A Forward Error Correction coding method comprises a generalised concatenated code comprising a plurality of outer component codes (Ai) and a plurality of inner component codes (B’i ). The outer components codes comprise Reed-Solomon (RS) codes and a plurality of binary codes of equal length but varying rates. The inner component codes have a nested structure and are defined by the sum of disjoint BoseChaudhuri-Hocquenghem (BCH) codes. The component codes Ai and B’i are selected such that the product of the minimum Hamming distances of the inner and outer component codes, Did’i , are as equal as possible. Moreover the component codes are selected by matching cyclotomic cosets of inner BCH codes and type and multiplicity of outer codes.

Forward error correction coding

DVB-H is a new broadcasting standard, which offers reliable high data rate reception of IP packets for mobile handheld battery-powered devices. A link layer with multiprotocol encapsulation (MPE), including Reed-Solomon forward error correction (FEC) combined with a cyclic redundancy check (CRC), is defined in the standard to work on top of the DVB-T physical layer. For error correction in the receiver the DVB-H standard suggests to use erasure decoding based on the CRC information. Yet, the decoding method is not strictly determined in the standard. This paper investigates the performance of five different Reed-Solomon decoding schemes for the DVB-H link layer forward error correction called MPE-FEC. They differ on utilization strategy of existing erasure information. The performance of different decoding methods are evaluated analytically in an binary symmetric channel (BSC) and with simulations in the additive white Gaussian noise (AWGN) and a mobile fading channel. For the simulations in the fading channel a packet channel model based on actual measurements is designed. It is shown that more sophisticated decoding methods than the one suggested in the standard are required for efficient retrieval of IP packets

The Performance Analysis of MPE-FEC Decoding Methods at the DVB-H Link Layer for Efficient IP Packet Retrieval

On Shortest Linear Recurrences

DVB-H, which is an amendment of DVB-T, offers reliable high data rate reception for mobile handheld and battery-powered devices. A link layer with error correction was defined to work on top of the DVB-T physical layer. The DVB-H standard suggests to use Reed-Solomon coding combined with CRC-32 error detection as the link layer FEC. This paper investigates the performance of the proposed error correction scheme, which is first analyzed theoretically and then by computer simulations. Results are compared to conventional Reed-Solomon decoding without utilizing CRC-32 error detection to illustrate drawbacks of the decoding solution in DVB-H standard

Analysis of Reed-Solomon Coding Combined with Cyclic Redundancy Check in DVB-H link layer

A practical definition of an erasure is presented and leads to new expressions for correct and incorrect decoding probabilities for Reed-Solomon codes, assuming an incomplete decoder. The main benefit of this approach is that, in contrast with the usual approach, one is able to analytically demonstrate the performance improvement provided by errors-and-erasures decoding relative to errors-only decoding. A technique is presented for evaluating the performance of Reed-Solomon codes for both types of decoding on an interleaved burst error channel such as is seen in digital magnetic tape recording. Several illustrative examples are included. >

A method of analysis for interleaved Reed-Solomon coding with erasure decoding on burst error channels

When a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance, the probability of decoding failure, the probability of erroneous decoding, and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code. For the symmetric erasure channel, numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known, and for linear maximum distance separable (MDS) codes. The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution. Numerical examples include a triple-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length 63 and a Reed-Solomon code of length 1023 and minimum distance 31. >

On the computation of the performance probabilities for block codes with a bounded-distance decoding rule

A novel fast algorithm is developed for computing the burst-correcting limit of a cyclic or shortened cyclic code from the parity-check polynomial of the cyclic code. The algorithm is similar to the algorithm of H.J. Matt and J.L. Massey (1980) which, up to now, has been the most efficient method for determining the burst-correcting limit of a cyclic code, but is based on apolarity of binary forms instead of linear complexity. The running times of implementations in C of both algorithms on an IBM RISC System/6000 are compared for several binary cyclic codes of practical interest. A table of the burst-correcting limit of primitive binary BCH codes of length up to 1023 is included. >

A fast algorithm to determine the burst-correcting limit of cyclic or shortened cyclic codes

BCH decoders based on the Peterson-Gorenstein-Zierler algorithm can malfunction and produce output vectors that are no codewords. To avoid this malfunction a simple additional check is proposed that can be performed before the computation of the error locations. The additional check consists of the minimum number of algebraic equations in the syndrome components that are necessary over a general field to obtain a bounded-distance decoder. >

A. Dur

Papers

On the computation of the performance probabilities for block codes with a bounded-distance decoding rule

A fast algorithm to determine the burst-correcting limit of cyclic or shortened cyclic codes

Avoiding decoder malfunction in the Peterson-Gorenstein-Zierler decoder