Engineering topics

Cheung, K.-M.

Publications and source records attributed to Cheung, K.-M..

26 records · Page 2

NASA NTRS1989

The weight distribution and randomness of linear codes

Finding the weight distributions of block codes is a problem of theoretical and practical interest. Yet the weight distributions of most block codes are still unknown except for a few classes of block codes. Here, by using the inclusion and exclusion principle, an explicit formula is derived which enumerates the complete weight distribution of an (n,k,d) linear code using a partially known weight distribution. This expression is analogous to the Pless power-moment identities - a system of equations relating the weight distribution of a linear code to the weight distribution of its dual code. Also, an approximate formula for the weight distribution of most linear (n,k,d) codes is derived. It is shown that for a given linear (n,k,d) code over GF(q), the ratio of the number of codewords of weight u to the number of words of weight u approaches the constant Q = q(-)(n-k) as u becomes large. A relationship between the randomness of a linear block code and the minimum distance of its dual code is given, and it is shown that most linear block codes with rigid algebraic and combinatorial structure also display certain random properties which make them similar to random codes with no structure at all.

Cheung, K.-M.↗

NASA NTRS1988

Long decoding runs for Galileo's convolutional codes

Decoding results are described for long decoding runs of Galileo's convolutional codes. A 1 k-bit/sec hardware Viterbi decoder is used for the (15, 1/4) convolutional code, and a software Viterbi decoder is used for the (7, 1/2) convolutional code. The output data of these long runs are stored in data files using a data compression format which can reduce file size by a factor of 100 to 1 typically. These data files can be used to replicate the long, time-consuming runs exactly and are useful to anyone who wants to analyze the burst statistics of the Viterbi decoders. The 1 k-bit/sec hardware Viterbi decoder was developed in order to demonstrate the correctness of certain algorithmic concepts for decoding Galileo's experimental (15, 1/4) code, and for the long-constraint-length codes in general. The hardware decoder can be used both to search for good codes and to measure accurately the performance of known codes.

Lahmeyer, C. R.↗

NASA NTRS1988

Performance of Galileo's concatenated codes with nonideal interleaving

The Galileo spacecraft employs concatenated coding schemes with Reed-Solomon interleaving depth 2. The bit error rate (BER) performance of Galileo's concatenated codes, assuming different interleaving depths (including infinite interleaving depth) are compared. It is observed that Galileo's depth 2 interleaving, when used with the experimental (15, 1/4) code, requires about 0.4 to 0.5 dB additional signal-to-noise ratio to achieve the same BER performance as the concatenated code with ideal interleaving. When used with the standard (7, 1/2) code, depth 2 interleaving requires about 0.2 dB more signal-to-noise ratio than ideal interleaving.

Cheung, K.-M.↗

NASA NTRS1988

Phobos lander coding system: Software and analysis

The software developed for the decoding system used in the telemetry link of the Phobos Lander mission is described. Encoders and decoders are provided to cover the three possible telemetry configurations. The software can be used to decode actual data or to simulate the performance of the telemetry system. The theoretical properties of the codes chosen for this mission are analyzed and discussed.

Cheung, K.-M.↗

NASA NTRS1988

A lower bound for the decoder error probability of the linear MDS code

A lower bound for the decoder error probability (P sub E (u)) of a linear maximum distance separable (MDS) code is derived by counting the dominant types of decoding words around code words. It is shown that the lower bound derived is similar in form, and close numerically, to the upper bound derived.

Cheung, K.-M.↗

NASA NTRS1988

A labeling procedure for linear finite-state codes

A method to define the labels of the state diagram of a linear finite-state code is presented and investigated. This method is particularly suitable for simple hardware implementation since it simplifies the encoder structure. The method can also be applied to the labeling of a state diagram that is not completely connected to obtain a linear finite state code with larger free distance.

Cheung, K.-M.↗

NASA NTRS1988

Further results on finite-state codes

A general construction for finite-state (FS) codes is applied to some well-known block codes. Subcodes of the (24,12) Golay code are used to generate two optimal FS codes with d sub free = 12 and 16. A partition of the (16,8) Nordstrom-Robinson code yields a d sub free = 10 FS code. Simulation results are shown and decoding algorithms are briefly discussed.

Pollara, F.↗

NASA NTRS1987

More on the decoder error probability for Reed-Solomon codes

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Cheung, K.-M.↗