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Soft-decision decoding of reed-muller codes: a simplified algorithm (2006)

by I Dumer
Venue:IEEE Trans. Inf. Theory
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Boucheret, ‘‘Multi-slot coded ALOHAwith irregular degree distribution

by Huyen-chi Bui, Marie-laure Boucheret - in Proc. ESTEL , 2012
"... Abstract—This paper proposes an improvement of the random multiple access scheme for satellite communication named Multi-slot coded ALOHA (MuSCA). MuSCA is a generalization of Contention Resolution Diversity Slotted ALOHA (CRDSA). In this scheme, each user transmits several parts of a single codewor ..."
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Abstract—This paper proposes an improvement of the random multiple access scheme for satellite communication named Multi-slot coded ALOHA (MuSCA). MuSCA is a generalization of Contention Resolution Diversity Slotted ALOHA (CRDSA). In this scheme, each user transmits several parts of a single codeword of an error correcting code instead of sending replicas. At the receiver level, the decoder collects all these parts and includes them in the decoding process even if they are interfered. In this paper, we show that a high throughput can be obtained by selecting variable code rates and user degrees according to a probability distribution. With an optimal irregular degree distribution, our system achieves a normalized throughput up to 1.43, resulting in a significant gain compared to CRDSA and MuSCA. The spectral efficiency and the implementation issues of the scheme are also analyzed. I.
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...y small in order to maintain a high throughput. We choose to protect these fields by Reed-Muller codes which have a fair performance/complexity trade-off for soft-decision decoding of short codewords =-=[14]-=-. For example, for a frame of length Ns = 100 slots, each location is represented by 7 bits. Users of degree 3 can adopt a ReedMuller code (14, 64). The signalization decoding is launched when a burst...

3) �xYP! S If �xYP! S, then

by Xyp P
"... 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
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.... Berrou, A. Glavieux, and P. Thitimajshima, “Near shannon limit error-correcting coding and decoding : Turbo-codes,” in Proc. Int. Conf. Communications, Geneva, Switzerland, May 1993, pp. 1064–1070. =-=[10]-=- H. R. Sadjadpour, N. J. A. Sloane, M. Salehi, and G. Nebe, “Interleaver design for turbo codes,” IEEE J. Sel. Areas Commun., vol. 19, no. 5, pp. 831–837, May 2001. [11] C. J. Corrada-Bravo and I. Rub...

2 Recursive Descriptions of Decoding Algorithms and Hardware Architectures for Polar Codes

by Noam Presman, Simon Litsyn
"... ar ..."
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...s in Dumer’s survey on GCCs [20]. In addition, the recursive decoding algorithms for Reed-Muller (RM) codes, utilizing their Plotkin (u+v, v) recursive GCC structure were extensively studied by Dumer =-=[21, 22]-=- and are closely related to the algorithms we present here. Actually, Dumer’s simplified decoding algorithm for RM codes [22, Section IV] is the SC decoding for the Arikan’s structure, we describe in ...

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