Iterative Decoding With Replicas

Replica shuffled versions of iterative decoders for low-density parity-check (LDPC) codes and turbo codes are presented. The proposed schemes can converge faster than standard and plain shuffled approaches. Two methods, density evolution and extrinsic information transfer (EXIT) charts, are used to analyze the performance of the proposed algorithms. Both theoretical analysis and simulations show that the new schedules offer good tradeoffs with respect to performance, complexity, latency, and connectivity     

Hybrid burst erasure correction of LDPC codes

In this letter, burst erasure correction of low density parity check codes based on a hybrid approach is presented. The proposed method preserves as much as possible the original low density representation and augments it by specific check sums judiciously selected.     

Box and match techniques applied to soft-decision decoding

In this paper, we improve the ordered statistics decoding algorithm by using matching techniques. This allows us: to reduce the worst case complexity of decoding (the error performance being fixed) or to improve the error performance (for a same complexity); to reduce the ratio between average complexity and worst case complexity; to achieve practically optimal decoding of rate-1/2 codes of lengths up to 128 (rate-1/2 codes are a traditional benchmark, for coding rates different from 1/2, the decoding is easier); to achieve near-optimal decoding of a rate-1/2 code of length 192, which could never be performed before.     

Bit-error probability for maximum-likelihood decoding of linearblock codes and related soft-decision decoding methods

In this correspondence, the bit-error probability P_b for maximum-likelihood decoding of binary linear block codes is investigated. The contribution P_b(j) of each information bit j to P_b is considered and an upper bound on P_b(j) is derived. For randomly generated codes, it is shown that the conventional approximation at high SNR P_b≈(d_H/N).P_s, where P_s represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P_b when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit-error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for soft-decision decoding methods which require a generator matrix with a particular structure such as trellis decoding, multistage decoding, or algebraic-based soft-decision decoding, equivalent schemes that reduce the bit-error probability are discussed. Although the gains achieved at practical bit-error rates are only a fraction of a decibel, they remain meaningful as they are of the same orders as the error performance differences between optimum and suboptimum decodings. Most importantly, these gains are free as they are achieved with no or little additional circuitry which is transparent to the conventional implementation     

A unified method for evaluating the error-correction radius ofreliability-based soft-decision algorithms for linear block codes

This paper presents a unified method for evaluating the error-correction radii of many reliability-based soft-decision decoding algorithms for binary linear block codes. Based on this unified method, these decoding algorithms as well as their potential improvements can be compared directly. The error-correction radius for each of these decoding algorithms is determined by finding the closest point on the boundary of the decision region of the soft-decision decoder to the transmitted signal sequence. It is shown that this problem can be formulated as a constrained optimization problem. Although no general closed-form expression is possible, a simple algorithm that always converges to the optimum solution of this optimization problem is presented. Based on these results, the error-correction radii of some well-known reliability-based soft-decision decoding algorithms are revisited and compared     

Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images

In this paper, a method to design regular (2, d_c)- LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.     

A new technique for computing the weight spectrum of turbo-codes

We obtain an accurate and simple analytical approximation to the bit error probability of maximum-likelihood decoding of parallel concatenated convolutional codes (turbo-codes) by extending a result from the paper by Fossorier et al. (see IEEE Trans. Inform. Theory, vol.45, no.5, p.1646-8, 1999), which investigates the weight enumerating function of terminated convolutional codes, to compute their conditional weight enumerating function     

Differential trellis decoding of convolutional codes

This paper investigates the principle of metric differences for trellis decoding of convolutional codes. Based on this differential method, a new algorithm, referred to as differential trellis decoding (DTD), is proposed. DTD offers an alternative to the conventional “add-compare-select” (ACS) method for implementing the Viterbi algorithm