752 research outputs found
Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel
We consider transmission over a wiretap channel where both the main channel
and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a
code construction method using two edge type LDPC codes based on the coset
encoding scheme. Using a standard LDPC ensemble with a given threshold over the
BEC, we give a construction for a two edge type LDPC ensemble with the same
threshold. If the given standard LDPC ensemble has degree two variable nodes,
our construction gives rise to degree one variable nodes in the code used over
the main channel. This results in zero threshold over the main channel. In
order to circumvent this problem, we numerically optimize the degree
distribution of the two edge type LDPC ensemble. We find that the resulting
ensembles are able to perform close to the boundary of the rate-equivocation
region of the wiretap channel.
There are two performance criteria for a coding scheme used over a wiretap
channel: reliability and secrecy. The reliability measure corresponds to the
probability of decoding error for the intended receiver. This can be easily
measured using density evolution recursion. However, it is more challenging to
characterize secrecy, corresponding to the equivocation of the message for the
wiretapper. M\'easson, Montanari, and Urbanke have shown how the equivocation
can be measured for a broad range of standard LDPC ensembles for transmission
over the BEC under the point-to-point setup. By generalizing the method of
M\'easson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how
the equivocation for the wiretapper can be computed. We find that relatively
simple constructions give very good secrecy performance and are close to the
secrecy capacity. However finding explicit sequences of two edge type LDPC
ensembles which achieve secrecy capacity is a more difficult problem. We pose
it as an interesting open problem.Comment: submitted to IEEE Transactions on Information Theory. Updated versio
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Spectral Shape of Doubly-Generalized LDPC Codes: Efficient and Exact Evaluation
This paper analyzes the asymptotic exponent of the weight spectrum for
irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient
numerical technique for its evaluation is presented, involving the solution of
a 4 x 4 system of polynomial equations. The expression is consistent with
previous results, including the case where the normalized weight or stopping
set size tends to zero. The spectral shape is shown to admit a particularly
simple form in the special case where all variable nodes are repetition codes
of the same degree, a case which includes Tanner codes; for this case it is
also shown how certain symmetry properties of the local weight distribution at
the CNs induce a symmetry in the overall weight spectral shape function.
Finally, using these new results, weight and stopping set size spectral shapes
are evaluated for some example generalized and doubly-generalized LDPC code
ensembles.Comment: 17 pages, 6 figures. To appear in IEEE Transactions on Information
Theor
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