411 research outputs found
High-Throughput Random Access via Codes on Graphs
Recently, contention resolution diversity slotted ALOHA (CRDSA) has been
introduced as a simple but effective improvement to slotted ALOHA. It relies on
MAC burst repetitions and on interference cancellation to increase the
normalized throughput of a classic slotted ALOHA access scheme. CRDSA allows
achieving a larger throughput than slotted ALOHA, at the price of an increased
average transmitted power. A way to trade-off the increment of the average
transmitted power and the improvement of the throughput is presented in this
paper. Specifically, it is proposed to divide each MAC burst in k sub-bursts,
and to encode them via a (n,k) erasure correcting code. The n encoded
sub-bursts are transmitted over the MAC channel, according to specific
time/frequency-hopping patterns. Whenever n-e>=k sub-bursts (of the same burst)
are received without collisions, erasure decoding allows recovering the
remaining e sub-bursts (which were lost due to collisions). An interference
cancellation process can then take place, removing in e slots the interference
caused by the e recovered sub-bursts, possibly allowing the correct decoding of
sub-bursts related to other bursts. The process is thus iterated as for the
CRDSA case.Comment: Presented at the Future Network and MobileSummit 2010 Conference,
Florence (Italy), June 201
Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access
In this paper, a random access scheme is introduced which relies on the
combination of packet erasure correcting codes and successive interference
cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph
representation of the SIC process, resembling iterative decoding of generalized
low-density parity-check codes over the erasure channel, is exploited to
optimize the selection probabilities of the component erasure correcting codes
via density evolution analysis. The capacity (in packets per slot) of the
scheme is then analyzed in the context of the collision channel without
feedback. Moreover, a capacity bound is developed and component code
distributions tightly approaching the bound are derived.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10
figure
A Decoding Algorithm for LDPC Codes Over Erasure Channels with Sporadic Errors
none4An efficient decoding algorithm for low-density parity-check (LDPC) codes on erasure channels with sporadic errors (i.e., binary error-and-erasure channels with error probability much smaller than the erasure probability) is proposed and its performance analyzed. A general single-error multiple-erasure (SEME) decoding algorithm is first described, which may be in principle used with any binary linear block code. The algorithm is optimum whenever the non-erased part of the received word is affected by at most one error, and is capable of performing error detection of multiple errors. An upper bound on the average block error probability under SEME decoding is derived for the linear random code ensemble. The bound is tight and easy to implement. The algorithm is then adapted to LDPC codes, resulting in a simple modification to a previously proposed efficient maximum likelihood LDPC erasure decoder which exploits the parity-check matrix sparseness. Numerical results reveal that LDPC codes under efficient SEME decoding can closely approach the average performance of random codes.noneG. Liva; E. Paolini; B. Matuz; M. ChianiG. Liva; E. Paolini; B. Matuz; M. Chian
Spatially-Coupled Random Access on Graphs
In this paper we investigate the effect of spatial coupling applied to the
recently-proposed coded slotted ALOHA (CSA) random access protocol. Thanks to
the bridge between the graphical model describing the iterative interference
cancelation process of CSA over the random access frame and the erasure
recovery process of low-density parity-check (LDPC) codes over the binary
erasure channel (BEC), we propose an access protocol which is inspired by the
convolutional LDPC code construction. The proposed protocol exploits the
terminations of its graphical model to achieve the spatial coupling effect,
attaining performance close to the theoretical limits of CSA. As for the
convolutional LDPC code case, large iterative decoding thresholds are obtained
by simply increasing the density of the graph. We show that the threshold
saturation effect takes place by defining a suitable counterpart of the
maximum-a-posteriori decoding threshold of spatially-coupled LDPC code
ensembles. In the asymptotic setting, the proposed scheme allows sustaining a
traffic close to 1 [packets/slot].Comment: To be presented at IEEE ISIT 2012, Bosto
On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes
In this paper, an expression for the asymptotic growth rate of the number of
small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC)
codes is derived. The expression is compact and generalizes existing results
for LDPC and generalized LDPC (GLDPC) codes. Assuming that there exist check
and variable nodes with minimum distance 2, it is shown that the growth rate
depends only on these nodes. An important connection between this new result
and the stability condition of D-GLDPC codes over the BEC is highlighted. Such
a connection, previously observed for LDPC and GLDPC codes, is now extended to
the case of D-GLDPC codes.Comment: 10 pages, 1 figure, presented at the 46th Annual Allerton Conference
on Communication, Control and Computing (this version includes additional
appendix
Spectral Shape of Check-Hybrid GLDPC Codes
This paper analyzes the asymptotic exponent of both the weight spectrum and
the stopping set size spectrum for a class of generalized low-density
parity-check (GLDPC) codes. Specifically, all variable nodes (VNs) are assumed
to have the same degree (regular VN set), while the check node (CN) set is
assumed to be composed of a mixture of different linear block codes (hybrid CN
set). A simple expression for the exponent (which is also referred to as the
growth rate or the spectral shape) is developed. This expression is consistent
with previous results, including the case where the normalized weight or
stopping set size tends to zero. Furthermore, it is shown how certain symmetry
properties of the local weight distribution at the CNs induce a symmetry in the
overall weight spectral shape function.Comment: 6 pages, 3 figures. Presented at the IEEE ICC 2010, Cape Town, South
Africa. A minor typo in equation (9) has been correcte
Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation
The growth rate of the weight distribution of irregular doubly-generalized
LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical
technique for its evaluation is presented. The solution involves simultaneous
solution of a 4 x 4 system of polynomial equations. This represents the first
efficient numerical technique for exact evaluation of the growth rate, even for
LDPC codes. The technique is applied to two example D-GLDPC code ensembles.Comment: 6 pages, 1 figure. Proc. IEEE Globecom 2009, Hawaii, USA, November 30
- December 4, 200
Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC
Using the EXIT chart approach, a necessary and sufficient condition is
developed for the local stability of iterative decoding of multi-edge type
(MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In
such code ensembles, the use of arbitrary linear block codes as component codes
is combined with the further design of local Tanner graph connectivity through
the use of multiple edge types. The stability condition for these code
ensembles is shown to be succinctly described in terms of the value of the
spectral radius of an appropriately defined polynomial matrix.Comment: 6 pages, 3 figures. Presented at Globecom 2011, Houston, T
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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