From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance
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We generalize the results about how to compute iterative decoding thresholds over the binary erasure channel of non-binary LDPC code ensembles of [16] to non-binary TLDPC codes [2], [3]. We show in this case how density evolution can be performed in order ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007
This work is concerned with codes, graphs and their links. Graph based codes have recently become very prominent in both information theory literature and practical applications. While most research has centered around their performance under iterative dec ...
We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the compound capacity u ...
Compilation of polymorphic code through type erasure gives compact code but performance on primitive types is significantly hurt. Full specialization gives good performance, but at the cost of increased code size and compilation time. Instead we propose a ...
It is shown that a correlation inequality of statistical mechanics can be applied to linear low-density parity-check codes. Thanks to this tool we prove that, under a natural assumption, the exponential growth rate of regular low-density parity-check (LDPC ...
Institute of Electrical and Electronics Engineers2007
The addition of a feedback link to a discrete memoryless channel does not increase its capacity, but it does bring with it other benefits. One of these benefits is an increase to the best achievable error exponent. In the first part of this thesis we revis ...
Polar codes, introduced recently by Arikan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation, are optimal in th ...
We consider communication through a cascade of discrete memoryless channels (DMCs). The source and destination node of this cascade are allowed to use coding schemes of arbi- trary complexity, but the intermediate relay nodes are restricted to process only ...
Institute of Electrical and Electronics Engineers2007
We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...
An encoder uses output symbol subsymbols to effect or control a tradeoff of computational effort and overhead efficiency to, for example, greatly reduce computational effort for the cost of a small amount of overhead efficiency. An encoder reads an ordered ...
