253 research outputs found
Successive Cancellation Decoding of Single Parity-Check Product Codes
We introduce successive cancellation (SC) decoding of product codes (PCs)
with single parity-check (SPC) component codes. Recursive formulas are derived,
which resemble the SC decoding algorithm of polar codes. We analyze the error
probability of SPC-PCs over the binary erasure channel under SC decoding. A
bridge with the analysis of PCs introduced by Elias in 1954 is also
established. Furthermore, bounds on the block error probability under SC
decoding are provided, and compared to the bounds under the original decoding
algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a
lower block error probability than Elias' decoding
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
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An approach to the performance of SPC product codes on the erasure channel
Product codes can be used to correct errors or recover erasures. In this work we consider the simplest form of a product code, this is, the single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. The code is actually capable of recovering a higher number of erasure patterns. We count the number of uncorrectable erasure patterns of size nĂn with t erasures, for t=8, 2nâ3, 2nâ2 and 2nâ1, using the relation between erasure patterns and bipartite graphs.The work of the first author was supported by a grant for postdoctoral students from FAPESP with process 2015/07246-0 and a grant for postdoctoral students from Generalitat Valenciana with reference APOSTD/2013/081
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
XJ-BP: Express Journey Belief Propagation Decoding for Polar Codes
This paper presents a novel propagation (BP) based decoding algorithm for
polar codes. The proposed algorithm facilitates belief propagation by utilizing
the specific constituent codes that exist in the factor graph, which results in
an express journey (XJ) for belief information to propagate in each decoding
iteration. In addition, this XJ-BP decoder employs a novel round-trip message
passing scheduling method for the increased efficiency. The proposed method
simplifies min-sum (MS) BP decoder by 40.6%. Along with the round-trip
scheduling, the XJ-BP algorithm reduces the computational complexity of MS BP
decoding by 90.4%; this enables an energy-efficient hardware implementation of
BP decoding in practice.Comment: submitted to GLOBECOMM 201
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