This letter describes a belief-propagation decoder for low-density lattice codes of finite dimension, in which the messages are represented as single Gaussian functions. Compared to previously-proposed decoders, memor...
详细信息
This letter describes a belief-propagation decoder for low-density lattice codes of finite dimension, in which the messages are represented as single Gaussian functions. Compared to previously-proposed decoders, memory is reduced because each message consists of only two values, the mean and variance. Complexity is also reduced because the check node operations are on single Gaussians, avoiding approximations needed previously, and because the variable node performs approximations on a smaller number of Gaussians. For lattice dimension n =1000 and 10,000, this decoder looses no more than 0.1 dB in SNR, compared to the decoders which use much more memory.
Two decoding procedures combined with a belief-propagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after...
详细信息
Two decoding procedures combined with a belief-propagation (BP) decoding algorithm for low-density parity-check codes over the binary erasure channel are presented. These algorithms continue a decoding procedure after the BP decoding algorithm terminates. We derive a condition that our decoding algorithms can correct an erased bit which is uncorrectable by the BP decoding algorithm. We show by simulation results that the performance of our decoding algorithms is enhanced compared with that of the BP decoding algorithm with little increase of the decoding complexity.
A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-su...
详细信息
A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-sum decoding, one can And that its WBF algorithm is the algorithm proposed by Jiang et al. For BP decoding, we propose a new WBF algorithm and show its performance advantage. The proposed WBF algorithms are parallelized to achieve rapid convergence. Two efficient simulation-based procedures are proposed for the optimization of the associated thresholds.
A new ensemble of low-density parity-check (LDPC) codes for correcting a solid burst erasure is proposed. This ensemble is an instance of a combined matrix ensemble obtained by concatenating some LDPC matrices. We der...
详细信息
A new ensemble of low-density parity-check (LDPC) codes for correcting a solid burst erasure is proposed. This ensemble is an instance of a combined matrix ensemble obtained by concatenating some LDPC matrices. We derive a new bound on the critical minimum span ratio of stopping sets for the proposed code ensemble by modifying the bound for ordinary code ensemble. By calculating this bound, we show that the critical minimum span ratio of stopping sets for the proposed code ensemble is better than that of the conventional one with keeping the same critical exponent of stopping ratio for both ensemble. Furthermore from experimental results, we show that the average minimum span of stopping sets for a solid burst erasure of the proposed codes is larger than that of the conventional ones.
In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable...
详细信息
In this correspondence, we consider the class of finite-state Markov channels (FSMCs) in which the channel behaves as a binary symmetric channel (BSC) in each state. Upper bounds on the rate of LDPC codes for reliable communication over this class of FSMCs are found. A simple upper bound for all noninverting FSMCs is first derived. Subsequently, tighter bounds are derived for the special case of Gilbert-Elliott (GE) channels. Tighter bounds are also derived over the class of FSMCs considered. The latter bounds hold almost-surely for any sequence of randomly constructed LDPC codes of given degree distributions. Since the bounds are derived for optimal maximum-likelihood decoding, they also hold for beliefpropagationdecoding. Using the derivations of the bounds on the rate, some lower bounds on the density of parity check matrices for given performance over FSMCs are derived.
This paper describes the design and analysis of low-density parity-check (LDPC) codes over rings and shows how these codes, when mapped onto appropriate signal constellations, can be used to effect bandwidth-efficient...
详细信息
This paper describes the design and analysis of low-density parity-check (LDPC) codes over rings and shows how these codes, when mapped onto appropriate signal constellations, can be used to effect bandwidth-efficient modulation. Specifically, LDPC codes are constructed over the integer rings Z(m) and G(m2) and mapped onto phase-shift keying (PSK)-type signal sets to yield geometrically uniform signal space codes. This paper identifies and addresses the design issues that affect code performance. Examples of codes over Z(8) and G(64) mapped onto 8-ary and 64-ary signal sets at a spectral efficiency of 1.5 and 2.0 bits per second per hertz (b/s/Hz) illustrate the approach;simulation of these codes over the additive white Gaussian noise (AWGN) channel demonstrates that this approach is a good alternative to bandwidth-efficient techniques based on binary LDPC codes-e.g., bit-interleaved coded modulation.
It is shown that idempotents based on cyclotomic cosets may be used to construct some new one-step majority-logic codes. The construction method produces the dual code idempotent which can be used to directly define t...
详细信息
It is shown that idempotents based on cyclotomic cosets may be used to construct some new one-step majority-logic codes. The construction method produces the dual code idempotent which can be used to directly define the parity-check matrix of the cyclic code. A feature of the cyclotomic idempotent codes is the incremental approach to the sparseness of the parity-check matrix and the property of parity-check bit orthogonality which is known to be useful in belief-propagation decoding. These codes have high minimum distance and a performance 0.4dB away from the theoretical limit is demonstrated.
Recently, the beliefpropagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo de...
详细信息
Recently, the beliefpropagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo decoding, In this paper, we investigate the performance achieved by the BP algorithm for decoding one-step majority logic decodable (OSMLD) codes. The BP algorithm is expressed in terms of likelihood ratios rather than probabilities, as conventionally presented. The proposed algorithm fits better the decoding of OSMLD codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding LDPC codes. Although it has been believed that OSMLD codes are far inferior to LDPC codes, we show that for medium code lengths (say between 200-1000 bits), the BP decoding of OSMLD codes can significantly outperform BP decoding of their equivalent LDPC codes, The reasons for this behavior are elaborated.
暂无评论