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Information and Computation

Algebraic decoding of block codes over a q-ary input, Q-ary output channel, Q greater than q.

S. Wainberg, Jack K. Wolf

Published Apr 1, 1973• 0 citations
OpenAlex

Abstract

Decoding algorithms designed for one output alphabet are shown to be effectively usable for channels with a different output alphabet. The described technique that makes this possible can be used in conjunction with an arbitrary distance measure between input and output vectors. Thus, Hamming distance, Lee distance, or a burst distance can be assumed. Examples are presented for each of these distances.

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Burst decoding of binary block codes on Q-ary output channels.

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IEEE Transactions on Information Theory•Sep 1, 1972•17 citations

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For the decoding of a binary block code of Hamming distance of d over AWGN channels, a soft-decision decoder is said to achieve bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-3-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder whose input sequences have nonzero entries confined in the most unreliable positions. Let ¿(d) denote the smallest size of input sequence sets of Chase-3-like algorithms which achieve BD decoding. In this paper, we show that there are positive numbers C1and C2such that C1¿ ¿(d)d-1/2¿ C2for sufficiently large d.

International Workshop on Signal Design and its Applications in Communications•Oct 1, 2009•1 citation

On Error Detection in Asymmetric Channels

Mladen Kovačević

We study the error detection problem in q-ary asymmetric channels, wherein every input symbol xiis mapped to an output symbol yisatisfying yi≥xi. A general setting is assumed, where the noise vectors are (potentially) restricted in: 1) the amplitude, yi-xi≤a, 2) the Hamming weight, Σi=1n1{yi≠xi}≤ h, and 3) the total weight, Σi=1n(yi-xi)≤t. Optimal codes detecting these types of errors are described for certain sets of parameters a, h, t, both in the standard and in the cyclic (mod q) version of the problem. It is also demonstrated that these codes are optimal in the large alphabet limit for every a, h, t and every block-length n.

arXiv:1706.04540•IEEE Communications Letters•Jun 19, 2017•2 citations
Decoding algorithms designed for one output alphabet are shown to be effectively usable for channels with a different output alphabet. The described technique that makes this possible can be used in conjunction with an arbitrary distance measure between input and output vectors. Thus, Hamming distance, Lee distance, or a burst distance can be assumed. Examples are presented for each of these distances.
For the decoding of a binary block code of Hamming distance of d over AWGN channels, a soft-decision decoder is said to achieve bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-3-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder whose input sequences have nonzero entries confined in the most unreliable positions. Let ¿(d) denote the smallest size of input sequence sets of Chase-3-like algorithms which achieve BD decoding. In this paper, we show that there are positive numbers C1and C2such that C1¿ ¿(d)d-1/2¿ C2for sufficiently large d.
We study the error detection problem in q-ary asymmetric channels, wherein every input symbol xiis mapped to an output symbol yisatisfying yi≥xi. A general setting is assumed, where the noise vectors are (potentially) restricted in: 1) the amplitude, yi-xi≤a, 2) the Hamming weight, Σi=1n1{yi≠xi}≤ h, and 3) the total weight, Σi=1n(yi-xi)≤t. Optimal codes detecting these types of errors are described for certain sets of parameters a, h, t, both in the standard and in the cyclic (mod q) version of the problem. It is also demonstrated that these codes are optimal in the large alphabet limit for every a, h, t and every block-length n.