James E. Mazo

Diversity coding for transparent self-healing and fault-tolerant communication networks

A channel coding approach called diversity coding is introduced for self-healing and fault-tolerance in digital communication networks for nearly instantaneous recovery from link failures. To achieve this goal, the problem of link failures is treated as an erasure channel problem. Implementation details of this technique in existing and future communication networks are discussed. >

On the minimum distance problem for faster-than-Nyquist signaling

The authors reconsider the problem of determining the minimum distance between output sequences of an ideal band-limiting channel that are generated by uncoded binary sequences transmitted at a rate exceeding the Nyquist rate. For signaling rates up to about 25% faster than the Nyquist rate, it is shown that the minimum distance does not drop below the value which it would have in the ideal case wherein there is not intersymbol interference. Mathematically, the problem is to decide if the best L/sup 2/ Fourier approximation to the constant 1 on the interval (- sigma pi , sigma pi ), 0 0, with coefficients restricted to be =1 or =0, occurs when all coefficients are zero. This is shown to be optimal for 0.802... >

An upper bound on the error probability in decision-feedback equalization

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the first J feedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of 2^J relative to the error probability in the absence of decision errors at high S/N ratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a high S/N ratio and a fast roll-off of the feedback tap gains.

Exact matched filter bound for two-beam Rayleigh fading

The matched filter bound (MFB) is exactly evaluated for a channel modeled by the sum of two delayed and independently Rayleigh-fading beams. It is shown that, if the two beams have comparable average powers, and if the delay spread is moderate or large, then considerable gain is obtained from a diversity-like effect. That is, it is as if the two beams could be detected separately and their results combined. This is true even though significant interference would seem to be present between the beams. >

Asymptotic distortion spectrum of clipped, DC-biased, Gaussian noise (optical communication)

Consider a zero-mean, stationary Gaussian process g(t), to which a large positive constant A has been added. Define a distortion process h/sub A/(t) as equal to g(t)+A when the latter is negative and equal to zero otherwise. The author calculates the power spectrum of the process h/sub A/(t) asymptotically as A becomes large. The results have application for estimating the nonlinear-distortion power in the recovered signal when many frequency-multiplexed subcarriers collectively modulate a lasers output power, as would be the case for CATV transmission over an optical fiber. The process h/sub A/(t) then models the nonlinear distortion caused by occasional clipping of the DC-biased laser input. >

Diversity coding: using error control for self-healing in communication networks

An error-control-based approach, called diversity coding, that provides nearly instantaneous self-healing digital communication networks is presented. This is achieved by constructing an error-correcting code across logically independent channels and by treating link failures within the framework of an erasure channel model. Diversity coding is more efficient than previous approaches to self-healing communication networks since it is nearly instantaneous, is transparent to the end user, minimizes the required extra capacity, and does not need rerouting, resynchronization, or a feedback channel. It is applicable to both circuit-switched and packet-switched networks and to a wide variety of network topologies. Diversity coding can be extended to provide protection from short-duration environmental disruptions, such as multipath fading in radio networks and polarization dispersion in fiber-optic networks, or, in conjunction with previous error detection schemes, to provide forward error correction for random and burst errors.<<ETX>>

Transmitter design for data transmission in the presence of a data-like interferer

In many digital communications systems, crosstalk, rather than additive noise, is the primary channel impairment. For such systems, it is known that the spectral support of the optimum transmitter is not, in general, restricted to a Nyquist set, in contrast to the case for the additive-noise channel. Nevertheless, the problem of determining the optimum transmitter shaping function for the crosstalk channel without the Nyquist restriction is a difficult one, and has so far remained unsolved. Motivated by current interest in the high-speed digital subscriber line (HDSL) and related crosstalk-dominated applications, we explore a subcase of this problem in which only a single interferer is present. When applied to HDSL-like systems with a single (or dominant) interferer, our analysis and numerical results confirm that wider-than-Nyquist transmitters provide a large performance advantage over Nyquist-limited transmitters. Several interesting and counter-intuitive results also arise. For example, PAM and QAM systems operating at the same spectral efficiency do not, in general, perform identically over the crosstalk channel, despite their essential equivalence in additive noise. We explain why this is so, and show that for channels qualitatively similar to the HDSL wire-pair, QAM has a significant advantage over PAM at high data rates. Finally, we show how the characteristics of HDSL-like channels can be exploited by optimizing the symbol rate. >

Error-burst detection with tandem CRCs

The authors investigate the efficacy of using two different cyclic redundancy check (CRC) codes in tandem to increase error-burst detecting capability. For a set of pairs of CRCs which are used in standards, it is found that the guaranteed detectable burst length is less than the sum of the individual guaranteed detectable burst lengths, but not much less. Thus strengthened CRC codes can readily be obtained using existing devices. >

On a method for calculating the strength of intermodulation distortion and products

Frigos recent method for approximately calculating intermodulation distortion products for nonlinear systems is clarified, and a derivation from first principle is provided. >

Spectral Properties of Single-Sideband Angle Modulation

The generation of single-sideband angle-modulated (SSB- \phiM ) waves compatible with conventional detection methods requires involved processing. The result of these operations yields a signal whose spectral properties are more complicated than simply being one-sided versions of the analogous double-sideband spectrum, and hence it is not obvious whether or not a saving in bandwidth results. Here the spectral properties of SSB- \phiM waves are investigated in detail when the modulating signal is a sample function of a stationary Gaussian process. It is shown that the power spectrum of SSB- \phiM is related to the modulating baseband spectrum through an integral equation. This equation is solved explicitly for small and large modulating indices, and it is shown how simple numerical techniques provide solutions for arbitrary index. It is concluded that SSB- \phiM exhibits properties very similar to SSB-AM with a strong carrier component When the modulation index is much less than unity. Therefore, if minimum bandwidth plus the attributes of incoherent demodulation are desired, and a Strong carrier can be tolerated, SSB- \phiM could find an application. On the other hand, for modulation indices larger than about 3, no advantage is gained since the SSB spectrum has a bandwidth equal to or larger than the bandwidth of conventional angle-modulated waves.