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Efficient Non-Recursive Design of Second-Order Spectral-Null Codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第6期62卷 3084-3102页

作者： Tallini, Luca G. Pelusi, Danilo Mascella, Raffaele Pezza, Laura Elmougy, Samir Bose, Bella Univ Teramo Fac Sci Comunicaz I-64100 Teramo Italy Univ Roma La Sapienza Dipartimento Sci Base & Applicate Ingn I-00161 Rome Italy Mansoura Univ Fac Comp & Informat Dept Comp Sci Mansoura 35516 Egypt King Saud Univ Coll Comp & Informat Sci Dept Comp Sci Riyadh 11543 Saudi Arabia Oregon State Univ Sch Elect Engn & Comp Sci Corvallis OR 97331 USA

A new efficient design of second-order spectral-null (2-OSN) codes is presented. The new codes are obtained by applying the technique used to design parallel decoding balanced (i.e., 1-OSN) codes to the random walk method introduced by some of the authors for designing 2-OSN codes. This gives new non-recursive efficient code designs, which are less redundant than the code designs found in the literature. In particular, if k is an element of IN is the length of a 1-OSN code then the new 2-OSN coding scheme has length n = k + r. IIN with an extra redundancy of r similar or equal to 2 log(2) k + (1/2) log(2) log(2) k -0.174 check bits, with k and r even and n multiple of 4. The whole coding process requires O(k log k) bit operations and O(k) bit memory elements.

关键词： High order spectral null codes balanced codes Knuth's complementation method parallel decoding scheme optical and magnetic recording

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m-ary Balanced Codes With parallel decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2015年第6期61卷 3251-3264页

作者： Pelusi, Danilo Elmougy, Samir Tallini, Luca G. Bose, Bella Univ Teramo Fac Sci Comunicaz I-64100 Teramo Italy King Saud Univ Dept Comp Sci Coll Comp & Informat Sci Riyadh 1153 Saudi Arabia Mansoura Univ Dept Comp Sci Fac Computers & Informat Mansoura 35516 Egypt Oregon State Univ Sch Elect Engn & Comp Sci Corvallis OR 97331 USA

An m-ary block code, m = 2, 3, 4,..., of length n E IN is called balanced if, and only if, every codeword is balanced;that is, the real sum of the codeword components, or weight, is equal to 1.(m - 1)n/2 J. This paper presents efficient encoding schemes to m-ary balanced codes with parallel (hence, fast) decoding. In fact, the decoding time complexity is O(1) digit operations. These schemes are a generalization to the m-ary alphabet of Knuth's complementation method with parallel decoding. Let ((n)(w))(m) indicate the number of m-ary words of length n and weight w is an element of 10, 1,... (m - 1)n). For any m is an element of IN m >= 2, a simple implementation of the method is given which uses r Eili check digits to balance k <= {(1(L)(m-l)(r)(r/2)]) - (m mod 2 + [(m - 1)k mod 2))/(m - 1) information digits with an encoding time complexity of O(mklog(m)k) digit operations. A refined implementation of the parallel decoding method is also given with r check digits and k <= (m(r) -1)1 (m - 1) information digits, where the encoding time complexity is O (k root log(m) k). Thus, the proposed codes are less redundant than the m-ary balanced codes with parallel decoding found in the literature and yet maintain the same complexity.

关键词： Balanced codes m-ary alphabet Knuth's complementation method parallel decoding scheme unidirectional error detection optical and magnetic recording

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On Redundancy Reduction of Non-Recursive Second-Order Spectral-Null Codes

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IEEE ACCESS 2019年 7卷 112171-112179页

作者： Pelusi, D. Univ Teramo Fac Commun Sci I-64100 Teramo Italy

The code design problem of non-recursive second-Order Spectral Null (2-OSN) codes is to convert balanced information words into 2-OSN words employing the minimum possible redundancy. Let k be the balanced information word length. If k is an element of 2IN then the 2-OSN coding scheme has length n = k + r, with 2-OSN redundancy r is an element of 2IN and n is an element of 41N. Here, we use a scheme with r = 2 log k + Theta(log log k). The challenge is to reduce redundancy even further for any given k. The idea is to exploit the degree of freedom to select from more than one possible 2-OSN encoding of a given balanced information word. To reduce redundancy, empirical results suggest that extra information delta(k) = 0.5 log k + Theta(log log k) is obtained. Thus, the proposed approach would give a smaller redundancy r' = 1.5 log k + Theta(log log k) less than r = 2 log k + Theta(log log k).

关键词： Balanced codes high order spectral null codes Knuth's complementation method parallel decoding scheme optical and magnetic recording

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parallel decoding of turbo codes using soft output T-algorithms

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IEEE COMMUNICATIONS LETTERS 2001年第8期5卷 352-354页

作者： Dasgupta, U Narayanan, KR Texas Instruments Inc DSPS R&D Ctr Dallas TX 75206 USA Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA

Turbo codes need to be used with reasonably long blocks of data which invariably lead to encoding delay (latency) and decoding delay of the order of O(N) due to the finite computational speed of the processor. Recently it was shown that if the hardware complexity of W > 1 processors was acceptable, then the decoding delay could be reduced to O(N/W) without much performance degradation, by decoding the turbo code in a parallel fashion. In this letter we show that the decoding delay could be further reduced if the component decoders use parallel versions of soft output T-algorithms instead of parallel versions of the MAP algorithm.

关键词： decoding delay iterative soft output decoding MAP-based decoding parallel decoding scheme T-algorithm

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JOSEPHSON MEMORY TECHNOLOGY

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PROCEEDINGS OF THE IEEE 1989年第8期77卷 1194-1207页

作者： WADA, Y NEC Corp. Kanagawa

Memory circuit architecture (decoder, cell, cell array, and sense circuit) is surveyed, with emphasis on implementing a memory with fast access and low power consumption. Recent progress in fabrication and circuit technology has improved memory performance. An AC powering scheme, instead of the earlier DC system, has been developed. The AC powering scheme eliminates complicated timing control, which restricts shortening access time, but introduces large power consumption and in-phase powering problems. A parallel decoding scheme that decreases the number of decoding stages is presented. It will decrease the decoding time and AND scheme decoder. An attractive OR-inverter scheme has been proposed for a decoder suitable for a memory with a large capacity. The chip performance strongly depends not only on whether the read mode is destructive or nondestructive but also on the cell connection method, which determines the line inductance. Because the cell input line inductance depends on layered construction of the lines, a planarizing technology for an Nb Josephson integrated circuit has been developed to reduce line inductance by thinning the insulators. Access time of less than 0.5 ns has been confirmed in 1-kb and 4-kb memories using the proposed memory architecture

关键词： 0.5 ns 1 kbit 4 kbit AC powering scheme AND scheme decoder Josephson integrated circuit Josephson memory technology Nb OR-inverter scheme access time cell array cell connection method cellular arrays decoding decoding time memory circuit architecture parallel decoding scheme planarizing technology power consumption reviews sense circuit superconducting memory circuits

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On Efficient Second-Order Spectral-Null Codes using Sets of m₁-Balancing Functions

On Efficient Second-Order Spectral-Null Codes using Sets of ...

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IEEE International Symposium on Information Theory (ISIT)

作者： Mascella, Raffaele Pelusi, Danilo Pezza, Laura Elmougy, Samir Tallini, Luca G. Bose, Bella Univ Teramo Dip Sci Comunicaz Teramo Italy Univ Roma La Sapienza Dip Me Mo Mat Rome Italy King Saud Univ Dept Comp Sci Riyadh Saudi Arabia Oregon State Univ Sch EECS Corvallis OR USA

ISBN: (纸本)9781479904464

A new efficient coding scheme is given for second-order spectral-null (2-OSN) codes. The new method applies the Knuth's optimal parallel decoding scheme for balanced (i.e., 1-OSN) codes to the random walk method introduced by Tallini and Bose to design 2-OSN codes. If k is an element of IN is the length of a 1-OSN code then the new 2-OSN coding scheme has length n = k+r is an element of IN with an extra redundancy of r greater than or similar to 2 log(2) k | (1/2) log(2) log(2) k -0.674 check bits. The whole coding process requires O(n log n) bit operations and O(n) bit memory elements.

关键词： high order spectral null codes balanced codes Knuth's complementation method parallel decoding scheme optical and magnetic recording

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On m-ary Balanced Codes with parallel decoding

On <i>m</i>-ary Balanced Codes with Parallel Decoding

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2010 IEEE International Symposium on Information Theory

作者： Pelusi, Danilo Tallini, Luca G. Bose, Bella Univ Teramo Dip Sci Comunicaz I-64100 Coste San Agostino Teramo Italy Oregon State Univ Sch EECS Corvallis OR 97331 USA

ISBN: (纸本)9781424469604

An m-ary block code, m = 2, 3, 4, ..., of length n is an element of IN is called balanced if, and only if, every codeword is balanced;that is, the real sum of the codeword components, or weight, is equal to left perpendicular(m - 1)n/2right perpendicular. This paper presents a tight generalization of Knuth's complementation method with parallel (hence, fast) decoding scheme. Let (n w)(m) indicate the number of m-ary words of length n and weight w is an element of {0, 1, ..., (m - 1)(n)}. A simple implementation of the scheme uses (m - 1) k + m mod 2 balancing functions to make a k is an element of IN digit information word to be balanced. So, r is an element of IN check digits can be used to balance k <= [left perpendicularr (m - 1)r/2right perpendicular)(m) - m mod 2]/(m - 1) information digits. A refined implementation of the parallel decoding scheme uses r check digits to balance k <= (m(r) - 1)/(m -1) information digits.

关键词： m-ary alphabet balanced codes Knuth's complementation method parallel decoding scheme unidirectional error detection optical and magnetic recording

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Construction of Efficient q-ary Balanced Codes

Construction of Efficient q-ary Balanced Codes

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IEEE AFRICON Conference - Powering Africa s Sustainable Energy for AD Agenda - The Role ofICT and Engineering.

作者： Mambou, Elie N. Swart, Theo G. Univ Johannesburg Dept Elect & Elect Engn Sci POB 524 ZA-2006 Auckland Pk South Africa

ISBN: (纸本)9781728132891

Knuth proposed a simple scheme for balancing codewords, which was later extended for generating q-ary balanced codewords. The redundancy of existing schemes for balancing q-ary sequences is larger than that of the full balanced set which is the minimum achievable redundancy. In this article, we present a simple and efficient method to encode the prefix that results in less redundancy for the construction of q-ary balanced codewords.

关键词： balanced codes balancing point redundancy q-ary alphabet parallel decoding scheme Knuth's scheme

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