Nedeljko Varnica

Optimized low-density parity-check codes for partial response channels

We optimize irregular low-density parity-check (LDPC) codes to closely approach the independent and uniformly distributed (i.u.d.) capacities of partial response channels. In our approach, we use the degree sequences optimization method for memoryless channels proposed by Richardson, Shokrollahi, and Urbanke and appropriately modify it for channels with memory. With this optimization algorithm we construct codes whose noise tolerance thresholds are within 0.15 dB of the i.u.d. channel capacities. Our simulation results show that irregular LDPC codes with block lengths 10/sup 6/ bits yield bit error rates 10/sup -6/ at signal-to-noise ratios 0.22 dB away from the channel capacities.

Augmented Belief-Propagation Decoding of Low-Density Parity-Check Codes

We propose an augmented belief propagation (BP) decoder for low-density parity check (LDPC) codes which can be utilized on memoryless or intersymbol interference channels. The proposed method is a heuristic algorithm that eliminates a large number of pseudocodewords that can cause nonconvergence in the BP decoder. The augmented decoder is a multistage iterative decoder, where, at each stage, the original channel messages on select symbol nodes are replaced by saturated messages. The key element of the proposed method is the symbol selection process, which is based on the appropriately defined subgraphs of the code graph and/or the reliability of the information received from the channel. We demonstrate by examples that this decoder can be implemented to achieve substantial gains (compared to the standard locally-operating BP decoder) for short LDPC codes decoded on both memoryless and intersymbol interference Gaussian channels. Using the Margulis code example, we also show that the augmented decoder reduces the error floors. Finally, we discuss types of BP decoding errors and relate them to the augmented BP decoder.

LDPC code ensembles for incremental redundancy hybrid ARQ

An LDPC code based hybrid ARQ scheme with random transmission assignments is analyzed. The spectrum properties of LDPC code ensembles that are necessary for this analysis are derived. Very good estimates of maximum-likelihood decoding error rates after each transmission are provided. The results are tested on practical code examples by simulation

Matched information rate codes for Partial response channels

In this paper, we design capacity-approaching codes for partial response channels. The codes are constructed as concatenations of inner trellis codes and outer low-density parity- check (LDPC) codes. Unlike previous constructions of trellis codes for partial response channels, we disregard any algebraic properties (e.g., the minimum distance or the run-length limit) in our design of the trellis code. Our design is purely probabilistic in that we construct the inner trellis code to mimic the transition probabilities of a Markov process that achieves a high (capacity-approaching) information rate. Hence, we name it a matched information rate (MIR) design. We provide a set of five design rules for constructions of capacity-approaching MIR inner trellis codes. We optimize the outer LDPC code using density evolution tools specially modified to fit the superchannel consisting of the inner MIR trellis code concatenated with the partial response channel. Using this strategy, we design degree sequences of irregular LDPC codes whose noise tolerance thresholds are only fractions of a decibel away from the capacity. Examples of code constructions are shown for channels both with and without spectral nulls.

Capacity of power constrained memoryless AWGN channels with fixed input constellations

We propose a numerical method to compute the capacity of a power constrained memoryless additive white Gaussian noise (AWGN) channel with finite and fixed input alphabets. The method is based on a two-part algorithm. The first part is a modified version of the Blahut-Arimoto algorithm and the second part is a simple maximization algorithm over a single parameter. The optimal input distribution we obtain can be utilized to construct probabilistic codes for this channel. These codes promise to bridge the shaping gap between the uniform-input information rate and the capacity of the channel.

Optimized LDPC codes for partial response channels

We construct codes that can closely approach (and possibly ultimately achieve) the i.i.d. capacity of an intersymbol interference (ISI) channel with inputs confined to binary values. We use the low-density-parity-check (LDPC) degree sequences optimization method proposed by Richardson, Shokrollahi and Urbanke (see IEEE Trans. Inform. Theory, vol.47, p.619-37, February 2001) and appropriately modify it for ISI channels.

Concatenated codes for deletion channels

We design concatenated codes suitable for the deletion channel. The inner code is a com- bination of a single deletion correcting Varshamov- Tenengolts block code and a marker code. The outer code is a low-density parity-check (LDPC) code. The inner decoder detects the synchronizing points in the received symbol sequence and feeds the outer LDPC decoder with soft information. Our simulation results with regular LDPC outer codes demonstrate that the bit error rates of can be obtained at rate 0.21 when the probability of deletion is 8%. I. CHANNEL MODEL AND CODE STRUCTURE In the memoryless deletion channel model (l), each trans- mitted symbol is independently deleted with probability Pd; otherwise it is transmitted correctly. As the codewords are passed through the deletion channel the location and the size of each codeword become unclear. Our coding scheme is shown in Figure 1. Information bits are first encoded by an outer low-density parity-check (LDPC) encoder (2). We denote the LDPC block length with N. Then the blocks of N encoded bits are broken into blocks of length k. The inner code consists of Varshamov-Tenengolts (VT) code (3) and Marker code (4). The VT encoder encodes k-bit blocks into blocks of length n. The marker code is used to solve the synchronization problem. A marker (header) is a set of bits with specific length (marker length), inserted between a predetermined number of bits in the code sequences encoded by the outer LDPC and inner VT encoder. The VT code VT,(n) is a single-deletion correcting set of length n binary strings = 21 ... xn satisfying n

Belief-propagation with information correction: improved near maximum-likelihood decoding of low-density parity-check codes

We propose an improved belief-propagation (BP) decoder for low-density parity-check (LDPC) codes based on channel information correction. We show that our algorithm achieves sizeable performance gains (in waterfall and error floor regions) compared to the standard BP decoder. We verify by examples that the proposed decoder almost achieves the maximum-likelihood decoding performance for short LDPC codes

Matched information rate codes for binary ISI channels

We propose a coding/decoding strategy to approach the channel capacities for binary intersymbol interference (ISI) channels. The proposed codes are serially concatenated codes: inner matched information rate codes and outer irregular low-density parity-check (LDPC) codes. The whole system is iteratively decodable.

Improvements in belief-propagation decoding based on averaging information from decoder and correction of clusters of nodes

In this letter we provide several methods to improve belief-propagation (BP) decoding of low-density parity-check codes. The methods use additional processing of the decoded information during the decoding process and are grouped into two categories. The first category is useful in the waterfall performance region and is based on processing averaged information obtained from the decoder. Several choices of the feedback information utilized in additional processing are introduced. The second category is useful in the error-floor performance region and is based on fixing clusters of symbols simultaneously, again utilizing the information obtained by monitoring the decoder. We demonstrate on a code example that our methods achieve sizeable gains compared to the original BP decoder