US 20010016079 A1 Abstract A multiple description (MD) joint source-channel (JSC) encoder in accordance with the invention encodes n components of a signal for transmission over m channels of a communication medium. In illustrative embodiments, the invention provides optimal or near-optimal transforms for applications in which at least one of n and m is greater than two, and applications in which the failure probabilities of the m channels are non-independent and non-equivalent. The signal to be encoded may be a data signal, a speech signal, an audio signal, an image signal, a video signal or other type of signal, and each of the m channels may correspond to a packet or a group of packets to be transmitted over the medium. A given n×m transform implemented by the MD JSC encoder may be in the form of a cascade structure of several transforms each having dimension less than n×m. The transform may also be configured to provide a substantially equivalent rate for each of the m channels.
Claims(24) 1. A method of encoding a signal for transmission, comprising the steps of:
encoding n components of the signal in a multiple description joint source-channel encoder for transmission over m channels, wherein at least one of n and m is greater than two; and transmitting the encoded components of the signal. 2. The method of claim 1 3. The method of claim 1 4. The method of claim 1 5. The method of claim 1 6. The method of claim 1 7. The method of claim 1 8. The method of claim 1 9. The method of claim 1 10. The method of claim 9 11. An apparatus for encoding a signal for transmission, comprising:
a processor for processing the signal to form components thereof; and a multiple description joint source-channel encoder for encoding n components of the signal for transmission over m channels, wherein at least one of n and m is greater than two. 12. The apparatus of claim 11 13. The apparatus of claim 11 14. The apparatus of claim 11 15. The apparatus of claim 11 16. The apparatus of claim 11 17. The apparatus of claim 11 18. The apparatus of claim 11 19. The apparatus of claim 11 20. The apparatus of claim 19 21. A method of decoding a signal received over a communication medium, comprising the steps of:
receiving encoded components of the signal over m channels of the medium; and decoding n of the components of the signal in a multiple description joint source-channel decoder, wherein at least one of n and m is greater than two. 22. An apparatus for decoding a signal received over a communication medium, comprising:
a multiple description joint source-channel decoder for decoding n components of the signal received over m channels of the medium, wherein at least one of n and m is greater than two. 23. A method of encoding a signal for transmission, comprising the steps of:
encoding n components of the signal in a multiple description joint source-channel encoder for transmission over m channels, wherein at least a subset of the m channels have probabilities of failure which are not independent of one another; and transmitting the encoded components of the signal. 24. An apparatus for encoding a signal for transmission, comprising:
a processor for processing the signal to form components thereof; and a multiple description joint source-channel encoder for encoding n components of the signal for transmission over m channels, wherein at least a subset of the m channels have probabilities of failure which are not independent of one another. Description [0001] The present invention relates generally to multiple description transform coding (MDTC) of data, speech, audio, images, video and other types of signals for transmission over a network or other type of communication medium. [0002] Multiple description transform coding (MDTC) is a type of joint source-channel coding (JSC) designed for transmission channels which are subject to failure or “erasure.” The objective of MDTC is to ensure that a decoder which receives an arbitrary subset of the channels can produce a useful reconstruction of the original signal. A distinguishing characteristic of MDTC is the introduction of correlation between transmitted coefficients in a known, controlled manner so that lost coefficients can be statistically estimated from received coefficients. This correlation is used at the decoder at the coefficient level, as opposed to the bit level, so it is fundamentally different than techniques that use information about the transmitted data to produce likelihood information for the channel decoder. The latter is a common element in other types of JSC coding systems, as shown, for example, in P. G. Sherwood and K. Zeger, “Error Protection of Wavelet Coded Images Using Residual Source Redundancy,” Proc. of the 31 [0003] A known MDTC technique for coding pairs of independent Gaussian random variables is described in M. T. Orchard et al., “Redundancy Rate-Distortion Analysis of Multiple Description Coding Using Pairwise Correlating Transforms,” Proc. IEEE Int. Conf. Image Proc., Santa Barbara, Calif., October 1997. This MDTC technique provides optimal 2×2 transforms for coding pairs of signals for transmission over two channels. However, this technique as well as other conventional techniques fail to provide optimal generalized n×m transforms for coding any n signal components for transmission over any m channels. Moreover, the optimality of the 2×2 transforms in the M. T. Orchard et al. reference requires that the channel failures be independent and have equal probabilities. The conventional techniques thus generally do not provide optimal transforms for applications in which, for example, channel failures either are dependent or have unequal probabilities, or both. This inability of conventional techniques to provide suitable transforms for arbitrary dimensions and different types of channel failure probabilities unduly restricts the flexibility of MDTC, thereby preventing its effective implementation in many important applications. [0004] The invention provides MDTC techniques which can be used to implement optimal or near-optimal n×m transforms for coding any number n of signal components for transmission over any number m of channels. A multiple description (MD) joint source-channel (JSC) encoder in accordance with an illustrative embodiment of the invention encodes n components of a signal for transmission over m channels of a communication medium, in applications in which at least one of n and m may be greater than two, and in which the failure probabilities of the m channels may be non-independent and non-equivalent. An n×m transform implemented by the MD JSC encoder may be in the form of a cascade structure of several transforms each having dimension less than n×m. An exemplary transform in accordance with the invention may include an additional degree of freedom not found in conventional MDTC transforms. This additional degree of freedom provides considerable improvement in design flexibility, and may be used, for example, to partition a total available rate among the m channels such that each channel has substantially the same rate. [0005] In accordance with another aspect of the invention, an MD JSC encoder may include a series combination of N “macro” MD encoders followed by an entropy coder, and each of the N macro MD encoders includes a parallel arrangement of M “micro” MD encoders. Each of the M micro MD encoders implements one of: (i) a quantizer block followed by a transform block, (ii) a transform block followed by a quantizer block, (iii) a quantizer block with no transform block, and (iv) an identity function. This general MD JSC encoder structure allows the encoder to implement any desired n×m transform while also minimizing design complexity. [0006] The MDTC techniques of the invention do not require independent or equivalent channel failure probabilities. As a result, the invention allows MDTC to be implemented effectively in a much wider range of applications than has heretofore been possible using conventional techniques. The MDTC techniques of the invention are suitable for use in conjunction with signal transmission over many different types of channels, including lossy packet networks such as the Internet as well as broadband ATM networks, and may be used with data, speech, audio, images, video and other types of signals. [0007]FIG. 1 shows an exemplary communication system in accordance with the invention. [0008]FIG. 2 shows a multiple description (MD) joint source-channel (JSC) encoder in accordance with the invention. [0009]FIG. 3 shows an exemplary macro MD encoder for use in the MD JSC encoder of FIG. 2. [0010]FIG. 4 shows an entropy encoder for use in the MD JSC encoder of FIG. 2. [0011]FIGS. 5A through 5D show exemplary micro MD encoders for use in the macro MD encoder of FIG. 3. [0012]FIGS. 6A, 6B and [0013]FIG. 7A shows a relationship between redundancy and channel distortion in an exemplary embodiment of the invention. [0014]FIG. 7B shows relationships between distortion when both of two channels are received and distortion when one of the two channels is lost, for various rates, in an exemplary embodiment of the invention. [0015]FIG. 8 illustrates an exemplary 4×4 cascade structure which may be used in an MD JSC encoder in accordance with the invention. [0016] The invention will be illustrated below in conjunction with exemplary MDTC systems. The techniques described may be applied to transmission of a wide variety of different types of signals, including data signals, speech signals, audio signals, image signals, and video signals, in either compressed or uncompressed formats. The term “channel” as used herein refers generally to any type of communication medium for conveying a portion of a encoded signal, and is intended to include a packet or a group of packets. The term “packet” is intended to include any portion of an encoded signal suitable for transmission as a unit over a network or other type of communication medium. [0017]FIG. 1 shows a communication system [0018]FIG. 2 illustrates the MD JSC encoder [0019]FIG. 4 indicates that the entropy coder [0020]FIGS. 5A through 5D illustrate a number of possible embodiments for each of the micro MD [0021]FIGS. 6A through 6C illustrate the manner in which the MD JSC encoder [0022] A general model for analyzing MDTC techniques in accordance with the invention will now be described. Assume that a source sequence {x [0023] An MDTC coding structure for implementation in the MD JSC encoder [0024] 1. The source vector x is quantized using a uniform scalar quantizer with step size Δ: x [0025] 2. The vector x [0026] 3. The components of y are independently entropy coded. [0027] 4. If m>n, the components of y are grouped to be sent over the m channels. [0028] When all of the components of y are received, the reconstruction process is to exactly invert the transform {circumflex over (T)} to get {circumflex over (x)}=x [0029] Starting with a linear transform T with a determinant of one, the first step in deriving a discrete version {circumflex over (T)} is to factor T into “lifting” steps. This means that T is factored into a product of lower and upper triangular matrices with unit diagonals T=T [0030] The lifting structure ensures that the inverse of {circumflex over (T)} can be implemented by reversing the calculations in (1): [0031] The factorization of T is not unique. Different factorizations yield different discrete transforms, except in the limit as Δ approaches zero. The above-described coding structure is a generalization of a 2×2 structure described in the above-cited M. T. Orchard et al. reference. As previously noted, this reference considered only a subset of the possible 2×2 transforms; namely, those implementable in two lifting steps. [0032] It is important to note that the illustrative embodiment of the invention described above first quantizes and then applies a discrete transform. If one were to instead apply a continuous transform first and then quantize, the use of a nonorthogonal transform could lead to non-cubic partition cells, which are inherently suboptimal among the class of partition cells obtainable with scalar quantization. See, for example, A. Gersho and R. M. Gray, “Vector Quantization and Signal Compression,” Kluwer Acad. Pub., Boston, Mass., 1992. The above embodiment permits the use of discrete transforms derived from nonorthogonal linear transforms, resulting in improved performance. [0033] An analysis of an exemplary MDTC system in accordance with the invention will now be described. This analysis is based on a number of fine quantization approximations which are generally valid for small Δ. First, it is assumed that the scalar entropy of y={circumflex over (T)}([x] [0034] The rate can be estimated as follows. Since the quantization is fine, y [0035] where k [0036] The minimum rate occurs when the product from i=1 to n of σ [0037] The distortion will now be estimated, considering first the average distortion due only to quantization. Since the quantization noise is approximately uniform, the distortion is Δ [0038] and is independent of T. [0039] The case when l>0 components are lost will now be considered. It first must be determined how the reconstruction will proceed. By renumbering the components if necessary, assume that y {circumflex over (x)}=E[x|y [0040] [0041] If the correlation matrix of y is partitioned in a way compatible with the partition of y as:
[0042] then it can be shown that the conditional signal y [0043] such that ||x−{circumflex over (x)}|| is given by:
[0044] where U is the last l columns of T [0045] The distortion with l erasures is denoted by D [0046] For a case in which each channel has a failure probability of p and the channel failures are independent, the weighting
[0047] makes the weighted sum {overscore (D)} the overall expected MSE. Other choices of weighting could be used in alternative embodiments. Consider an image coding example in which an image is split over ten packets. One might want acceptable image quality as long as eight or more packets are received. In this case, one could set α [0048] The above expressions may be used to determine optimal transforms which minimize the weighted sum {overscore (D)} for a given rate R. Analytical solutions to this minimization problem are possible in many applications. For example, an analytical solution is possible for the general case in which n=2 components are sent over m=2 channels, where the channel failures have unequal probabilities and may be dependent. Assume that the channel failure probabilities in this general case are as given in the following table.
[0049] If the transform T is given by:
[0050] minimizing (2) over transforms with a determinant of one gives a minimum possible rate of: [0051] The difference ρ=R−R* is referred to as the redundancy, i.e., the price that is paid to reduce the distortion in the presence of erasures. Applying the above expressions for rate and distortion to this example, and assuming that σ [0052] The optimal value of bc is then given by:
[0053] The value of (bc) [0054] If p [0055] Using a transform from this set gives:
[0056] This relationship is plotted in FIG. 7A for values of σ [0057] Although the conventional 2×2 transforms described in the above-cited M. T. Orchard et al. reference can be shown to fall within the optimal set of transforms described herein when channel failures are independent and equally likely, the conventional transforms fail to provide the above-noted extra degree of freedom, and are therefore unduly limited in terms of design flexibility. Moreover, the conventional transforms in the M. T. Orchard et al. reference do not provide channels with equal rate (or, equivalently, equal power). The extra degree of freedom in the above example can be used to ensure that the channels have equal rate, i.e., that R [0058] As previously noted, the invention may be applied to any number of components and any number of channels. For example, the above-described analysis of rate and distortion may be applied to transmission of n=3 components over m=3 channels. Although it becomes more complicated to obtain a closed form solution, various simplifications can be made in order to obtain a near-optimal solution. If it is assumed in this example that σ [0059] Optimal or near-optimal transforms can be generated in a similar manner for any desired number of components and number of channels. [0060]FIG. 8 illustrates one possible way in which the MDTC techniques described above can be extended to an arbitrary number of channels, while maintaining reasonable ease of transform design. This 4×4 transform embodiment utilizes a cascade structure of 2×2 transforms, which simplifies the transform design, as well as the encoding and decoding processes (both with and without erasures), when compared to use of a general 4×4 transform. In this embodiment, a 2×2 transform T [0061] The above-described embodiments of the invention are intended to be illustrative only. It should be noted that a complementary decoder structure corresponding to the encoder structure of FIGS. 2, 3, Referenced by
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