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On the Undetected Error Probability of m-out-of-n Codes on the Binary Symmetric Channel

Fang‐Wei Fu, Torleiv Kløve, Shu‐Tao Xia

Springer eBooksJan 1, 20007 citations

Error detecting codes for the q-ary symmetric channel

Series on coding theory and cryptologyApr 1, 20070 citations

Analysis of error floors of generalized non-binary LDPC codes over q-ary memoryless symmetric channels

隆之野﨑, Kenta Kasai, KOHICHI SAKANIWA

Jul 1, 20120 citations

Analysis of error floors of generalized non-binary LDPC codes over q-ary memoryless symmetric channels

隆之野崎, T. Nozaki, 健太笠井 +3 more

Jun 1, 20120 citations

On the monotonic property of the probability of undetected error for a shortened code

Toru Fujiwara, Tadao Kasami, Shou-Ping Feng

The monotonic property of the probability of undetected error is considered when a shortened code of a linear code over GF(q) is used for error detection on a q-ary symmetric channel. Some conditions are presented under which the probability of undetected error is (or is not) monotonic with respect to the code length or the symbol error probability. It is shown that the probability of undetected error for a maximum distance separable code is monotonic with respect to the codelength. It is also shown that the probability of undetected error of a shortened code of any binary cyclic Hamming code generated by a trinomial is not monotonic with respect to the bit-error rate if the code length is short.>The monotonic property of the probability of undetected error is considered when a shortened code of a linear code over GF(q) is used for error detection on a q-ary symmetric channel. Some conditions are presented under which the probability of undetected error is (or is not) monotonic with respect to the code length or the symbol error probability. It is shown that the probability of undetected error for a maximum distance separable code is monotonic with respect to the codelength. It is also shown that the probability of undetected error of a shortened code of any binary cyclic Hamming code generated by a trinomial is not monotonic with respect to the bit-error rate if the code length is short.>

IEEE Transactions on Information TheoryJan 1, 19916 citations

Good error-detection codes satisfying the expurgated bound

Takeshi Hashimoto

A q-ary (n, k) linear code is said to be proper if, as an error-detection code, the probability of undetectable error P/sub ud/ satisfies P/sub ud//spl les/q/sup -(n-k)/ for completely symmetric channels. We show that a proper code, as an error-correction code, satisfies the expurgated bound on the decoding error probability for a class of channels with the associated Bhattacharyya distance being completely symmetric. Known results on the undetectable error probability then immediately imply that the expurgated exponent is satisfied exactly by, for example, all the binary perfect codes, binary first-order Reed-Muller codes, binary (extended) Hamming code, binary 2-error correcting primitive BCH code, and all the maximum distance separable (MDS) codes, and asymptotically by some class of the binary t-error-correcting primitive BCH codes.>A q-ary (n, k) linear code is said to be proper if, as an error-detection code, the probability of undetectable error P/sub ud/ satisfies P/sub ud//spl les/q/sup -(n-k)/ for completely symmetric channels. We show that a proper code, as an error-correction code, satisfies the expurgated bound on the decoding error probability for a class of channels with the associated Bhattacharyya distance being completely symmetric. Known results on the undetectable error probability then immediately imply that the expurgated exponent is satisfied exactly by, for example, all the binary perfect codes, binary first-order Reed-Muller codes, binary (extended) Hamming code, binary 2-error correcting primitive BCH code, and all the maximum distance separable (MDS) codes, and asymptotically by some class of the binary t-error-correcting primitive BCH codes.>

IEEE Transactions on Information TheoryJan 1, 19955 citations

On Probability of Undetected Error for Hamming Codes over Q-ary Symmetric Channel

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