15 research outputs found
The Effect of Saturation on Belief Propagation Decoding of LDPC Codes
We consider the effect of LLR saturation on belief propagation decoding of
low-density parity-check codes. Saturation occurs universally in practice and
is known to have a significant effect on error floor performance. Our focus is
on threshold analysis and stability of density evolution.
We analyze the decoder for certain low-density parity-check code ensembles
and show that belief propagation decoding generally degrades gracefully with
saturation. Stability of density evolution is, on the other hand, rather
strongly affected by saturation and the asymptotic qualitative effect of
saturation is similar to reduction of variable node degree by one.Comment: Submitted to ISIT. Longer version to be submitted to IT Transactions
in preparatio
From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes
Cages, defined as regular graphs with minimum number of nodes for a given
girth, are well-studied in graph theory. Trapping sets are graphical structures
responsible for error floor of low-density parity-check (LDPC) codes, and are
well investigated in coding theory. In this paper, we make connections between
cages and trapping sets. In particular, starting from a cage (or a modified
cage), we construct a trapping set in multiple steps. Based on the connection
between cages and trapping sets, we then use the available results in graph
theory on cages and derive tight upper bounds on the size of the smallest
trapping sets for variable-regular LDPC codes with a given variable degree and
girth. The derived upper bounds in many cases meet the best known lower bounds
and thus provide the actual size of the smallest trapping sets. Considering
that non-zero codewords are a special case of trapping sets, we also derive
tight upper bounds on the minimum weight of such codewords, i.e., the minimum
distance, of variable-regular LDPC codes as a function of variable degree and
girth
Relaxed Half-Stochastic Belief Propagation
Low-density parity-check codes are attractive for high throughput
applications because of their low decoding complexity per bit, but also because
all the codeword bits can be decoded in parallel. However, achieving this in a
circuit implementation is complicated by the number of wires required to
exchange messages between processing nodes. Decoding algorithms that exchange
binary messages are interesting for fully-parallel implementations because they
can reduce the number and the length of the wires, and increase logic density.
This paper introduces the Relaxed Half-Stochastic (RHS) decoding algorithm, a
binary message belief propagation (BP) algorithm that achieves a coding gain
comparable to the best known BP algorithms that use real-valued messages. We
derive the RHS algorithm by starting from the well-known Sum-Product algorithm,
and then derive a low-complexity version suitable for circuit implementation.
We present extensive simulation results on two standardized codes having
different rates and constructions, including low bit error rate results. These
simulations show that RHS can be an advantageous replacement for the existing
state-of-the-art decoding algorithms when targeting fully-parallel
implementations