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Recursive Decoding and Its Performance for Low-Rate Reed–Muller Codes
, 2004
"... Recursive decoding techniques are considered for Reed–Muller (RM) codes of growing length and fixed order. An algorithm is designed that has complexity of order ��� and corrects most error patterns of weight up to @I P A given that exceeds I P. This improves the asymptotic bounds known for decoding ..."
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Cited by 13 (3 self)
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Recursive decoding techniques are considered for Reed–Muller (RM) codes of growing length and fixed order. An algorithm is designed that has complexity of order ��� and corrects most error patterns of weight up to @I P A given that exceeds I P. This improves the asymptotic bounds known for decoding RM codes with nonexponential complexity. To evaluate decoding capability, we develop a probabilistic technique that disintegrates decoding into a sequence of recursive steps. Although dependent, subsequent outputs can be tightly evaluated under the assumption that all preceding decodings are correct. In turn, this allows us to employ second-order analysis and find the error weights for which the decoding error probability vanishes on the entire sequence of decoding steps as the code length grows.
On Unequal Error Protection LDPC Codes Based on Plotkin-type
- Constructions,” Proceedings of the Global Telecommunications Conference
, 2004
"... We introduce a new family of unequal error protection (UEP)codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among ..."
Abstract
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Cited by 7 (0 self)
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We introduce a new family of unequal error protection (UEP)codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among the code bits is also influenced by the choice of the LDPC component-codes, and by some new reliability features incorporated into the decoding process. The proposed scheme offers a very good trade-off between code performance on one side and encoding/decoding and storage complexity on the other side. The novel approach to UEP also allows for finding simple approximations for the achievable degrees of UEP, which can be used to govern practical code design implementations. 1
3) �xYP! S If �xYP! S, then
"... b IX By Lemma 3.3, if �xYP 0 I b�pYP! �pYP. Consequently, if �xYP is even ..."
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b IX By Lemma 3.3, if �xYP 0 I b�pYP! �pYP. Consequently, if �xYP is even
