드를 탑재한 4레벨 펄스 진폭 변조 송신기와 고정된 데이터와 참조 레벨을 가지는 4레벨 펄스 진폭 변조 적응형 수신기에 대한 내용이 기술되었다. 4레벨 펄스 진폭 변조 송신기에서는 교류 연결 링크 시스템에 대응하기 위한 면적 및 전력 효율성이 좋은 10B6Q 코드가 제안되었다. 이 코드는 직류 밸런스를 맞추고 연속적으로 같은 심볼을 가지는 길이를 6개로 제한 시킨다. 비록 여기서는 입력 데이터 길이 10비트를 사용하였지만, 제안된 기술은 카메라의 다양한 데이터 타입에 대응할 수 있도록 입력 데이터 길이에 대한 확장성을 가진다. 반면, 4레벨 펄스 진폭 변조 적응형 수신기에서는, 샘플러의 옵셋을 최적으로 제거하여 더 낮은 비트에러율을 얻기 위해서, 기존의 데이터 및 참조 레벨을 조절하는 대신, 이 레벨들은 고정시키고 가변 게인 증폭기를 적응형으로 조절하도록 하였다. 상기 10B6Q 코드 및 고정 데이터 및 참조레벨 기술을 가진 프로토타입 칩들은 40 나노미터 상호보완형 메탈 산화 반도체 공정으로 제작되었고 칩 온 보드 형태로 평가되었다. 10B6Q 코드는 합성 게이트 숫자는 645개와 함께 단 0.0009 mm2 의 면적 만을 차지한다. 또한, 667 MHz 동작 주파수에서 단 0.23 mW 의 전력을 소모한다. 10B6Q 코드를 탑재한 송신기에서 8-Gb/s 4레벨 펄스 진폭 변조 신호를 고정 데이터 및 참조 레벨을 가지는 적응형 수신기로 12-m 케이블 (22-dB 채널 로스) 을 통해서 보낸 결과 최소 비트 에러율 108 을 달성하였고, 비트 에러율 105 에서는 아이 마진이 0.15 UI x 50 mV 보다 크게 측정되었다. 송수신기를 합친 전력 소모는 65.2 mW (PLL 제외) 이고, 성과의 대표수치는 0.37 pJ/b/dB 를 보여주었다. 첫번째 프로토타입 설계을 포함하여 개선된 두번째 프로토타입 설계에서는, 12-Gb/s 4레벨 펄스 진폭 변조 정방향 채널 신호와 125-Mb/s 2레벨 펄스 진폭 변조 역방향 채널 신호를 탑재한 비대칭 동시 양방향 송수신기에 대해 기술되고 검증되었다. 제안된 넓은 선형 범위를 가지는 하이브리드는 gmC 저대역 통과 필터와 에코 제거기와 함께 아웃바운드 신호를 24 dB 이상 효율적으로 감소시켰다. 또한, 넓은 선형 범위를 가지는 하이브리드와 함께 게인 감소기를 형성하게 되는 선형 범위 증폭기를 통해 4레벨 펄스 진폭 변조 신호의 선형성과 진폭의 트레이드 오프 관계를 깨는 것이 가능하였다. 동시 양방향 송수신기 칩은 40 나노미터 상호보완형 메탈 산화 반도체 공정으로 제작되었다. 상기 설계 기술들을 이용하여, 4레벨 펄스 진폭 변조 및 2레벨 펄스 진폭 변조 송수신기 모두 5m 채널 (채널 로스 15.9 dB) 에서 1E-12 보다 낮은 비트 에러율을 달성하였고, 총 78.4 mW 의 전력 소모를 기록하였다. 종합적인 송수신기는 성과 대표지표로 0.41 pJ/b/dB 와 함께 동시 양방향 통신 아래에서 4레벨 펄스 진폭 변조 신호 및 2레벨 펄스 진폭 변조 신호 각각에서 아이 마진 0.15 UI 와 0.57 UI 를 달성하였다. 이 수치는 성과 대표지표 0.5 이하를 가지는 기존 동시 양방향 송수신기와의 비교에서 최고의 아이 마진을 기록하였다.In this dissertation, design techniques of a highly asymmetric simultaneous bidirectional (SB) transceivers with high-speed PAM-4 and low-speed PAM-2 signals are proposed and demonstrated for the next-generation automotive camera link. In a first prototype design, a PAM-4 transmitter with 10B6Q DC balance code and a PAM-4 adaptive receiver with fixed data and threshold levels (dtLevs) are presented. In PAM-4 transmitter, an area- and power-efficient 10B6Q code for an AC coupled link system that guarantees DC balance and limited run length of six is proposed. Although the input data width of 10 bits is used here, the proposed scheme has an extensibility for the input data width to cover various data types of the camera. On the other hand, in the PAM-4 adaptive receiver, to optimally cancel the sampler offset for a lower BER, instead of adjusting dtLevs, the gain of a programmable gain amplifier is adjusted adaptively under fixed dtLevs. The prototype chips including above proposed 10B6Q code and fixed dtLevs are fabricated in 40-nm CMOS technology and tested in chip-on-board assembly. The 10B6Q code only occupies an active area of 0.0009 mm2 with a synthesized gate count of 645. It also consumes 0.23 mW at the operating clock frequency of 667 MHz. The transmitter with 10B6Q code delivers 8-Gb/s PAM-4 signal to the adaptive receiver using fixed dtLevs through a lossy 12-m cable (22-dB channel loss) with a BER of 1E-8, and the eye margin larger than 0.15 UI x 50 mV is measured for a BER of 1E-5. The proto-type chips consume 65.2 mW (excluding PLL), exhibiting an FoM of 0.37 pJ/b/dB. In a second prototype design advanced from the first prototypes, An asymmetric SB transceivers incorporating a 12-Gb/s PAM-4 forward channel and a 125-Mb/s PAM-2 back channel are presented and demonstrated. The proposed wide linear range (WLR) hybrid combined with a gmC low-pass filter and an echo canceller effectively suppresses the outbound signals by more than 24dB. In addition, linear range enhancer which forms a gain attenuator with WLR hybrid breaks the trade-off between the linearity and the amplitude of the PAM-4 signal. The SB transceiver chips are separately fabricated in 40-nm CMOS technology. Using above design techniques, both PAM-4 and PAM-2 SB transceivers achieve BER less than 1E-12 over a 5-m channel (15.9 dB channel loss), consuming 78.4 mW. The overall transceivers achieve an FoM of 0.41 pJ/b/dB and eye margin (at BER of 1E-12) of 0.15 UI and 0.57 UI for the forward PAM-4 and back PAM-2 signals, respectively, under SB communication. This is the best eye margin compared to the prior art SB transceivers with an FoM less than 0.5.CHAPTER 1 INTRODUCTION 1 1.1 MOTIVATION 1 1.2 DISSERTATION ORGANIZATION 4 CHAPTER 2 BACKGROUND ON AUTOMOTIVE CAMERA LINK 6 2.1 OVERVIEW 6 2.2 SYSTEM REQUIREMENTS 10 2.2.1 CHANNEL 10 2.2.2 POWER OVER DIFFERENTIAL LINE (PODL) 12 2.2.3 AC COUPLING AND DC BALANCE CODE 15 2.2.4 SIMULTANEOUS BIDIRECTIONAL COMMUNICATION 18 2.2.4.1 HYBRID 18 2.2.4.2 ECHO CANCELLER 20 2.2.5 ADAPTIVE RECEIVE EQUALIZATION 22 CHAPTER 3 AREA AND POWER EFFICIENT 10B6Q ENCODER FOR DC BALANCE 25 3.1 INTRODUCTION 25 3.2 PRIOR WORKS 28 3.3 PROPOSED AREA- AND POWER-EFFICIENT 10B6Q PAM-4 CODER 30 3.4 DESIGN OF THE 10B6Q CODE 33 3.4.1 PAM-4 DC BALANCE 35 3.4.2 PAM-4 TRANSITION DENSITY 35 3.4.3 10B6Q DECODER 37 3.5 IMPLEMENTATION AND MEASUREMENT RESULTS 40 CHAPTER 4 PAM-4 TRANSMITTER AND ADAPTIVE RECEIVER WITH FIXED DATA AND THRESHOLD LEVELS 45 4.1 INTRODUCTION 45 4.2 PRIOR WORKS 47 4.3 ARCHITECTURE AND IMPLEMENTATION 49 4.2.1 PAM-4 TRANSMITTER 49 4.2.2 PAM-4 ADAPTIVE RECEIVER 52 4.3 MEASUREMENT RESULTS 62 CHAPTER 5 ASYMMETRIC SIMULTANEOUS BIDIRECTIONAL TRANSCEIVERS USING WIDE LINEAR RANGE HYBRID 68 5.1 INTRODUCTION 68 5.2 PRIOR WORKS 70 5.3 WIDE LINEAR RANGE (WLR) HYBRID 75 5.3 IMPLEMENTATION 78 5.3.1 SERIALIZER (SER) DESIGN 78 5.3.2 DESERIALIZER (DES) DESIGN 79 5.4 HALF CIRCUIT ANALYSIS OF WLR HYBRID AND LRE 82 5.5 MEASUREMENT RESULTS 88 CHAPTER 6 CONCLUSION 97 BIBLIOGRAPHY 99 초 록 106박

List Decoding Random Euclidean Codes and Infinite Constellations

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $P$ and $N$ respectively, the list decoding capacity is equal to $\frac{1}{2}\log\frac{P}{N}$. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain number-theoretic conjecture is true, then the list size grows as a polynomial function of the gap-to-capacity