Sulaiman Al-Bassam

On balanced codes

In a balanced code each codeword contains equally many 1s and 0s. Parallel decoding balanced codes with 2/sup r/ (or 2/sup r/-1) information bits are presented, where r is the number of check bits. The 2/sup 2/-r-1 construction given by D.E. Knuth (ibid., vol.32, no.1, p.51-3, 1986) is improved. The new codes are shown to be optimal when Knuths complementation method is used. >

Design of efficient balanced codes

All words in a balanced code have equal number of ones and zeros. Denote by DC(n,k) a balanced (or dc-free) code of length n, and 2/sup k/ code words. We design an efficient DC(k+r, k) code with k=2/sup r+1//spl minus/0.8/spl radic/(r/spl minus/2). These codes are optimal up to the construction method, introduced by D.E. Knuth (1986). >

Asymmetric/unidirectional error correcting and detecting codes

Introduces the theory and design of codes that correct t asymmetric errors and simultaneously detect d(d>t) asymmetric errors (t-AEC/d-AED). These codes have a much higher information rate than symmetric error correcting/detecting codes and yet maintain the same encoding and decoding complexity as existing error correcting codes. They are suited for asymmetric channels such as digital transmission over optical fiber or metallic cable and recording of data on optical disks. The authors also improve the design of the best-known t-EC/AUED (t symmetric error correcting and all unidirectional error detecting) codes and t-EC/d-UED (t symmetric error correcting and d unidirectional error detecting) codes. >

On the capacity and codes for the Z-channel

Let p be the 1 to 0 bit error probability and h(p)=-p log/sub 2/ p-(1-p) log/sub 2/ (1-p). The capacity of the Z-channel is given by C/sub Z/=log/sub 2/ (1+(1-p)p/sup p/(1-p)/). For small p, it is shown that C/sub Z//spl ap/1-(1/2)h(p) (vs., C/sub BS/(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.

Feedback Codes Achieving the Capacity of the Z-Channel

Given the 1 to 0 bit error probability, pisin[0, 1], the capacity of the Z-channel is given by Cz=log2(1+pp/(1-p)-p1/(1-p)). Some new error free feedback coding schemes that achieve the Z-channel capacity are presented.

On efficient high-order spectral-null codes

Let S (N,q) be the set of all words of length N over the bipolar alphabet (-1,+1), having a qth order spectral-null at zero frequency. Any subset of S (N,q) is a spectral-null code of length N and order q. This correspondence gives an equivalent formulation of S(N,q) in terms of codes over the binary alphabet (0,1), shows that S(N,2) is equivalent to a well-known class of single-error correcting and all unidirectional-error detecting (SEC-AUED) codes, derives an explicit expression for the redundancy of S(N,2), and presents new efficient recursive design methods for second-order spectral-null codes which are less redundant than the codes found in the literature.

On systematic single asymmetric error correcting codes

Summary form only given. In the asymmetric channel it is assumed that the transmitted binary sequence may suffer errors of one type only, say 1/spl rarr/0; the 0/spl rarr/1 errors are rare. Since errors are of one type they are called asymmetric errors as opposed to symmetric errors in which both 1/spl rarr/0 and 0/spl rarr/1 are expectable. Obviously, any symmetric error correcting code is also an asymmetric error correcting code. One would expect to obtain systematic asymmetric error correcting codes that have higher information rate than the symmetric ones; however, this is mostly not the case. We show in this paper that for any code dimension n (except for n=2/sup r/ and n=2/sup r/1 where r is a positive integer) the systematic asymmetric error correcting codes are not better than the symmetric codes.

New single asymmetric error-correcting codes

New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n=12 and n=15. In many cases one can construct a code C containing at least [2/sup n//n] codewords. It is known that a code with |C|/spl ges/[2/sup n//(n+1)] can be easily obtained. It should be noted that the proposed codes for n=12 and n=15 are also the best known codes that can be explicitly constructed, since the best of the existing codes for these values of n are based on combinatorial arguments. Useful partitions of binary vectors are also presented.

Design of efficient error-correcting balanced codes

New constructions of t-error correcting balanced codes, for 1>or=t>or=4, are presented. In a balanced code, all the words have an equal number of 1s and 0s. In many cases, the information rates of the new codes are better than the existing codes given in the literature. The proposed codes also have efficient encoding and decoding algorithms.

Byte unidirectional error correcting and detecting codes

Efficient byte unidirectional error correcting codes that are better than byte symmetric error correcting codes are presented. The encoding and decoding algorithms are discussed. A lower bound on the number of check bits for byte unidirectional error correcting codes is derived. It is then shown that these codes are close to optimal. Capability of these codes for asymmetric error correction is also described. Codes capable of detecting double byte unidirectional errors are also given. >