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Linear Block Codes

2020
As usual, in this chapter we consider that p denotes a prime number, q is a prime power and \({\mathbb F}_{q}\) is the finite field with q elements. We begin by defining the general concept of a code over \({\mathbb F}_{q}\); after this, we present the concept of a linear code that is the more important class of codes in coding and information theory ...
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Speech coding using efficient block codes

ICASSP '82. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005
Digital coders invariably introduce errors into analog signals such as speech. The importance of adjusting the spectrum of the error so as to minimize the subjective distortion is now well recognized. The optimum noise spectrum for minimum subjective distortion is in general non-flat.
M. Schroeder, B. Atal
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Linear Block Codes

1999
Some elementary concepts of block codes are introduced in Chapter 1. In general, it is known that the encoding and decoding of 2 k codewords of length n can be quite complicated when n and k are large unless the encoder has certain special structures. In this chapter, a class of block codes, called linear block codes, is discussed.
Irving S. Reed, Xuemin Chen
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Linear Block Codes

2015
This chapter deals with linear block codes covering their fundamental concepts, generator and parity check matrices, error-correcting capabilities, encoding and decoding, and performance analysis.
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Block truncation coding with entropy coding

IEEE Transactions on Communications, 1995
Block truncation coding (BTC) is a simple and fast image compression algorithm which achieves a constant bit rate of 2.0 bits per pixel. The method is however suboptimal. We propose a modification of BTC in which the compression ratio is improved by coding the quantization data and the bit plane by arithmetic coding with an adaptive modelling scheme ...
P. Franti, O. Nevalainen
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Linear Block Codes

1998
Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. We mainly present the basic concepts of encoding and decoding of linear block codes and state some facts without ...
Shu Lin   +3 more
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Low state complexity block codes via convolutional codes

IEEE International Symposium on Information Theory, 2003. Proceedings., 2003
A new class of block codes with low state complexity of their conventional trellis representations called double zero-tail terminated convolutional codes (DZT codes) is introduced. It is shown that there exist DZT-codes meeting the Varshamov-Gilbert bound on the minimum distance and having asymptotically optimal state complexity.
I.E. Bocharova   +2 more
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Synchronization methods for block codes

IEEE Transactions on Information Theory, 1962
Summary: Efficient use of block codes to communicate over a telemetry channel is dependent upon the knowledge of the instants, in time, that one code waveform, or code word, ends and the succeeding waveform begins. This word synchronization is the subject of concern in this paper.
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Block Truncation Coding

2009
In block truncation coding (BTC), an image is segmented into n x— n (typically, 4 x— 4) nonoverlapping blocks of pixels, and a two-level (one-bit) quantizer is independently designed for each block. Both the quantizer threshold and the two reconstruction levels are varied in response to the local statistics of a block.
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Linear Block Codes

2019
In this chapter, we will explain the construction of linear block codes. Since linear block codes are vector subspaces, we advise to the reader to study Chap. 1 before proceeding to Chap. 2. Without the knowledge of basic concepts of linear algebra, such as groups, fields, vector spaces, and subspaces, it is difficult to comprehend the philosophy ...
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