Burst Erasure Research Articles

Information rates of photon-limited overlapping pulse position modulation channels

A direct-detection photon-limited optical communication channel that uses pulse position modulation (PPM) under a pulsewidth constraint is considered. Overlapping PPM (OPPM) allows multiple positions per pulsewidth, as well as fractional modulation indices (number of pulsewidths per frame) requiring more refined timing than that needed for conventional disjoint PPM (DJPPM). It is shown that even at moderate values of the expected photon count per pulse <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(Q)</tex> --such as needed for high data rates--OPPM outperforms on-off keying (OOK) in both capacity and cutoff rate, even though OOK is uniformly superior to DJPPM. Moreover, efficient use of OPPM is possible with equiprobable input symbols, whereas OOK requires inconvenient asymmetrical inputs to achieve capacity and high cutoff rate efficiencies (nats/ photon). At lower data rates, where capacity efficiency is the prime criterion, a significant advantage (- 20 percent) over DJPPM can be achieved up to efficiencies of about 0.7 nats/ photon. The M-ary photon-limited OPPM channel can be viewed as an ambiguity and erasure channel, in the sense that some channel outputs are ambiguous in only some input symbols and only if no photons are counted is there ambiguity in all input symbols. For large <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> ambiguities cause bursts of erasures of data symbols. Massey's interlaced encoding, as well as conventional encoding followed by interleaving, are adaptable to this bursty channel, and effect an increase in its cutoff rate comparable to the increase obtainable with DJPPM by the same techniques.

Burst-error-correcting array codes

Classes of array codes for correcting bursts of errors, bursts of erasures, and mixed error-and-erasure bursts, are described. A specific example of a burst-error-correcting array code, and its decoder, is given. These codes have relatively high rates, small decoding delay, simple encoding and decoding algorithms, and are capable of high-speed operation. Array codes have a wide range of application in digital communications.

Viterbi Decoder Performance in Gaussian Noise and Periodic Erasure Bursts

In this paper, we evaluate the performance of noninterleaved convolutional codes in the presence of Gaussian noise and periodic erasure bursts, with maximum likelihood (Viterbi) decoding. The results show that even for burst lengths that are a significant fraction of the code constraint length, the performance degradation is surprisingly small. It is then shown that in many of these cases the use of interleaving would provide very little performance gain. In addition, for burst lengths that are so long that interleaving is unavoidable, these results demonstrate the robustness of fixed periodic interleavers against variability in the parameters of the burst process.

Determination of the mean square error in the transmission of information by a binary irredundant code

1. The error dispersion for transmission of information by means of a binary irredundant code over a communication channel with independent errors depends weakly on the asymmetry coefficient α of the channel and decreases only by a factor 1−p when α is varied from 1 to ∞. Therefore, for practical calculations in the case of small p and for any α one may use (6) with an error not exceeding p/(1−p). For accurate calculations, depending on the channel characteristic, one should use (6), (16), or (20). 2. The reduced error dispersion for operation in channels having both independent and burst errors depends weakly on the length n of the code word (in the latter case-for erasure of the symbols encompassed by the error). In particular, for a channel with independent errors the error in using the approximate expressions (7), (17), and (21) does not exceed the value 2/(2П + 1. 3. The dispersion of the error in working in a channel with erasure bursts depends weakly on the lengthl of the burst.

Burst Distance and Multiple-Burst Correction*

This paper is concerned with burst error, burst erasure and combined burst-error and burst-erasure correction. Part I introduces the concept of burst distance and subsequently develops burst-correcting properties of a code relative to its burst distance. Part II discusses product codes for multiple-burst correction (MBC). The MBC properties of a product of two codes are derived from the properties of the original codes. The correction of spot errors is generalized to multiple-spot correction. Theorems are presented which strengthen the single-burst correcting (SBC) properties of some codes. A class of codes which corrects single, triple and quadruple bursts and 5 single errors is developed, and a decoding procedure is given. Finally, a code from the new class of MBC codes is compared with three other MBC codes.

Correction of two erasure bursts (Corresp.)

Correction of two erasure bursts (Corresp.)

A class of convolution codes

This paper describes a class of infinite convolution codes which are designed to minimize the time required to recover from an erasure burst on the binary erasure channel. It is shown that for any given rate, there exists a unique optimum erasure burst correcting code. For rates of the restricted form R = n /( n + 1), an algorithm is given by which the code of this rate may be written down by inspection. For other rates, the codes can be determined by a more complicated procedure based on evaluating large binary determinants.