Engineering topics

Costello, D. J., Jr.

Publications and source records attributed to Costello, D. J., Jr..

At least 19 records

NASA NTRS1994

Achieving unequal error protection with convolutional codes

This paper examines the unequal error protection capabilities of convolutional codes. Both time-invariant and periodically time-varying convolutional encoders are examined. The effective free distance vector is defined and is shown to be useful in determining the unequal error protection (UEP) capabilities of convolutional codes. A modified transfer function is used to determine an upper bound on the bit error probabilities for individual input bit positions in a convolutional encoder. The bound is heavily dependent on the individual effective free distance of the input bit position. A bound relating two individual effective free distances is presented. The bound is a useful tool in determining the maximum possible disparity in individual effective free distances of encoders of specified rate and memory distribution. The unequal error protection capabilities of convolutional encoders of several rates and memory distributions are determined and discussed.

Mills, D. G.↗

NASA NTRS1986

Error control techniques for satellite and space communications

High rate concatenated coding systems with trellis inner codes and Reed-Solomon (RS) outer codes for application in satellite communication systems are considered. Two types of inner codes are studied: high rate punctured binary convolutional codes which result in overall effective information rates between 1/2 and 1 bit per channel use; and bandwidth efficient signal space trellis codes which can achieve overall effective information rates greater than 1 bit per channel use. Channel capacity calculations with and without side information performed for the concatenated coding system. Concatenated coding schemes are investigated. In Scheme 1, the inner code is decoded with the Viterbi algorithm and the outer RS code performs error-correction only (decoding without side information). In scheme 2, the inner code is decoded with a modified Viterbi algorithm which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, while branch metrics are used to provide the reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. These two schemes are proposed for use on NASA satellite channels. Results indicate that high system reliability can be achieved with little or no bandwidth expansion.

Costello, D. J., Jr.↗

NASA NTRS1986

Error control techniques for satellite and space communications

The performance of NASA Telecommand System was analyzed. A random coding approach was taken to determine the optimum code rate to use in forward error correcting (FEC) system with a fixed signal energy to noise power density ration, but no bandwidth constraint. Capacity and cutoff rates of concatened coding systems were determined. A lower bound on the minium distance growth rate between unmerged codewords was obtained for time invarient convolutional codes.

Costello, D. J., Jr.↗

NASA NTRS1986

Error control techniques for satellite and space communications

The performance anlaysis of NASA's telecommand systems was summarized. It is assumed that the decoded frames are scrambled prior to decoding by the outer code. The average decoded bit error rate are examined which allows the possibility of evaluating many different frame coding options. The capacity and cutoff rate of the outer channel formed by the combination of the actual physical channel and the inner encoder and decoder in a concatenated coding system were analyzed. The best combination of inner and outer codes to use in a concatenated coding system were determined. It was established that in general: (1) it is better not to interleave between the inner and outer codes; and (2) for a fixed overall code rate, it is better to use higher rate inner codes and lower rate outer codes. Inner convolutional codes are considered. The analysis is more difficult in this case because the inner decoder error events do not appear in blocks of fixed length but can be of many different lengths.

Costello, D. J., Jr.↗

NASA NTRS1985

Error control for reliable digital data transmission and storage systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. In this paper we present some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative alorithm to find the error locator polynomial. Two codes are considered: (1) a d sub min = 4 single-byte-error-correcting (SBEC), double-byte-error-detecting (DBED) RS code; and (2) a d sub min = 6 double-byte-error-correcting (DBEC), triple-byte-error-detecting (TBED) RS code.

Costello, D. J., Jr.↗

NASA NTRS1984

The undetected error probability for shortened hamming codes

Hamming or shortened Hamming codes are widely used for error detection in data communications. For example, the CCITT (International Telegraph and Telephone Consultative Committee) recommendation X.25 for packet-switched data networks adopts a distance-4 cyclic Hamming code with 16 parity-check bits for error detection. The natural length of this code is n = 2(15)-1 = 32,767. In practice the length of a data packet is no more than a few thousand bits which is much shorter than the natural length of the code. Consequently, a shortened version of thecode is used. Often the length of a data packet varies, say from a few hundred bits to a few thousand bits, hence the code must be shortened by various degrees. Shortening affects the performance of the code. The error-detection performance of shortened Hamming codes, particularly the codes obtained from the distance-4 Hamming codes adopted by CCITT recommendation X.25, is investigated. A method for computing the probability of an undetected error is presented.

Costello, D. J., Jr.↗

NASA NTRS1984

Probability of undetected error after decoding for a concatenated coding scheme

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Costello, D. J., Jr.↗

NASA NTRS1984

Reed Solomon codes for error control in byte organized computer memory systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Lin, S.↗

NASA NTRS1984

ARQ schemes for data transmission in mobile radio systems

The problem of providing data communications over a land mobile radio channel is considered, taking into account error detection combined with retransmission on request as a means of obtaining reliability in digital data transmission. The considered systems are referred to as automatic RQ (repeat-request) or ARQ. It is pointed out that the distinguishing features of a land mobile radio (LMR) system, as far as the ARQ protocol is concerned, are a frequency or pair of frequencies shared by a large population of half-duplex users which cannot transmit and receive simultaneously. A description is presented of those variations of ARQ which are adaptable to an LMR system. A new channel model for a fading LMR channel is developed, and several ARQ protocols and some new protocol combinations are described. The relationships are developed for a description of the various protocols in terms of channel failure probabilities. Undetected error probabilities are developed and compared.

Comroe, R. A.↗

NASA NTRS1984

On the undetected error probability of a concatenated coding scheme for error control

Consider a concatenated coding scheme for error control on a binary symmetric channel, called the inner channel. The bit error rate (BER) of the channel is correspondingly called the inner BER, and is denoted by Epsilon (sub i). Two linear block codes, C(sub f) and C(sub b), are used. The inner code C(sub f), called the frame code, is an (n,k) systematic binary block code with minimum distance, d(sub f). The frame code is designed to correct + or fewer errors and simultaneously detect gamma (gamma +) or fewer errors, where + + gamma + 1 = to or d(sub f). The outer code C(sub b) is either an (n(sub b), K(sub b)) binary block with a n(sub b) = mk, or an (n(sub b), k(Sub b) maximum distance separable (MDS) code with symbols from GF(q), where q = 2(b) and the code length n(sub b) satisfies n(sub)(b) = mk. The integerim is the number of frames. The outercode is designed for error detection only.

Deng, H.↗

NASA NTRS1984

Performance analysis of the word synchronization properties of the outer code in a TDRSS decoder

A self-synchronizing coding scheme for NASA's TDRSS satellite system is a concatenation of a (2,1,7) inner convolutional code with a (255,223) Reed-Solomon outer code. Both symbol and word synchronization are achieved without requiring that any additional symbols be transmitted. An important parameter which determines the performance of the word sync procedure is the ratio of the decoding failure probability to the undetected error probability. Ideally, the former should be as small as possible compared to the latter when the error correcting capability of the code is exceeded. A computer simulation of a (255,223) Reed-Solomon code as carried out. Results for decoding failure probability and for undetected error probability are tabulated and compared.

Costello, D. J., Jr.↗

NASA NTRS1984

Cut-off rate calculations for the outer channel in a concatenated cooling system

Concatenated codes were long used as a practical means of achieving long block or constraint lengths for combating errors on very noisy channels. The inner and outer encoders are normally separated by an interleaver, so that decoded error bursts coming from the inner decoder are randomized before entering the outer decoder. The effectiveness of this interleaver is examined by calculating the cut-off rate of the outer channel seen by the outer decoder with and without interleaving. Interleaving never hurts the performance of a concatenated code, and when the inner code rate is near the cut-off rate of the inner channel, interleaving significantly improves code performance.

Herro, M. A.↗

NASA NTRS1984

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.

Costello, D. J., Jr.↗

NASA NTRS1983

Fast decoding of a d(min) = 6 RS code

A method for high speed decoding a d sub min = 6 Reed-Solomon (RS) code is presented. Properties of the two byte error correcting and three byte error detecting RS code are discussed. Decoding using a quadratic equation is shown. Theorems and concomitant proofs are included to substantiate this decoding method.

Deng, H.↗

NASA NTRS1983

An extended d(min) = 4 RS code

A minimum distance d sub m - 4 extended Reed - Solomon (RS) code over GF (2 to the b power) was constructed. This code is used to correct any single byte error and simultaneously detect any double byte error. Features of the code; including fast encoding and decoding, are presented.

Deng, H.↗

NASA NTRS1983

Permanence analysis of a concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however, the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.

Costello, D. J., Jr.↗

NASA NTRS1983

Symbol synchronization for the TDRSS decoder

Each 8 bits out of the Viterbi decoder correspond to one symbol of the R/S code. Synchronization must be maintained here so that each 8-bit symbol delivered to the R/S decoder corresponds to an 8-bit symbol from the R/S encoder. Lack of synchronization, would cause an error in almost every R/S symbol since even a - 1-bit sync slip shifts every bit in each 8-bit symbol by one position, therby confusing the mapping betweeen 8-bit sequences and symbols. The error correcting capability of the R/S code would be exceeded. Possible ways to correcting this condition include: (1) designing the R/S decoder to recognize the overload and shifting the output sequence of the inner decoder to establish a different sync state; (2) using the characteristics of the inner decoder to establish symbol synchronization for the outer code, with or without a deinterleaver and an interleaver; and (3) modifying the encoder to alternate periodically between two sets of generators.

Costello, D. J., Jr.↗

NASA NTRS1983

BCH codes for large IC random-access memory systems

In this report some shortened BCH codes for possible applications to large IC random-access memory systems are presented. These codes are given by their parity-check matrices. Encoding and decoding of these codes are discussed.

Lin, S.↗