1,552 research outputs found
On the Construction and Decoding of Concatenated Polar Codes
A scheme for concatenating the recently invented polar codes with interleaved
block codes is considered. By concatenating binary polar codes with interleaved
Reed-Solomon codes, we prove that the proposed concatenation scheme captures
the capacity-achieving property of polar codes, while having a significantly
better error-decay rate. We show that for any , and total frame
length , the parameters of the scheme can be set such that the frame error
probability is less than , while the scheme is still
capacity achieving. This improves upon 2^{-N^{0.5-\eps}}, the frame error
probability of Arikan's polar codes. We also propose decoding algorithms for
concatenated polar codes, which significantly improve the error-rate
performance at finite block lengths while preserving the low decoding
complexity
Adaptive Linear Programming Decoding of Polar Codes
Polar codes are high density parity check codes and hence the sparse factor
graph, instead of the parity check matrix, has been used to practically
represent an LP polytope for LP decoding. Although LP decoding on this polytope
has the ML-certificate property, it performs poorly over a BAWGN channel. In
this paper, we propose modifications to adaptive cut generation based LP
decoding techniques and apply the modified-adaptive LP decoder to short
blocklength polar codes over a BAWGN channel. The proposed decoder provides
significant FER performance gain compared to the previously proposed LP decoder
and its performance approaches that of ML decoding at high SNRs. We also
present an algorithm to obtain a smaller factor graph from the original sparse
factor graph of a polar code. This reduced factor graph preserves the small
check node degrees needed to represent the LP polytope in practice. We show
that the fundamental polytope of the reduced factor graph can be obtained from
the projection of the polytope represented by the original sparse factor graph
and the frozen bit information. Thus, the LP decoding time complexity is
decreased without changing the FER performance by using the reduced factor
graph representation.Comment: 5 pages, 8 figures, to be presented at the IEEE Symposium on
Information Theory (ISIT) 201
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