Distributed Source Coding based Audio Coding Minyue Li

Distributed Source Coding based Audio Coding Minyue Li Sound and Image Processing Lab School of Electrical Engineering KTH Sweden

Conventional Audio Coding

Distributed Source Coding based Audio Coding

Advantages • Low complexity in encoder – Low power demand in recorder • Low coding delay – Sample-by-sample processing in encoder – Delay exists in decoder • Robustness – No necessity of synchronicity between encoder and decoder – No error propagation • Joint source-channel coding – Channel coding methods for distributed source coding

What does theory say Slepian-Wolf Coding (lossless) • Two Sources R 1+R 2 ¸ H(X, Y) R 1 ¸ H(X|Y) R 2 ¸ H(Y|X) Multiple Sources R(S) > H(X(S)|X(Sc)) where S µ {1, 2, …, m} R(S) = i 2 S Ri

What does theory say Wyner-Ziv Coding (lossy) • Multiple Sources Rtot (D) ? • One Source with Side Information RX (D) = inff. X, ˆX I(X, ˆX| Y) RXWZ (D)¸ RX (D) Gaussian, Mean Squared Error: RXWZ (D)= RX (D) General distribution, MSE RXWZ (D)- RX (D) < 0. 5 bit

Example of Distributed Source Coding City & Weather City B City A Sun Cloud Rain Snow Sun 0. 25 0 0 0 Cloud 0 0. 2 0. 025 Rain 0 0. 025 0. 2 0. 025 Snow 0 0. 025 0. 2 A scenerio • A joint distribution of weather from two cities. • Encode cities’ weather separately. • 1 bit is assigned to each city. • Minimize error probability. Strategies • Choose 2 largest marginal probabilities. – Not optimal – Fails in case of uniform distribution • Binning

Example of Distributed Source Coding City & Weather City B City A Sun Cloud Rain Snow Sun 0. 25 0 0 0 Cloud 0 0. 2 0. 025 Rain 0 0. 025 0. 2 0. 025 Snow 0 0. 025 0. 2 For City A • Two bins: {sun, rain}, {cloud, snow}

Example of Distributed Source Coding City & Weather City B City A Sun Cloud Rain Snow Sun 0. 25 0 0 0 Cloud 0 0. 2 0. 025 Rain 0 0. 025 0. 2 0. 025 Snow 0 0. 025 0. 2 For City A • Two bins: {sun, rain}, {cloud, snow} For City B • Two bins: {sun, snow}, {cloud, rain} 4 Cosets {sun_sun, sun_snow, rain_sun, rain_snow} → sun_sun {sun_cloud, sun_rain, rain_cloud} → rain_rain {snow_sun, snow_snow, cloud_sun, cloud_snow} → snow_snow {cloud_cloud, cloud_rain, snow_cloud} → cloud_cloud

Example of Distributed Source Coding City & Weather City B Cloud Rain Snow Sun 0. 25 0 0 0 Cloud 0 0. 2 0. 025 Rain 0 0. 025 0. 2 0. 025 Snow 0 0. 025 0. 2 City A Sun City & Weather City B Sun Cloud Rain Snow Sun 0. 25 0 0 0 Cloud 0 0. 2 0. 025 Rain 0 0. 025 0. 2 0. 025 Snow 0 0. 025 0. 2

Continuous Case Vector Quantization Convex cell shape In-cell reconstruction point Distributed Quantization Non-contiguous hyperrectangular cell shape

Example of Distributed Quantization Gaussian Distribution N (0, 1) MSE Non-contiguous cell can be beneficial. Depend on distribution density.

Coding Architecture In essence, a quantization problem Maximum likelihood decoding is a maximum likelihood estimation (MLE).

Coding Architecture Simplified as a binning problem. Quantization guarantees distortion requirement. Coding achieves lossless. Quantization exceeds distortion requirement. Coding minimizes distortion increments.

Optimal Binning Complexity of binning optimization – n bit quantization – k bit transmission – m dimensional source – 2 k bins, 2 n-k in each bin – Possible binnings

Optimal Binning Genetic Algorithm – Chromosome: binning configuration – Fitness: inverse distortion – Selection: possibility proportional to fitness – Crossover: – Mutation: – Finalization:

Future Works 1. 2. 3. Better binning optimization algorithm Lossless coding in discrete case Distributed quantization method

Thank you!