Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

Twitto, M.; Sason, Igal; Shamai, Shlomo

doi:10.1109/isit.2006.261625

Cited by 13 publications

(17 citation statements)

References 26 publications

(28 reference statements)

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“…In a companion paper [14], new upper bounds on the block and bit error probabilities of linear block codes are derived. These bounds improve the tightness of the Shulman and Feder bound [13] and therefore also reproduce the random coding error exponent.…”

Section: Discussionmentioning

confidence: 99%

On the Error Exponents of Improved Tangential Sphere Bounds

Twitto

Sason

2007

IEEE Trans. Inform. Theory

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The performance of maximum-likelihood (ML) decoded binary linear block codes over the AWGN channel is addressed via the tangential sphere bound (TSB) and two of its recent improved versions. The paper is focused on the derivation of the error exponents of these bounds. Although it was exemplified that some recent improvements of the TSB tighten this bound for finite-length codes, it is demonstrated in this paper that their error exponents coincide. For an arbitrary ensemble of binary linear block codes, the common value of these error exponents is explicitly expressed in terms of the asymptotic growth rate of the average distance spectrum.

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Section: Discussionmentioning

confidence: 99%

On the Error Exponents of Improved Tangential Sphere Bounds

Twitto

Sason

2007

IEEE Trans. Inform. Theory

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“…In this respect we also mention that some high rate turbo-product codes with moderate block lengths (see [4]) exhibit a gap of 0.75 -0.95 dB with respect to the information-theoretic limitation provided by the ISP bound. Based on numerical results in [33] for the ensemble of uniformly interleaved (1144, 1000) turbo-block codes whose components are random systematic, binary and linear block codes, the gap in Eb N0 between the ISP lower bound and an upper bound under ML decoding is 0.9 dB for a block error probability of 10 −7 . These results exemplify the strength of the sphere-packing bounds for assessing the theoretical limitations of block codes and the power of iteratively decoded codes (see also [9], [15], [16], [24], [36]).…”

Section: Minimal Block Length As a Function Of Performancementioning

confidence: 99%

An improved sphere-packing bound for finite-length codes over symmetric memoryless channels

Wiechman

Sason

2008

2008 Information Theory and Applications Workshop

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This paper derives an improved sphere-packing (ISP) bound for finite-length codes whose transmission takes place over symmetric memoryless channels, and which are decoded with an arbitrary list decoder. We first review classical results, i.e., the 1959 sphere-packing (SP59) bound of Shannon for the Gaussian channel, and the 1967 sphere-packing (SP67) bound of Shannon et al. for discrete memoryless channels. An improvement on the SP67 bound by Valembois and Fossorier is also discussed. These concepts are used for the derivation of a new lower bound on the error probability of list decoding (referred to as the ISP bound) which is uniformly tighter than the SP67 bound and its improved version. The ISP bound is applicable to symmetric memoryless channels, and some of its applications are exemplified. Its tightness under ML decoding is studied by comparing the ISP bound to previously reported upper and lower bounds on the ML decoding error probability, and also to computer simulations of iteratively decoded turbo-like codes. This paper also presents a technique which performs the entire calculation of the SP59 bound in the logarithmic domain, thus facilitating the exact calculation of this bound for moderate to large block lengths without the need for the asymptotic approximations provided by Shannon.

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“…The effectiveness of the bound in (26) for an L-list permutation invariant linear code C is mainly affected by its weight distribution and the relation of the latter to the multinomial distribution. Indeed, the larger term F C in the denominator of the double exponent of (26) is, the looser the specific bound of Theorem 2 becomes for the output symmetric discrete memoryless channels.…”

Section: A Refinement Of the Bound Of Theoremmentioning

confidence: 99%

List Permutation Invariant Linear Codes: Theory and Applications

Xenoulis

2014

IEEE Trans. Inform. Theory

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The class of q-ary list permutation invariant linear codes is introduced in this paper along with probabilistic arguments that validate their existence when certain conditions are met. The specific class of codes is characterized by an upper bound that is tighter than the generalized Shulman-Feder bound and relies on the distance of the codes' weight distribution to the binomial (multinomial, respectively) one. The bound applies to cases where a code from the proposed class is transmitted over a q-ary output symmetric discrete memoryless channel and list decoding with fixed list size is performed at the output. In the binary case, the new upper bounding technique allows the discovery of list permutation invariant codes whose upper bound coincides with sphere-packing exponent. Furthermore, the proposed technique motivates the introduction of a new class of upper bounds for general q-ary linear codes whose members are at least as tight as the DS2 bound as well as all its variations for the discrete channels treated in this paper.

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Tightened Upper Bounds on the ML Decoding Error Probability of Binary Linear Block Codes

Cited by 13 publications

References 26 publications

On the Error Exponents of Improved Tangential Sphere Bounds

On the Error Exponents of Improved Tangential Sphere Bounds

An improved sphere-packing bound for finite-length codes over symmetric memoryless channels

List Permutation Invariant Linear Codes: Theory and Applications

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