Taux d'erreur | EPFL Graph Search

Le taux d'erreur ou B.E.R., abréviation de l'expression anglaise Bit Error Rate, désigne une valeur, relative au taux d'erreur, mesurée à la réception d'une transmission numérique, relative au niveau d'atténuation et/ou de perturbation d'un signal transmis. Ce phénomène survient également lors de l'échantillonnage (numérisation), lors de la lecture et de la sauvegarde des données (CD-R, DVD-R, disque dur, RAM...). Ce taux détermine le nombre d'erreurs apparues entre la modulation et juste après la démodulation du signal. Ce taux d’erreur ne tient généralement pas compte du codage des données sauf dans le cas d'une norme de transmission combinant modulation et correction d'erreur (exemple : QPSK). La cause des perturbations, donc de l'augmentation du taux d'erreur, peut être multiple : équipement ou réseau défectueux, pointage incorrect d'une antenne, interférences, longueur des câbles, etc. Le taux d'erreur (BER) s'exprime en puissance négative. Par exemple, 10^{-3}

A Novel Conflict-Free Memory and Processor Architecture for DVB-T2 LDPC Decoding

Alberto Jimenez Pacheco

In this paper, we present a flexible architecture for an LDPC decoder that fully exploits the structure of the codes defined in the DVB-T2 standard (Digital Video Broadcasting - Second Generation Terrestrial). We propose a processor and memory architecture which uses the flooding schedule and has no memory access conflicts, which are encountered in serial schedule decoders proposed in the literature. Thus, unlike previous works, we do not require any extra logic or ad hoc designs to resolve memory conflicts. Despite the typically slower convergence of flooding schedule compared to serial schedule decoders, our ar- chitecture meets the throughput and BER requirements specified in the DVB-T2 standard. Our design allows a trade-off between memory size and performance by the selection of the number of bits per message without affecting the general memory arrangement. Besides, our architecture is not algorithm specific: any check-node message processing algorithm can be used (Sum-Product, Min-Sum, etc.) without modifying the basic architecture. Furthermore, by simply adding relevant small ROM tables, we get a decoder that is fully compatible with all three second generation DVB standards (DVB-T2, DVB-S2 and DVB-C2). We present simulation results to demonstrate the viability of our solution both functionally and in terms of the bit-error rate performance. We also discuss the memory requirements and the throughput of the architecture, and present preliminary synthesis results in CMOS 130nm technology.

2011

Coding for Communications and Secrecy

Mani Bastaniparizi

Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, Arikan discovered polar codes; the only class of explicitly constructed low-complexity codes that achieve the capacity of any binary-input memoryless symmetric-output channel. Arikan's polar transform turns independent copies of a noisy channel into a collection of synthetic almost-noiseless and almost-useless channels. Polar codes are realized by sending data bits over the almost-noiseless channels and recovering them by using a low-complexity successive-cancellation (SC) decoder, at the receiver. In the first part of this thesis, we study polar codes for communications. When the underlying channel is an erasure channel, we show that almost all correlation coefficients between the erasure events of the synthetic channels decay rapidly. Hence, the sum of the erasure probabilities of the information-carrying channels is a tight estimate of the block-error probability of polar codes when used for communication over the erasure channel. We study SC list (SCL) decoding, a method for boosting the performance of short polar codes. We prove that the method has a numerically stable formulation in log-likelihood ratios. In hardware, this formulation increases the decoding throughput by 53% and reduces the decoder's size about 33%. We present empirical results on the trade-off between the length of the CRC and the performance gains in a CRC-aided version of the list decoder. We also make numerical comparisons of the performance of long polar codes under SC decoding with that of short polar codes under SCL decoding. Shannon's framework also quantifies the secrecy of communications. Wyner, in 1975, proposed a model for communications in the presence of an eavesdropper. It was shown that, at rates below the secrecy capacity, there exist reliable communication schemes in which the amount of information leaked to the eavesdropper decays exponentially in the block-length of the code. In the second part of this thesis, we study the rate of this decay. We derive the exact exponential decay rate of the ensemble-average of the information leaked to the eavesdropper in Wyner's model when a randomly constructed code is used for secure communications. For codes sampled from the ensemble of i.i.d. random codes, we show that the previously known lower bound to the exponent is exact. Our ensemble-optimal exponent for random constant-composition codes improves the lower bound extant in the literature. Finally, we show that random linear codes have the same secrecy power as i.i.d. random codes. The key to securing messages against an eavesdropper is to exploit the randomness of her communication channel so that the statistics of her observation resembles that of a pure noise process for any sent message. We study the effect of feedback on this approximation and show that it does not reduce the minimum entropy rate required to approximate a given process. However, we give examples where variable-length schemes achieve much larger exponents in this approximation in the presence of feedback than the exponents in systems without feedback. Upper-bounding the best exponent that block codes attain, we conclude that variable-length coding is necessary for achieving the improved exponents.

EPFL2017

Gaussian channel transmission of images and audio files using cryptcoding

Vladimir Ilievski

Random codes based on quasigroups (RCBQ) are cryptcodes, i.e. they are error-correcting codes, which provide information security. Cut-Decoding and 4-Sets-Cut-Decoding algorithms for these codes are defined elsewhere. Also, the performance of these codes for the transmission of text messages is investigated elsewhere. In this study, the authors investigate the RCBQ's performance with Cut-Decoding and 4-Sets-Cut-Decoding algorithms for transmission of images and audio files through a Gaussian channel. They compare experimental results for both coding/decoding algorithms and for different values of signal-to-noise ratio. In all experiments, the differences between the transmitted and decoded image or audio file are considered. Experimentally obtained values for bit-error rate and packet error rate and the decoding speed of both algorithms are compared. Also, two filters for enhancing the quality of the images decoded using RCBQ are proposed.

2019

Coding for Communications and Secrecy

Mani Bastaniparizi

EPFL2017