Gallager bounds on the performance of maximum‐likelihood decoded linear binary block codes in AWGN interference

Yousefi, Shahram

doi:10.1002/ett.1092

Cited by 3 publications

(4 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As we mentioned before, if we only use G 1 D Q P for the decoding, the error-correction capability will be t max from Equation (17). However, for the factorisation process described here, we also use G 2 .…”

Section: Factorisation Stepmentioning

confidence: 99%

See 1 more Smart Citation

Collaborative algebraic decoding of interleaved Reed–Solomon codes

Shayegh

Soleymani

2011

Trans. Emerging Tel. Tech.

View full text Add to dashboard Cite

We derive and analyse an algorithm for collaborative decoding of heterogeneous interleaved Reed–Solomon (IRS) codes. They are generated by interleaving several codewords from different Reed–Solomon codes with the same length over the same Galois field. The basis of the decoding algorithm is similar to the Guruswami–Sudan (GS) decoding method. However, here multivariate interpolation is used to decode all the codewords of the interleaved scheme simultaneously. In the presence of burst errors, we show that the error‐correction capability of this algorithm is larger than that of independent decoding of each codeword using the standard GS method. In the latter case, the error‐correction capability is equal to the decoding radius of the GS algorithm for the Reed–Solomon code with the largest dimension. Also, concatenated codes using IRS codes as their outer codes and binary linear block codes as their inner codes are considered. Assuming maximum likelihood decoding of the inner code, we derive upper and lower bounds for the word error probability of concatenated codes over additive white Gaussian noise channel with binary phase‐shift keying modulation for both cases of independent and collaborative decoding of the outer IRS codes. We show that collaborative decoding provides considerable coding gain compared with independent decoding. Copyright © 2011 John Wiley & Sons, Ltd.

show abstract

Section: Factorisation Stepmentioning

confidence: 99%

“…Unfortunately, the exact analytical calculation of ML performance is generally not possible. However, there are several known upper and lower bounds . Here, we use Poltyrev's tangential sphere bound (TSB) for the upper bound.…”

Section: Interleaved Reed–solomon Codes In Concatenated Code Designmentioning

confidence: 99%

Collaborative algebraic decoding of interleaved Reed–Solomon codes

Shayegh

Soleymani

2011

Trans. Emerging Tel. Tech.

View full text Add to dashboard Cite

show abstract

“…such as Kuai-Alajaji-Takahara (KAT) bounds [4] (also see references therein), bounds by Yousefi et al [2,5,6], and lower bounds of Cohen and Merhav (CM bounds) [7]. More recently, Bonferroni-type bounds have also found their way in the analysis of space-time codes [8,9]: an increasingly popular trend applicable to many multiple-input multipleoutput (MIMO) systems.…”

mentioning

confidence: 99%

Cohen–Merhav bounds on the symbol error rate of uncoded signalling in AWGN interference

Yousefi

Holmes

2007

Trans Emerging Tel Tech

Self Cite

View full text Add to dashboard Cite

SUMMARYUsing a recent Bonferroni-type inequality proposed by Cohen and Merhav, we develop new tight lower bounds on the word error probability of uncoded systems with optimal Maximum A Posteriori (MAP) coherent detection for non-uniform signalling over additive white Gaussian noise channel. Our results are compared to the state-of-the-art Kuai-Alajaji-Takahara (KAT) lower bounds and it is shown that the superiority of one bound to another is dependent on the signal constellation, the amount of non-uniformity of the Bernoulli source to be communicated and the SNR range of interest. It is noted that bounding techniques for the performance evaluation of communication systems are receiving increasing attention today, thanks to their suitability for a wide variety of schemes ranging from uncoded signalling to space-time-coded multiple-input multiple-output (MIMO) systems.

show abstract

“…To analyze the frame error probability, it is sufficient to consider the equivalent channel model [10] , for 1,2, , In essence, every new bound must improve the union bound in some way. There are such results in probability theory, which are generally called Bonferroni-type bounds [91].…”

Section: Future Workmentioning

confidence: 99%

Near-optimum decoding and performance bounds for multiple-antenna communication

Ling¹

View full text Add to dashboard Cite

Multiple-antenna communication promises substantially enhanced data rate and diversity over rich-scattering fading channels. Coding for multiple-input multiple-output (MIMO) channels addresses three related problems: design of MIMO codes, MIMO decoding and performance analysis. In this dissertation, we look at selected topics in the latter two problems. In particular, we present near-optimum MIMO differential decoding algorithms, aiming at high decoding speed or improved performance in continuous fading, and derive tight performance bounds for space-time codes. The analysis of decoding algorithms and performance bounds herein may provide useful insights into code design and facilitate computer search for good codes. A number of MIMO differential decoders have been given in literature. However, most decoders are natural extensions of the traditional differential phase-shift keying (DPSK) techniques and do not really address some fundamental differences of the MIMO differential scheme. As a result, most decoders are limited to small constellation sizes and follow the linear prediction structure, which does not necessarily match the matrix signaling of MIMO. In this dissertation, we propose differential lattice decoding that is significantly faster for large constellation sizes. Moreover, noncoherent decoders wellmatched to the matrix signaling over continuously fading channels are presented. Proper approximations are made to obtain practical decoding complexity, which nonetheless guarantee near-optimum performance. The standard union bound is quite loose (in fact often divergent) for either coherent or noncoherent space-time codes. This phenomenon is especially pronounced in a quasistatic fading channel. We present tight performance bounds for space-time codes in the general framework of Gallager's bounding techniques. Closed-form upper bounds are proposed that are surprisingly tight in terms of the frame error probability. The proposed bounds only assume the knowledge of the weight spectrum, and can be evaluated very fast. In addition, we present novel methods of weight enumeration, which, in conjunction with the bounding techniques, give a complete treatment of performance bounds for space-time codes. The bounds are then extended to noncoherent MIMO schemes.

show abstract

Gallager bounds on the performance of maximum‐likelihood decoded linear binary block codes in AWGN interference

Cited by 3 publications

References 46 publications

Collaborative algebraic decoding of interleaved Reed–Solomon codes

Collaborative algebraic decoding of interleaved Reed–Solomon codes

Cohen–Merhav bounds on the symbol error rate of uncoded signalling in AWGN interference

Near-optimum decoding and performance bounds for multiple-antenna communication

Contact Info

Product

Resources

About