267 research outputs found
Constructions of Generalized Concatenated Codes and Their Trellis-Based Decoding Complexity
In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis omplexity than Euclidean geometry (EG), Reed–Muller (RM), or Bose–Chaudhuri–Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed
Decoding Reed-Muller codes over product sets
We give a polynomial time algorithm to decode multivariate polynomial codes
of degree up to half their minimum distance, when the evaluation points are
an arbitrary product set , for every . Previously known
algorithms can achieve this only if the set has some very special algebraic
structure, or if the degree is significantly smaller than . We also
give a near-linear time randomized algorithm, which is based on tools from
list-decoding, to decode these codes from nearly half their minimum distance,
provided .
Our result gives an -dimensional generalization of the well known decoding
algorithms for Reed-Solomon codes, and can be viewed as giving an algorithmic
version of the Schwartz-Zippel lemma.Comment: 25 pages, 0 figure
Self-concatenated code design and its application in power-efficient cooperative communications
In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions
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