Eran Sharon

Lazy scheduling forLDPC decoding

A complexity reducing method for iterative message passing decoding algorithms of low-density parity-check (LDPC) codes is described. It is based on lazy scheduling which involves a partial update of messages in the iterations. A density evolution (DE) approach is developed for optimization of the parameters for choice of the messages to be updated. Combined with an efficient serial scheduling, the resulting method reduces the decoding complexity by about 70-75% compared to the classical belief propagation (BP) scheme, while maintaining the same performance

Analysis of Low-Density Parity-Check Codes Based on EXIT Functions

We exploit extrinsic information transfer functions of single parity-check and repetition codes over the binary input additive white Gaussian noise (biAWGN) channel, derived by the authors, for asymptotic performance analysis of belief propagation decoding of low-density parity-check codes. The approach is based on a Gaussian approximation (GA) of the density evolution algorithm using the mutual information measure. We show that this method allows more accurate prediction of the decoding threshold in the biAWGN channel than the earlier known GA methods

EXIT functions for binary input memoryless symmetric channels

Use of extrinsic information transfer (EXIT) functions, characterizing the amplification of mutual information between the input and output of the maximum a posteriori (MAP) decoder, significantly facilitates analysis of iterative coding schemes. Previously, EXIT functions derived for binary erasure channels (BECs) were used as an approximation for other channels. Here, we improve on this approach by introducing more accurate methods to construct EXIT functions for binary-input memoryless symmetric (BMS) channels. By defining an alternative pseudo-MAP decoder coinciding with the MAP decoder over BEC, we provide an expression for the EXIT functions of block codes over BEC. Furthermore, we draw a connection between the EXIT function over BEC and the EXIT function over the BMS channel under certain conditions. This is used for deriving accurate or approximate expressions of EXIT functions over BMS channels in certain scenarios

Improved decoding of LDPC coded modulations

A coded modulation belief propagation (CMBP) decoder is proposed for decoding LDPC codes with multilevel modulations. The decoder takes into account statistical dependencies among bits originating in the same symbol, providing better performance than the marginal BP (MBP) decoder. Asymptotically it converges to MAP decoding. The CMBP decoder is based on a single-level coding (SLC) scheme and does not suffer from practical disadvantages of multi-level coding (MLC) schemes. Furthermore, the CMBP decoder can close the capacity gap of the bit interleaved coded modulation (BICM) SLC scheme. The BICM capacity gap increases when the modulation size increases and in scenarios where gray mapping is not possible.

Efficient layers-based schedules for iterative decoding of LDPC codes

Efficient serial decoding schedules for LDPC codes are described. The schedules are based on dividing the Tanner graph to sub-graphs. This yields an improvement in complexity and performance over the standard schedules. An application of the introduced schedules to decoding codes based on lifted graphs is described. An analysis based on density evolution is presented and is used to predict the behavior of different schedules.

EXIT functions for binary memoryless symmetric channels

Use of extrinsic information transfer (EXIT) functions characterizing mutual information between the input and output of constituent decoders significantly facilitates performance analysis of iterative decoding schemes. Previously EXIT functions derived for binary erasure channel (BEC) were used as an approximation for other binary memoryless symmetric (BMS) Channels. Here we improve on this approach by introducing a more accurate method to compute EXIT functions of some block codes for BMS channels. A general expression is derived for the extrinsic mutual information at the output of MAP decoder. Using this expression we are able to compute EXIT functions for single parity-check codes over all BMS channels. Application of this result to analysis of convergence thresholds of LDPC codes is described. Using an alternative decoder coinciding with MAP decoder over BEC, we derive an expression for EXIT function over BEC, and based on it approximation to the EXIT function over AWGN channel for some block codes.

Convergence analysis of generalized serial message-passing schedules

Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code in the process of decoding. Schedules affect the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed, exhibiting significantly faster convergence compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be achieved are identified. Specific code constructions from lifted graphs are further proposed, efficiently supporting the schedules. Examples based on regular LDPC codes are provided, in which the schedules achieve convergence speedup factors of up to 6 in comparison with the flooding schedule. Higher speedup factors are predicted by the analysis for irregular codes.

Decreasing error floor in LDPC codes by parity-check matrix extensions

High error floors in optimized irregular LDPC codes limit their usage in applications that require low error rates. We introduce new methods for lowering the error floor of LDPC codes, based on enhancing the codes parity-check matrix with additional linearly dependent and independent parity-checks. We prove NP hardness of certain optimization problems related to proposed methods and provide upper bound on the number of parity-checks that need to be added. We show that the proposed methods can lower the error floor of the code significantly, by several orders of magnitude, at negligible or no rate penalty.

A Method for Constructing LDPC Codes with Low Error Floor

This paper describes a novel progressive edge growth (PEG) algorithm for constructing LDPC codes with minimized block error probability over the binary erasure channel (BEC). The constructed codes provide superior performance and lower error floor compared to codes generated by previously known algorithms. Furthermore, an upper bound on the expected block error probability in the error floor region of the generated code is derived

Analysis of LDPC decoding schedules

Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code during decoding. Schedules may significantly differ in the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed. They provide significant convergence rate speedup factors compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be obtained are identified.