Alien noise in the vectored very-high-speed digital subscriber line (VDSL) system is part of the additive noise at the receiver and exhibits strong correlation among users. We present a per-tone co-operative alien noise cancellation (CoMAC) algorithm for the upstream (US) VDSL that can be applied subsequent to any self far-end-crosstalk (FEXT) mitigation strategy. CoMAC operates by predicting the noise seen by a given user based on the error samples from the remaining users. These errors are conveniently obtained after slicing the self-FEXT canceled signal of all the vectored users. We show that if the estimation of these errors is accurate, the proposed alien canceler achieves the Cramer-Rao lower bound (CRLB). In practice, the seamless rate adaptation (SRA) operation, which enables increased bit rate by increasing the bit-loading per-tone, can cause decision errors in any decision directed strategy. We also analyze the impact of these decision errors - an issue not addressed in the literature. We propose a strategy for bit-loading during the SRA operation by formulating a max-min optimization problem and demonstrate a possibility of a guaranteed (minimum) improvement in the per-user rate. Simulations indicate that performance of the algorithm can exceed the minimum value significantly in practical situations.

We present cooperative MIMO for alien noise cancellation (CoMAC): a per-tone, blind, low-complexity, linear, and adaptive noise whitening algorithm for alien crosstalk mitigation in upstream vectored VDSL systems. CoMAC directly acts on the residual errors of the vectored users after self-FEXT cancellation and frequency domain equalization, and thus, leverages the inherent alien-crosstalk-induced spatial correlation across users. CoMAC employs a low-complexity recursion scheme derived from the optimal MMSE noise whitener to non-disruptively initialize, engage, and adapt the noise canceller while the vectored users operate in data mode. Assuming reliable transmit symbol estimation at its input, we show that CoMAC achieves the Cramer-Rao lower bound. Further, the SNR improvements accruing from CoMAC can be translated into substantial rate improvements for upstream vectored VDSL.

We develop an analytical framework to evaluate the probability-of-miss and probability-of-false-alarm performance of an impulse noise (IN) detection algorithm for orthogonal frequency-domain multiplexing (OFDM) symbols based on monitoring the post-frequency-domain-equalizer (FEQ) instantaneous error at the output of the QAM constellation demapper over a range of tones (sub-carriers). Using the VDSL system as a reference, we further analyze the impact of impulse-noise detection error events at the scale of the OFDM symbol (miss and false alarm) on the bit-error-rate (BER) performance of interleaved Reed-Solomon (RS) codes with erasure-decoding. The analysis culminates with a sequence of steps to design the parameters of the frequency-domain IN detector based on the design BER of the communication system and practical transceiver features such as noise-margin and seamless-rate-adaptation (SRA). We conclude that a tone-error based frequency-domain IN detector monitoring 100 tones is capable of providing IN detection performance that does not cause a deterioration of the average BER below the VDSL system design BER of 10-7when interleaved RS coding with erasure-decoding is employed.

This paper introduces a new family of per frequency linear pre-coders, called off-diagonal MIMO pre-coders (ODMP), for discrete multi-tone (DMT) based digital subscriber line (DSL) systems. ODMP target pre-compensation of the off- diagonal self far-end cross talk (FEXT) terms in the downstream DSL-MIMO channel matrix. We derive a low complexity and adaptive ODMP that simultaneously maximizes the Shannon Capacities per tone, experienced by the (non-cooperative) end-users. The updating scheme makes use of the error samples computed in each receiver. No matrix inversion is required in the algorithm which may be used for learning, tracking, and incrementing the ODMP without any disruption of data service. Finite precision simulation results reveal that coding the complex error with 16 bits allows for the algorithm to reach "self-FEXT free" performance after only 150 iterations in the learning phase and 450 iterations in the incrementing phase.

We present an importance sampling (IS) technique for evaluating the word-error rate (WER) and bit-error rate (BER) performance of binary linear block codes under hard-decision decoding. This IS technique takes advantage of the invariance of the decoding outcome to the transition probability of the binary symmetric channel given a received error pattern, and is equivalent to the method of stratification for variance reduction. A thorough analysis of the accuracy of the proposed signal-to-noise-ratio- invariant IS (IIS) estimator based on computing its relative bias and standard deviation is provided. Under certain conditions, which may be achieved fairly easily for certain code and decoder combinations, we demonstrate that it is possible to use the proposed IIS technique to accurately evaluate the WER and BER to arbitrarily low values. Further, in all cases, the probability estimates obtained via IIS always serve as a lower bound on the true probability values.

We study the word-error-rate (WER) performance and the WER-minimizing decision thresholds$\pm t^{\ast}$for the class of row-column-diagonal (RCD) array codes and their generalizations on the binary symmetric channel with erasures (BSC/E) where decoding is via an extended bounded-distance decoder (e-BDD). This model applies to very-high-data-rate systems where soft-decision iterative decoding is impractical. We demonstrate that substantial WER performance gain can be obtained, especially at higher channel signal-to-noise ratio (CSNR) ($\hbox{CSNR}\triangleq 10\log_{10} (1/2\sigma^{2})$) values, by employing two optimal thresholds$(\pm t^{\ast})$chosen to minimize WER. We study the WER improvement and signal-to-noise ratio (SNR) performance gain as a function of code length$(n)$for fixed minimum distance$(d_{\min})$, and as a function of$(d_{\min})$for fixed$(n)$. A distinct difference in the behavior of WER versus the threshold$t$, and the optimal threshold$t^{\ast}$versus SNR, is observed between codes with odd and even$d_{\min}$, with the even$d_{\min}$codes exhibiting larger performance improvements when employing a BSC/E instead of a BSC.