Ali S. Khayrallah

Coding for channels with cost constraints

We address the problem of finite-state code construction for the costly channel. This channel model is a generalization of the hard-constrained channel, also known as a subshift. Adler et al. (1986) developed the powerful state-splitting algorithm for use in the construction of finite-state codes for hard-constrained channels. We extend the state-splitting algorithm to the costly channel. We construct synchronous (fixed-length to fixed-length) and asynchronous (variable-length to fixed-length) codes. We present several examples of costly channels related to magnetic recording, the telegraph channel, and shaping gain in modulation. We design a number of codes, some of which come very close to achieving capacity.

Nonlinear filters in joint source channel coding of images

We address the problem of data compression and transmission applied to images. We present a differential pulse coded modulation (DPCM) scheme whose prediction filter is the Ll filter. We also present an ECC decoder which takes advantage of information to selectively filter reconstructed prediction difference sequence, using the weighted median filter. We apply our schemes to some test images, and we compare their performance to the appropriate baseline schemes. Our techniques exhibit a lot of resilience to noise, even for very noisy channels.

On the minimum bit-error rate of linear codes

We investigate the bit-error rate (BER) of linear block codes. The BER is a function of the encoder realization of the code. We express the BER in terms of the weight profiles of the subspaces of the code. We also discuss the relation between the Hadamard transform and the BER. >

The expansion factor of error-control codes

We investigate the expansion factor of a linear block code. The expansion factor /spl Delta/(C) of an (n,k;d) code with codebook C is the maximum over all generator matrices G whose row space is C, of the minimum of w(xG) - w(x) over all nonzero inputs x. One can view /spl Delta/(C) as a measure of the continuity of the code. It indicates how well the code preserves and expands the distance relations of the input. We show that the expansion factor is bounded as d - k/spl les//spl Delta/(C) /spl les/ d - 1. We also relate it to the weight distribution of the code, and the output length n. Finally we find the expansion factor for a number of codes, including Hamming, Equidistant, Golay, and BCH codes.

A source-channel coding study of ARQ for the transmission of images

We investigate the transmission of images over a noisy channel using an ARQ scheme. The images are compressed using the JPEG standard. The error control coding is provided by BCH codes. The ARQ mechanism is selective repeat ARQ. The error control decoding is bounded distance decoding. We look at three figures of merit: the overall distortion, the throughput, and the delay. We can vary three parameters: the source coding rate, the error control coding rate, and the radius of the error control decoder. We try to find the parameter combination that yields the best figure of merit, or combination of figures of merit.

Shaping codes constructed from cost-constrained graphs

We give a general procedure for constructing shaping codes from costly constrained graphs. The codes have finite-state encoders and sliding-block decoders. The shaping codes are in the spirit of Calderbank and Ozarow (1990), where shaping is achieved by nonequiprobable signaling on T subconstellations of a signal constellation /spl Omega/. We show how nonequiprobable signaling relates to a costly constrained channel. Khayrallah and Neuhoff developed a procedure for constructing codes with rates close to the capacity-cost function of the general cost-constrained channel, and we use their procedure to construct asynchronous (variable-length to fixed-length) shaping codes. Comparisons are made with shaping codes having comparable gain. The codes presented here are less complex and have lower peak-to-average power and lower constellation expansion ratio.

Robust source coding of images for very noisy channels

Robust source coding provides the compression and noise mitigation necessary for image transmission over noisy channels. Two methods are compared-differential pulse code modulation (DPCM) and predictive trellis coded quantisation (PTCQ)-incorporating linear and nonlinear filters. Findings show that although PTCQ has better rate-distortion properties, DPCM provides better performance in noise. Additionally, the nonlinear filter yields better images.

Robust source coding for images over very noisy channels

Robust source coding provides both compression and noise mitigation without channel coding. Two methods of robust source coding are presented. The first is DPCM incorporating a nonlinear filter; the second is predictive trellis-coded quantization (PTCQ), whose prediction filter is also nonlinear. Findings show that the incorporation of the nonlinear filter provides the ability to conceal the effects of noise and minimize the propagation of error. A comparison is made between the performance of the two methods in a noisy environment. It is demonstrated that the PTCQ scheme provides a method of least distortion at low BER. However, at higher BER the DPCM scheme outperforms PTCQ. Robust source coding of images employing PTCQ or DPCM with the nonlinear prediction filter exhibits low sensitivity to bit errors and yields, visually, a better reconstructed image after transmission over very noisy channels.

Differential coding with a modified feedback loop

We address the problem of data compression and transmission applied to images. The noisy channel requires the use of a compression scheme with low sensitivity to bit errors. We present a DPCM scheme with a modified feedback loop containing a nonlinear filter in addition to the familiar linear predictor. This greatly improves the channel response of DPCM, without significantly degrading its compression performance.

Expansion property of feedforward convolutional encoders

We study the input/output (i/o) relations of feedforward convolutional encoders. Namely, we investigate expansion factor /spl delta/, which measures the increase in distance from input sequence pairs to their corresponding code sequence pairs. We derive a bound to /spl delta/ based on the codes weight profile. We discuss how extending the memory affects /spl delta/.<<ETX>>