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IEEE Transactions on Information Theory

Burst decoding of binary block codes onQ-ary output channels (Corresp.)

S. Wainberg, Jack K. Wolf

Published Sep 1, 1972• 17 citations
Publisher

Abstract

The burst-bdistance between two binary vectors is defined and shown to be a metric. This definition is applied to a binary-input,Q-ary output channel where errors occur in bursts. A decoding algorithm is presented for such a channel that is an extension of Weldon's [2] weighted erasure decoding. Examples are presented illustrating the techniques.

DOI
10.1109/tit.1972.1054871

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The burst-bdistance between two binary vectors is defined and shown to be a metric. This definition is applied to a binary-input,Q-ary output channel where errors occur in bursts. A decoding algorithm is presented for such a channel that is an extension of Weldon's [2] weighted erasure decoding. Examples are presented illustrating the techniques.
Iterative algorithms for decoding over erasure-burst channels have attracted much interest lately due to their simplicity. Although the performance of these techniques is typically good, it may not be optimal if the underlying matrix used for decoding is not properly chosen. In this paper, we construct matrices that lead to optimal performance when used with iterative decoding over erasure-burst channels. We also develop a simple decoding technique that makes use of these same matrices to decode any linear code over error-burst channels. For cyclic codes, this algorithm is optimal.
Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors in real-life channels seem to occur in bursts rather than independently, suggesting that these channels exhibit some statistical dependence or memory. Nonetheless, the same algebraic codes are still commonly used in current communication systems that employ interleaving to spread channel error bursts over the set of received codewords to make the channel appear memoryless to the block decoder. This method suffers from immediate shortcomings as it fails to exploit the channel’s memory while adding delay to the system. We study optimal maximum likelihood block decoding of binary codes sent over several binary additive channels with infinite and finite memory. We derive conditions on general binary codes and channels parameters under which maximum likelihood and minimum distance decoding are equivalent. The channels considered in this work are the infinite and finite memory Polya contagion channels [1],
A coset representation of the bit error probabilities for binary linear block codes and arbitrary symmetric memoryless channels is derived. Such a representation leads to simple upper bounds on the bit error probabilities for code components expressed via 2n code spectra, where n is the code length, and to a "bounded distance decoding" algorithm. The performance of the algorithm is illustrated for the (23,12) Golay code and a particular channel having non-binary output alphabet where it attains a sub-optimum performance.