arXiv subjects

Kohichi Sakaniwa

Publications and source records attributed to Kohichi Sakaniwa.

22 records · Page 2Linked to original sources

arXiv2010

Fountain Codes with Multiplicatively Repeated Non-Binary LDPC Codes

We study fountain codes transmitted over the binary-input symmetric-output channel. For channels with small capacity, receivers needs to collects many channel outputs to recover information bits. Since a collected channel output yields a check node in the decoding Tanner graph, the channel with small capacity leads to large decoding complexity. In this paper, we introduce a novel fountain coding scheme with non-binary LDPC codes. The decoding complexity of the proposed fountain code does not depend on the channel. Numerical experiments show that the proposed codes exhibit better performance than conventional fountain codes, especially for small number of information bits.

cs.IT↗

arXiv2009

Finite-Length Analysis of Irregular Expurgated LDPC Codes under Finite Number of Iterations

Communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding is considered. The average bit error probability of an irregular LDPC code ensemble after a fixed number of iterations converges to a limit, which is calculated via density evolution, as the blocklength $n$ tends to infinity. The difference between the bit error probability with blocklength $n$ and the large-blocklength limit behaves asymptotically like $α/n$, where the coefficient $α$ depends on the ensemble, the number of iterations and the erasure probability of the BEC\null. In [1], $α$ is calculated for regular ensembles. In this paper, $α$ for irregular expurgated ensembles is derived. It is demonstrated that convergence of numerical estimates of $α$ to the analytic result is significantly fast for irregular unexpurgated ensembles.

cs.IT↗

arXiv2009

Analytical Solution of Covariance Evolution for Regular LDPC Codes

The covariance evolution is a system of differential equations with respect to the covariance of the number of edges connecting to the nodes of each residual degree. Solving the covariance evolution, we can derive distributions of the number of check nodes of residual degree 1, which helps us to estimate the block error probability for finite-length LDPC code. Amraoui et al.\ resorted to numerical computations to solve the covariance evolution. In this paper, we give the analytical solution of the covariance evolution.

cs.IT↗

arXiv2008

The Asymptotic Bit Error Probability of LDPC Codes for the Binary Erasure Channel with Finite Iteration Number

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. The bit error probability for infinite block length is known by density evolution and it is well known that a difference between the bit error probability at finite iteration number for finite block length $n$ and for infinite block length is asymptotically $α/n$, where $α$ is a specific constant depending on the degree distribution, the iteration number and the erasure probability. Our main result is to derive an efficient algorithm for calculating $α$ for regular ensembles. The approximation using $α$ is accurate for $(2,r)$-regular ensembles even in small block length.

cs.IT↗