Patent Application
20080019443
The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:
The encoding side and decoding side of the method of the present invention are shown in
In contrast to prior art encoding as illustrated in
To illustrate the encoding process, let us look at
In the example shown in
c
1
=a
11
v
1
+a
21
v
2
+a
41
v
4
+a
51
v
5
+a
71
v
7
+a
81
v
8.
Suppose also that the finite field A is GF(4) consisting of 4 elements 0, 1, 2, and 3. To perform the arithmetic in GF(4), we need to first map the integer set from which v1v2 . . . v8 is drawn to A (equivalently, GF(4)). A common mapping method is to use modular arithmetic. Hence, v1=2 (mod 4), v2=3 (mod 4), v4=1 (mod 4), v5=2 (mod 4), v7=1 (mod 4), and v8=0 (mod 4). Then according to finite field arithmetic defined over GF(4),
c1=(2+3)+(1+2)+(1+0)=1+3+1=3.
Suppose that each symbol in the field A is represented by log(M) bits, where “log” denotes the logarithm function to base 2 throughout this document. Since m is generally much smaller than n, compression is achieved. The resulting compression rate in bits per symbol is (mlog(M))/n. In practice, the encoder 420 selects m and M according to the length of the input sequence x and the expected compression rate estimated from the statistical model 240. The estimation is performed for each frame to be encoded. Note that once M is chosen, the encoder 420 knows how to choose m to achieve the desired compression rate.
A video sequence 205 typically consists of integer numbers (ranging, say, from 0 to 255″). After DCT transform 210 and quantization 220, quantized sequence x 225 is another sequence of integer numbers (typically with a larger range). This sequence is encoded by using the above described method. Say, for example, a number 13 is to be encoded and the field size is 4. We can use modulo 4 operation to convert 13 into 1. The M-ary encoding operations 420 are then performed arithmetically in finite field GF(4) to produce syndrome sequence z 425. Compression is achieved since the number of bits used to represent the syndrome sequence z is often much less than the number bits used to represent the input quantized sequence.
In this invention, the field size M to be used to generate an M-ary code is estimated from the statistical model 240. Specifically, suppose that the alphabet of the quantized sequence x is an integer set. The estimation process seeks a subset of M integers such that the probability (determined by the statistical model 240) of x containing symbols outside the size M subset is smaller than a prescribed threshold. To facilitate computation in different computing platforms, one may also want to constrain the selection of M to satisfy certain properties, for example, being an integral power of two.
On the decoder 430 side, the improved method shown in
Note that, in principle, the encoder 420 and decoder 430 may be distant from one another. By matching the learning method and the data used to learn the model, we can make sure that the encoder 420 and the decoder 430 are using the same statistical model 240 and, thus, generate the same bipartite graph. Assuming a given statistical relationship, there are various ways to learn the relationship in practice. One such way is to use a portion of the video frames for the learning.
In general, an M-ary code described by a bipartite graph with n variable nodes and m check nodes can be used to encode any sequence of length n into its syndrome sequence of length m. The value of n is given by the input sequence x, whereas m is determined from the statistical model 240. For any pair (n,m), the encoder 420 and the decoder 430 generate the same bipartite graph (hence, the same code) from the statistical model 240.
The decoding rule can be either the MAP (maximum a posteriori) decoding rule or its approximations. By using the MAP decoding rule, the decoder tries to find the most probable sequence given y (that is, most probable according to the statistical model 240) whose syndrome sequence is equal to z in the generated bipartite graph.
Enforcing the MAP decoding rule is computationally expensive. An alternative is to approximate the MAP decoding rule by using an iterative decoding process. The process can be described as follows. Let G denote the bipartite graph describing the M-ary code 420 generated from the statistical model 240.
Step 1: Initialize a counter k as 1. Let v(k) denote the sequence in the variable nodes of G at the kth iteration. Initialize v(1) as y.
Step 2: Calculate the syndrome sequence of v(k) in G. If the syndrome sequence is equal to z, the process terminates; otherwise, the decoder finds a new sequence v(k+1) according to the statistical model and G. One possible method in determining the new sequence v(k+1) is the well-known belief propagation method generalized to a finite field of size M.
Step 3: Increase the counter k by one. If k is greater than a prescribed threshold, the process terminates; otherwise, go to Step 2.
At the end of the above iterative process, the decoder outputs x as v(k). Note that if the above iterative process terminates with a sequence v(k) whose syndrome sequence is NOT z in G, the decoder detects a decoding failure.
It should be noted that use of the bi-partite graph provides a computationally effective methodology for iterative decoding, and is therefore the best mode of implementing the invention. However, in principle, the invention is also operable for any M-ary linear code H, where H is an m by n matrix from a finite field with M elements and where the encoder calculates z=Hx.
While the invention has been described in terms of a single preferred embodiment, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims.
