SNR merits of binary modulation codes in equalized digitalrecording systems

For a digital recording system with a binary modulation encoder and a linearly dispersive channel with additive noise, the author determines optimum mean-square performance of the linear, partial-response, and decision-feedback equalizers. The analysis revolves around the power spectral density A(Ω) of the code and the folded signal-to-noise ratio X(Ω) of the channel. The latter function is analyzed for stylized optical and magnetic recording channels. For all equalizers it is shown that the effect of coding is similar to increasing X(Ω) by an additive portion 1/A(Ω). This favors depressions of A(Ω) at frequencies where X(Ω) is poor. However, for A(Ω) to have any depressions, the signaling rate must be increased with respect to uncoded storage, and this inevitably degrades X(Ω). At high information densities the degradation is often too large for coding to be rewarding. Examples serve to illustrate these results     

A note on the Shannon capacity of run-length-limited codes (Corresp.)

It is proven that 100-percent efficient fixed-rate codes for run-length-limited (RLL)(d,k)and RLL charge-constrained(d, k; c)channels are possible in only two eases, namely(d,k; c)=(0,1;1)and(1,3;3). Specifically, the binary Shannon capacity of RLL(d, k)constrained systems is shown to be irrational for all values of(d, k),0 leq d < k. For RLL charge-constrained systems with parameters(d, k;c), the binary capacity is irrational for all values of(d, k; c),0 leq d < k,2c geq k + 1, except(0,1; 1)and(1,3;3), which both have binary capacity1/2.     

On the construction of bounded-delay encodable codes forconstrained systems

We present a new technique to construct sliding-block modulation codes with a small decoding window. Our method, which involves both state splitting and look-ahead encoding, crucially depends on a new “local” construction method for bounded-delay codes. We apply our method to construct several new codes, all with a smaller decoding window than previously known codes for the same constraints at the same rate     

Joint synchronization and SNR estimation for turbo codes in AWGN channels

Turbo codes are sensitive to both (timing) synchronization errors and signal-to-noise ratio (SNR) mismatch. Since turbo codes are intended to work in environments with very low SNR, conventional synchronization methods often fail. This paper investigates blind symbol-timing synchronization and SNR estimation based on oversampled data frames. The technique is particularly suitable for low-rate turbo codes operating in additive white Gaussian noise at low SNR and modest data-transfer rates, as in deep space, satellite, fixed wireless, or wireline communications. In accordance with the turbo principle, intermediate decoding results are fed back to the estimator, thereby facilitating decision-directed estimation. The analytical and simulated results show that with three or more samples per symbol and raised cosine-rolloff pulse shaping, performance approaches that of systems with perfect timing and SNR knowledge at the receiver.     

On the design of mean-square error channel coding systems using cyclic codes

Channel coding systems that employ linear block codes can be designed according to a mean-square error criterion. The optimum encoder and decoder pair is determined by selecting special elements in a generalized frequency domain based upon the values of key parameters called ratio weights. Systems may be designed that employ either hard or soft decision variables in the decoder. When cyclic codes are used, a minimal ideal decomposition of the code space shows that the ratio weights possess constant values on certain subsets in the frequency domain. This permits a drastic reduction in the number of ratio weights that need to be computed. For a cyclic code withtminimal ideals, this design procedure narrows the search for constancy subsets of the ratio weights to(2^{t}-1)subsets of the general space. Only one ratio weight needs to be computed for each constancy subset.     

On efficient code acquisition of optical orthogonal codes in optical CDMA systems

This letter presents an efficient method for optical code division multiple access (OCDMA) code acquisition based on unipolar optical orthogonal codes. We propose a two-dwell acquisition procedure and provide closed form expressions to analyze the system?s error probabilities. Our results match the Multiple Shift (MS) algorithm, recently introduced in the literature, and show that our procedure can achieve the same system performance with a lower computational complexity.     

Measuring audio SNR on digital broadcast systems

A spectrum analysis technique is described which will measure the quantization noise in a digital audio system with a signal present. An estimate of the power density spectrum is interpreted to find the signal to quantization noise ratio. Additional information derived from real life spectrum measurements is explained     

On the cardinality of systematic authentication codes viaerror-correcting codes

In both open and private communication the participants face potential threats from a malicious enemy who has access to the communication channel and can insert messages (impersonation attack) or alter already transmitted messages (substitution attack). Authentication codes (A-codes) have been developed to provide protection against these threats. In this paper we introduce a new distance, called the authentication distance (A-distance), and show that an A-code can be described as a code for the A-distance. The A-distance is directly related to the probability P_S of success in a substitution attack. We show how to transform an error-correcting code into an A-code and vice versa. We further use these transformations to provide both upper and lower bounds on the size of the information to be authenticated, and study their asymptotic behavior. As examples of obtained results, we prove that the cardinality of the source state space grows exponentially with the number of keys provided P_S>P_I, we generalize the square-root bound given by Gilbert, MacWilliams, and Sloane in 1979, and we provide very efficient constructions using concatenated Reed-Solomon codes     

On balanced codes

In a balanced code each codeword contains equally many 1's and 0's. Parallel decoding balanced codes with 2^r (or 2^r -1) information bits are presented, where r is the number of check bits. The 2²-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 Knuth's complementation method is used     

On the equivalence of generalized concatenated codes andgeneralized error location codes

We show that the generator matrix of a generalized concatenated code (GCC code) of order L consists of L submatrices, where the lth submatrix is the Kronecker product of the generator matrices of the lth inner code and the lth outer code. In a similar way we show that the parity-check matrix of a generalized error location code (GEL code) of order L consists of L submatrices, where the lth submatrix is the Gronecker product of the parity-check matrices of the lth inner code and the lth outer code. Then we use these defining matrices to show that for any GCC code there exists an equivalent GEL code and vice versa     

On the weight distribution of linear block codes formed fromconvolutional codes

We explain how to obtain the weight enumerator and the performance of linear block codes formed in several distinct ways from a convolutional code     

On expander codes

Sipser and Spielman (see ibid., vol.42, p.1717-22, Nov. 1996) have introduced a constructive family of asymptotically good linear error-correcting codes-expander codes-together with a simple parallel algorithm that will always remove a constant fraction of errors. We introduce a variation on their decoding algorithm that, with no extra cost in complexity, provably corrects up to 12 times more errors     

On runlength codes

Several results on binary (d, k) codes are given. First, a novel derivation for the capacity of these codes based on information-theoretic principles is given. Based on this result the spectrum of a (d, k) code is computed. Finally, the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the (d, k ) constraint is considered. Lower bounds on the capacity of such a channel are derived     

On the covering radius of codes

The covering radiusRof a code is the maximal distance of any vector from the code. This work gives a number of new results concerningt[n, k], the minimal covering radius of any binary code of lengthnand dimensionk. For examplet[n, 4]andt[n, 5]are determined exactly, and reasonably tight bounds ont[n, k]are obtained for anykwhennis large. These results are found by using several new constructions for codes with small covering radius. One construction, the amalgamated direct sum, involves a quantity called the norm of a code. Codes with normleq 2 R + 1are called normal, and may be combined efficiently. The paper concludes with a table giving bounds ont[n, k]forn leq 64.     

On the decoding of algebraic-geometric codes

A decoding algorithm for algebraic-geometric codes arising from arbitrary algebraic curves is presented. This algorithm corrects any number of errors up to [(d-g-1)/2], where d is the designed distance of the code and g is the genus of the curve. The complexity of decoding equals σ(n³) where n is the length of the code. Also presented is a modification of this algorithm, which in the case of elliptic and hyperelliptic curves is able to correct [(d-1)/2] errors. It is shown that for some codes based on plane curves the modified decoding algorithm corrects approximately d/2-g/4 errors. Asymptotically good q-ary codes with a polynomial construction and a polynomial decoding algorithm (for q⩾361 on some segment their parameters are better than the Gilbert-Varshamov bound) are obtained. A family of asymptotically good binary codes with polynomial construction and polynomial decoding is also obtained, whose parameters are better than the Blokh-Zyablov bound on the whole interval 0<σ<1/2     

Application of turbo codes in satellite mobile systems

Turbo codes are considered in a mobile channel with FSK modulation and LDI detection. Numerical results are presented for narrowband Gaussian, land mobile and satellite mobile channels separately. Numerical results show that turbo codes can significantly improve the performance over uncoded signalling     

The dynamics of group codes: Dual abelian group codes and systems

Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian (LCA) groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C/sup /spl perp// are dual codes, then the state spaces of C act as the character groups of the state spaces of C/sup /spl perp//. The controllability properties of C are the observability properties of C/sup /spl perp//. In particular, C is (strongly) controllable if and only if C/sup /spl perp// is (strongly) observable, and the controller memory of C is the observer memory of C/sup /spl perp//. The controller granules of C act as the character groups of the observer granules of C/sup /spl perp//. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.     

Sliding block codes between constrained systems

The construction of finite-state codes between constrained systems called sofic systems introduced by R. Karabed and B. Marcus (1988) is continued. It is shown that if Σ is a shift of finite type and S is a sofic system with k/n=h(S )/h(Σ), where h denotes entropy, there is a noncatastrophic finite-state invertible code from Σ to S at rate k:n if Σ and S satisfy a certain algebraic condition involving dimension groups, and Σ and S satisfy a certain condition on their periodic points. Moreover, if S is an almost finite type sofic system, then the decoder can be sliding block     

On the impact of SNR estimation error on adaptive modulation

In this letter we investigate the impact of signal-to-noise ratio (SNR) estimation on the performance of adaptive modulation. The adaptive modulation technique uses an estimate of the SNR at the receiver to choose a modulation scheme so that a given performance target is met. By adapting the modulation scheme, the link is able to improve the spectral efficiency as compared to static modulation. An analytic expression for the impact of SNR estimation error is derived and it is shown that SNR estimation has minimal impact on the performance.