Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coding Theorems for Repeat Multiple Accumulate Codes   In this paper the ensemble of codes formed by a serial concatenation of a
repetition code with multiple accumulators connected through random
interleavers is considered. Based on finite length weight enumerators for these
codes, asymptotic expressions for the minimum distance and an arbitrary number
of accumulators larger than one are derived using the uniform interleaver
approach. In accordance with earlier results in the literature, it is first
shown that the minimum distance of repeat-accumulate codes can grow, at best,
sublinearly with block length. Then, for repeat-accumulate-accumulate codes and
rates of 1/3 or less, it is proved that these codes exhibit asymptotically
linear distance growth with block length, where the gap to the
Gilbert-Varshamov bound can be made vanishingly small by increasing the number
of accumulators beyond two. In order to address larger rates, random puncturing
of a low-rate mother code is introduced. It is shown that in this case the
resulting ensemble of repeat-accumulate-accumulate codes asymptotically
achieves linear distance growth close to the Gilbert-Varshamov bound. This
holds even for very high rate codes.

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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph