Toyoo Takata

Suboptimum decoding of decomposable block codes

To decode a long block code with a large minimum distance by maximum likelihood decoding is practically impossible because the decoding complexity is simply enormous. However, if a code can be decomposed into constituent codes with smaller dimensions and simpler structure, it is possible to devise a practical and yet efficient scheme to decode the code. This paper investigates a class of decomposable codes, their distance and structural properties. It is shown that this class includes several classes of well-known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage (soft-decision or hard-decision) decoding scheme for decomposable codes, their translates or unions of translates is devised, and its error performance is analyzed for an AWGN channel. The two-stage soft-decision decoding is suboptimum. Error performances of some specific decomposable codes based on the proposed two-stage soft-decision decoding are evaluated. It is shown that the proposed two-stage suboptimum decoding scheme provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length. >

On bit-error probability of a concatenated coding scheme

This paper presents a bit error probability analysis of a concatenated coding scheme over an AWGN BPSK channel. The inner code is a binary (64, 40) block code which is obtained from the third order Reed-Muller code of length 84 by setting two specific information bits to 0 and is decoded with soft-decision maximum likelihood decoding. The outer code is the NASA standard (255, 223) RS code over GF(2 ) with minimum distance 33 and is designed to correct 16 or fewer symbol errors. The outer code is interleaved to depth 5. Error performance of the proposed concatenated coding scheme is analyzed by a combination of simulation with analysis. The split weight enumerators for maximum distance separable codes are derived.

An upper bound on the effective error coefficient of two-stage decoding, and good two-level decompositions of some Reed-Muller codes

An upper bound on the effective error coefficient of a two-level code with two-stage decoding is presented. This bound provides a guideline for constructing two-level codes to achieve a good trade-off between the error performance and decoding complexity. Based on this bound, good two-level decompositions of some Reed-Muller codes for two-stage decoding are found. Simulation results on the error performances of some Reed-Muller codes of lengths up to 64 with two-stage soft-decision suboptimum decoding based on their two-level decompositions are given. >

An approximation to the weight distribution of binary primitive BCH codes with designed distances 9 and 11 (Corresp.)

Recently Kasami {\em et al.} presented a linear programming approach to the weight distribution of binary linear codes [2]. Their approach to compute upper and lower bounds on the weight distribution of binary primitive BCH codes of length 2^{m} - 1 with m \geq 8 and designed distance 2t + 1 with 4 \leq t \leq 5 is improved. From these results, the relative deviation of the number of codewords of weight j\leq 2^{m-1} from the binomial distribution 2^{-mt} \left( \stackrel{2^{m}-1}{j} \right) is shown to be less than 1 percent for the following cases: (1) t = 4, j \geq 2t + 1 and m \geq 16 ; (2) t = 4, j \geq 2t + 3 and 10 \leq m \leq 15 ; (3) t=4, j \geq 2t+5 and 8 \leq m \leq 9 ; (4) t=5,j \geq 2t+ 1 and m \geq 20 ; (5) t=5, j \geq 2t+ 3 and 12 \leq m \leq 19 ; (6) t=5, j \geq 2t+ 5 and 10 \leq m \leq 11 ; (7) t=5, j \geq 2t + 7 and m=9 ; (8) t= 5, j \geq 2t+ 9 and m = 8 .

A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes

This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.

The least stringent sufficient condition on the optimality of a suboptimally decoded codeword using the most reliable basis

Suppose a binary linear block code C with weight profile W is used for error control over the AWGN channel. A codeword c is mapped into the BPSK sequence x. Let r denote the received noisy vector and z=(z/sub 1/,...,z/sub N/) denote the corresponding bit-by-bit hard decoded sequence. Let V/sup N/ represent the set all binary N-tuples. For u=(u/sub 1/,...,u/sub N/) in V/sup N/, we define D/sub 1/(u)={i:u/sub i//spl ne/z/sub i/,i/spl les/N}, n(u)=|D/sub l/(u)| and D/sub 0/(u)={1,...,N}-D/sub l/(u). Then the maximum likelihood decoding (MLD) solution is the codeword c/sub opt/ which minimize the correlation discrepancy L(c)=/spl Sigma//sub i/spl isin/D1(c)/|Ti|. Consequently if for c*/spl isin/C and /spl alpha/(c*)=min/sub c/spl epsiv/C,c/spl ne/c*/{L(c)}, L(c*)/spl les//spl alpha/(c*), then c*=c/sub opt/. Therefore any lower bound on /spl alpha/(c*) will provide a sufficient condition on the optimality of a candidate codeword.

The least stringent sufficient condition on the optimality of suboptimally decoded codewords

The number of iterations of an iterative optimal or suboptimal decoding scheme for binary linear block codes without any effect on its error performance can be reduced by testing a sufficient condition on the optimality of a candidate codeword. The least stringent sufficient condition on the optimality of a decoded codeword is investigated under the assumption that the available information on the code is restricted to (1) the minimum weight or the distance profile and (2) for a given positive integer h, h or fewer already generated candidate codewords. The least stringent sufficient conditions of optimality for 1/spl les/h/spl les/3 are presented. Cond/sub 1/ is the same as the one given by Taipale and Pursley (1991), Cond/sub 2/ is less stringent than the one given by Kaneko, Nishijima, Inazumi and Hirasawa (see IEEE Trans. Inform. Theory, vol.IT-40, no.3, p.320, 1994), and Cond/sub 1/ and Cond/sub 2/ are derived from Cond/sub 3/ as special cases. These conditions can be used effectively to save computer simulation time for evaluating the error probability for maximum likelihood decoding.

A Defense Method against Distributed Slow HTTP DoS Attack

Threat of Distributed Denial of Service (DDoS) attack, that attempts to make a machine or network resource unavailable is getting serious. A service provided for load testing was abused to perform a DDoS attack targeting online game company in September, 2014. Such services are bringing serious threat for most services on the Internet. Slow HTTP DoS attack is one of the DoS attack methods that targets HTTP servers. This method obstructs the service by saturating the connection pool with slow and many requests. It is known that Slow HTTP DoS attack by just one attacker can be prevented effectively by limiting the number of connections for each IP address. On the other hand, it is also known that it is difficult to defend from Slow HTTP DoS attack from multiple attackers (i.e. Distributed Slow HTTP DoS attack). The threat of DDoS attack is getting serious, so we need a effective defense method against Distributed Slow HTTP DoS attack. In this paper, we propose and evaluate a defense method against Distributed Slow HTTP DoS attack by disconnecting the attack connections selectively by focusing on the number of connections for each IP address and the duration time. We show in our research that our proposed defense method is effective against Distributed Slow HTTP DoS attack.

On error performance analysis of closest coset decoding

The authors study closest coset decoding for decomposable codes. They analyse the proposed two-stage suboptimum decoding. The new upper bound, the conventional union bound and the simulation result are shown.<<ETX>>

A Study of Packet Sampling Methods for Protecting Sensors Deployed on Darknet

A darknet monitoring system is developed to grasp malicious activities on the Internet in an early stage and to copewith them. The darknet monitoring system consists of network sensors deployed widely on the Internet. The sensors capture incoming unsolicited packets. A goal of this system analyzes captured malicious packets and provides effective informationfor protecting good Internet users from malicious activities. To provide effective and reliable information, sensors mustbe deployed in secret and hidden from outside. On the otherhand, attackers intend to detect sensors for evading them. This attempt is known as localization attacks to darknet monitoring systems. If actual location of sensors is revealed to attackers, itis almost impossible to grasp the latest tactics used by attackers. Thus in our previous work, we proposed a packet sampling method, which samples incoming packets based on an attribute of packets sender, to increase a tolerance to a localization attack and to keep a high quality of information publicized by the system. As a result, we almost succeeded to counter from a localization attack, which generates spike on the publicized graph to detect a sensor. However in some cases, proposed sampling method works to attackers advantage and spikes appear clearly on the graph. Therefore, we propose advancedsampling methods, which sample incoming packets based on multiple attributes of packets sender. In this paper, we presentour improved methods and show a promising evaluation result obtained from the simulation.