Presentation III Irvanda Kurniadi V. (20127734) 2013.5.13 Digital Communication Source Coding (5&6) Presentation III Irvanda Kurniadi V. (20127734) 2013.5.13

Outline Block Coding Transform Coding Vector Quantizing Codebook, Tree, and Trellis Coders Code Population Searching Transform Coding Quantization for Transform Coding Sub-band Coding

Layering of Source Coding

Block Coding Block-coding techniques are often classified by their mapping techniques, which include vector quantizers, various orthogonal transform coders, and channelized coders, such as subband coders. Block coders are further described by their algorithmic structures, such as codebook, tree, trellis, discrete Fourier transform, discrete cosine transform, discrete Walsh-Hadamard transform, discrete Karhunen-Loeve transform, and quadrature mirror filter-bank coders.

Vector Quantizing Vector quantizers represent an extension of conventional scalar quantization. In scalar quantization, a scalar value is selected from a finite list of possible values to represent an input sample. The description of a vector quantizer can be cast as two distinct tasks. The first is the code-design task, which deals with the problem of performing the multidimensional volume quantization (or partition) and selecting the allowable output sequences. The second task is that of using the code, and deals with searching for the particular volume with this partition that corresponds (according to some fidelity criterion) to the best description of the source. The form of the algorithm selected to control the complexity of encoding and decoding may couple the two tasks – the partition and the search.

Vector Quantizing Codebook, tree, and trellis coding algorithm. The codebook coders are essentially table look-up algorithms. A list of candidate patterns (codewords) is stored in the codebook memory. The tree and trellis coders are sequential coders. This is similar to the structure of the sequential error-detection-and-correction algorithm, which traverse the branches of a graph while forming the branch weight approximation to the input sequence. Coding routine List of Pattern Receiver’s codebook transmit search Tree Graph Trellis Graph

Vector Quantizing Code Population Code Design Code Population The methods of determining the code population are classically deterministic, stochastic, and iterative. The deterministic population is a list of pre-assigned possible outputs based on a simple suboptimal or user-perception fidelity criterion or based on a simple decoding algorithm. An example of the former is the coding of the samples in 3-space of the red, green, and blue (RGB) components of a color TV signal. Deterministic coding is the easiest to implement but leads to the smallest coding gain (smallest reduction in bit rate for a given SNR). Notes: quantization could be performed independently in the alternative space by the use of transform coding

Vector Quantizing Searching Using the code Searching An exhaustive search over all possible contenders will assure the best match. But an exhaustive search over a large dimension may be prohibitively time consuming. Examples of search algorithms include single-path (best leaving branch) algorithms, multiple-path algorithms, and binary (successive approximation) codebook algorithms. Coding routine List of Pattern Receiver’s codebook transmit search

Transform Coding Transform coding entails the following set of operations: An invertible transform is applied to the input vector. The coefficients of the transform are quantized. The quantized coefficients are transmitted and received. The transform is inverted with quantized coefficients. N Forward transform Threshold editor and quantizer L Inverse transform Encoder Decoder Source coding N-term Input vector transformed L-term quantized Zero extended Encode output Block diagram: Transform coding

Transform Coding The task of the transform coding  to map a correlated input sequence into a different coordinate system in which the coordinates have reduced correlation. Examples of such transforms are the discrete Fourier transform (DFT), discrete Walsh-Hadamard transform, discrete cosine transform (DCT), and the discrete slant transform (DST). The transformation can also be derived from the data vector, as is done in the discrete Karhunen-Loeve transform (DKLT), sometimes called the principal component transform (PCT). The data-independent transforms are easiest to implement but do not perform as well as the data dependent transforms.

Quantization for Transform Coding Transform coders are called spectral encoders because the signal is described in terms of a spectral decomposition. The spectral terms are computed for non-overlapped successive blocks of input data. Thus, the output of a transform coder can be viewed as a set of time series, one series for each spectral term. The variance of each series can be determined and each can be quantized with a different number of bits. By permitting independent quantization of each transform coefficient, we have the option of allocating a fixed number of bits among the transform coefficients to obtain a minimum quantizing error.

Sub-band Coding Sub-band coding (SBC) is any form of transform coding that breaks a signal into a number of different frequency bands and encodes each one independently. SBC Channelization Trans-multiplexer Equal & unequal BW TDM Channel

Sub-band Coding A sub-band coder, which performs a spectral channelization by a bank of contiguous narrowband filters, can be considered as a special case of a transform coder. For example, the quantizing noise generated in a band with large variance, not spilling into a nearby band with low variance and hence susceptible to low-level signals being masked by noise. There are two options of forming filters with equal or unequal bandwidths. Thus, we can assign to its appropriate bandwidth and variance. The sub-band coder can be designed as a trans-multiplexer. Input signal is composed as independent narrow-bandwidth sub-channel. Encoder channelizes the input signal into TDM channels. After quantization and transmission, the decoder reverses the filtering and re-sampling process, converting the TDM channels back to the original signal.

Question Mention the set of operation in transform coding! Thank You